Survival analysis - Knowledge

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not yet at the previous examination. Interval censoring often occurs in HIV/AIDS studies. Indeed, time to HIV seroconversion can be determined only by a laboratory assessment which is usually initiated after a visit to the physician. Then one can only conclude that HIV seroconversion has happened between two examinations. The same is true for the diagnosis of AIDS, which is based on clinical symptoms and needs to be confirmed by a medical examination.

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recur during those 13 weeks. It is possible that this patient was enrolled near the end of the study, so that they could be observed for only 13 weeks. It is also possible that the patient was enrolled early in the study, but was lost to follow up or withdrew from the study. The table shows that other subjects were censored at 16, 28, and 45 weeks (observations 17, 6, and

1096: 4953: 288:. Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of 1223: 1231:

relative event rate compared to the root. In the node on the far left, the values 1/33 indicate that one of the 33 subjects in the node had an event, and that the relative event rate is 0.122. In the node on the far right bottom, the values 11/15 indicate that 11 of 15 subjects in the node had an event, and the relative event rate is 2.7.

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of latent variable mixture models to model the time-to-event distribution as a mixture of parametric or semi-parametric distributions while jointly learning representations of the input covariates. Deep learning approaches have shown superior performance especially on complex input data modalities such as images and clinical time-series.

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Left censoring occurs for example when a permanent tooth has already emerged prior to the start of a dental study that aims to estimate its emergence distribution. In the same study, an emergence time is interval-censored when the permanent tooth is present in the mouth at the current examination but

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An alternative to building a single survival tree is to build many survival trees, where each tree is constructed using a sample of the data, and average the trees to predict survival. This is the method underlying the survival random forest models. Survival random forest analysis is available in the

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Stratification. The subjects can be divided into strata, where subjects within a stratum are expected to be relatively more similar to each other than to randomly chosen subjects from other strata. The regression parameters are assumed to be the same across the strata, but a different baseline hazard

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The last observation (11), at 161 weeks, is censored. Censoring indicates that the patient did not have an event (no recurrence of aml cancer). Another subject, observation 3, was censored at 13 weeks (indicated by status=0). This subject was in the study for only 13 weeks, and the aml cancer did not

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Recent advancements in deep representation learning have been extended to survival estimation. The DeepSurv model proposes to replace the log-linear parameterization of the CoxPH model with a multi-layer perceptron. Further extensions like Deep Survival Machines and Deep Cox Mixtures involve the use

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The p-value for all three overall tests (likelihood, Wald, and score) are significant, indicating that the model is significant. The p-value for log(thick) is 6.9e-07, with a hazard ratio HR = exp(coef) = 2.18, indicating a strong relationship between the thickness of the tumor and increased risk of

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Censoring / Censored observation: Censoring occurs when we have some information about individual survival time, but we do not know the survival time exactly. The subject is censored in the sense that nothing is observed or known about that subject after the time of censoring. A censored subject may

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While many prametric models assume a continous-time, discrete-time survival models can be mapped to a binary classification problem. In a discrete-time survival model the survival period is artifically resampled in intervals where for each interval a binary target indicator is recorded if the event

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In some cases alternative partitions give more accurate classification or quantitative estimates. One set of alternative methods are tree-structured survival models, including survival random forests. Tree-structured survival models may give more accurate predictions than Cox models. Examining both

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Time-varying covariates. Some variables, such as gender and treatment group, generally stay the same in a clinical trial. Other clinical variables, such as serum protein levels or dose of concomitant medications may change over the course of a study. Cox models may be extended for such time-varying

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By contrast, the p-value for sex is now p=0.088. The hazard ratio HR = exp(coef) = 1.58, with a 95% confidence interval of 0.934 to 2.68. Because the confidence interval for HR includes 1, these results indicate that sex makes a smaller contribution to the difference in the HR after controlling for

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compares the survival times of two or more groups. This example uses a log-rank test for a difference in survival in the maintained versus non-maintained treatment groups in the aml data. The graph shows KM plots for the aml data broken out by treatment group, which is indicated by the variable "x"

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Kaplan–Meier curves and log-rank tests are most useful when the predictor variable is categorical (e.g., drug vs. placebo), or takes a small number of values (e.g., drug doses 0, 20, 50, and 100 mg/day) that can be treated as categorical. The log-rank test and KM curves don't work easily with

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function cox.zph(). A p-value which is less than 0.05 indicates that the hazards are not proportional. For the melanoma data we obtain p=0.222. Hence, we cannot reject the null hypothesis of the hazards being proportional. Additional tests and graphs for examining a Cox model are described in the

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The null hypothesis for a log-rank test is that the groups have the same survival. The expected number of subjects surviving at each time point in each is adjusted for the number of subjects at risk in the groups at each event time. The log-rank test determines if the observed number of events in

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These three tests are asymptotically equivalent. For large enough N, they will give similar results. For small N, they may differ somewhat. The last row, "Score (logrank) test" is the result for the log-rank test, with p=0.011, the same result as the log-rank test, because the log-rank test is a

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of the data given the parameters of the model. It is customary to assume that the data are independent given the parameters. Then the likelihood function is the product of the likelihood of each datum. It is convenient to partition the data into four categories: uncensored, left censored, right

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Left-censored data can occur when a person's survival time becomes incomplete on the left side of the follow-up period for the person. For example, in an epidemiological example, we may monitor a patient for an infectious disorder starting from the time when he or she is tested positive for the

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Each branch in the tree indicates a split on the value of a variable. For example, the root of the tree splits subjects with grade < 2.5 versus subjects with grade 2.5 or greater. The terminal nodes indicate the number of subjects in the node, the number of subjects who have events, and the

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At the far right end of the KM plot there is a tick mark at 161 weeks. The vertical tick mark indicates that a patient was censored at this time. In the aml data table five subjects were censored, at 13, 16, 28, 45 and 161 weeks. There are five tick marks in the KM plot, corresponding to these

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A vertical drop indicates an event. In the aml table shown above, two subjects had events at five weeks, two had events at eight weeks, one had an event at nine weeks, and so on. These events at five weeks, eight weeks and so on are indicated by the vertical drops in the KM plot at those time

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exp(coef) = 1.94 = exp(0.662) - The log of the hazard ratio (coef= 0.662) is transformed to the hazard ratio using exp(coef). The summary for the Cox model gives the hazard ratio for the second group relative to the first group, that is, male versus female. The estimated hazard ratio of 1.94

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std.err is the standard error of the estimated survival. The standard error of the Kaplan–Meier product-limit estimate it is calculated using Greenwood's formula, and depends on the number at risk (n.risk in the table), the number of deaths (n.event in the table) and the proportion surviving

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More generally, survival analysis involves the modelling of time to event data; in this context, death or failure is considered an "event" in the survival analysis literature – traditionally only a single event occurs for each subject, after which the organism or mechanism is dead or broken.

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The randomForestSRC package includes an example survival random forest analysis using the data set pbc. This data is from the Mayo Clinic Primary Biliary Cirrhosis (PBC) trial of the liver conducted between 1974 and 1984. In the example, the random forest survival model gives more accurate

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The Cox PH regression model is a linear model. It is similar to linear regression and logistic regression. Specifically, these methods assume that a single line, curve, plane, or surface is sufficient to separate groups (alive, dead) or to estimate a quantitative response (survival time).

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the thickness of the tumor, and only trend toward significance. Examination of graphs of log(thickness) by sex and a t-test of log(thickness) by sex both indicate that there is a significant difference between men and women in the thickness of the tumor when they first see the clinician.

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estimate of the cumulative hazard rate function. These estimators require lifetime data. Periodic case (cohort) and death (and recovery) counts are statistically sufficient to make nonparametric maximum likelihood and least squares estimates of survival functions, without lifetime data.

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is a form of missing data problem in which time to event is not observed for reasons such as termination of study before all recruited subjects have shown the event of interest or the subject has left the study prior to experiencing an event. Censoring is common in survival analysis.

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each group is significantly different from the expected number. The formal test is based on a chi-squared statistic. When the log-rank statistic is large, it is evidence for a difference in the survival times between the groups. The log-rank statistic approximately has a

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study, subjects are not observed at all until they have reached a certain age. For example, people may not be observed until they have reached the age to enter school. Any deceased subjects in the pre-school age group would be unknown. Left-truncated data are common in

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For the example data, the log-rank test for difference in survival gives a p-value of p=0.0653, indicating that the treatment groups do not differ significantly in survival, assuming an alpha level of 0.05. The sample size of 23 subjects is modest, so there is little

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Survival models can be usefully viewed as ordinary regression models in which the response variable is time. However, computing the likelihood function (needed for fitting parameters or making other kinds of inferences) is complicated by the censoring. The

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The Cox model extends the log-rank test by allowing the inclusion of additional covariates. This example use the melanoma data set where the predictor variables include a continuous covariate, the thickness of the tumor (variable name = "thick").

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analysis. Cox PH models work also with categorical predictor variables, which are encoded as {0,1} indicator or dummy variables. The log-rank test is a special case of a Cox PH analysis, and can be performed using Cox PH software.

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The textbook by Kleinbaum has examples of survival analyses using SAS, R, and other packages. The textbooks by Brostrom, Dalgaard and Tableman and Kim give examples of survival analyses using R (or using S, and which run in R).

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9 with status=0). The remaining subjects all experienced events (recurrence of aml cancer) while in the study. The question of interest is whether recurrence occurs later in maintained patients than in non-maintained patients.

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The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data, Bruce W. Turnbull, Journal of the Royal Statistical Society. Series B (Methodological) Vol. 38, No. 3 (1976), pp. 290-295 (6 pages),

4948:{\displaystyle L(\theta )=\prod _{T_{i}\in unc.}\Pr(T=T_{i}\mid \theta )\prod _{i\in l.c.}\Pr(T<T_{i}\mid \theta )\prod _{i\in r.c.}\Pr(T>T_{i}\mid \theta )\prod _{i\in i.c.}\Pr(T_{i,l}<T<T_{i,r}\mid \theta ).} 1129:

may exist for each stratum. Stratification is useful for analyses using matched subjects, for dealing with patient subsets, such as different clinics, and for dealing with violations of the proportional hazard assumption.

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survival data set "aml" from the "survival" package in R. The data set is from Miller (1997) and the question is whether the standard course of chemotherapy should be extended ('maintained') for additional cycles.

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C prostate cancer patients in the data set stagec in rpart. Rpart and the stagec example are described in Atkinson and Therneau (1997), which is also distributed as a vignette of the rpart package.

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Time: The time from the beginning of an observation period (such as surgery or beginning treatment) to (i) an event, or (ii) end of the study, or (iii) loss of contact or withdrawal from the study.

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Description of the transformation of continuous-time survival data to discrete-time survival data. Individual 4 is censored and for individual 5 the event happens outside the observation window 5.

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n.risk is the number of subjects at risk immediately before the time point, t. Being "at risk" means that the subject has not had an event before time t, and is not censored before or at time t.

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Empirical Likelihood in Survival Analysis, Gang Li (U.S.A.), Runze Li (U.S.A.), and Mai Zhou (U.S.A.), Contemporary Multivariate Analysis and Design of Experiments. March 2005, 337-349,

3058: 1620: 2996: 1500:. This reflects the notion that survival to a later age is possible only if all younger ages are attained. Given this property, the lifetime distribution function and event density ( 1092:

transform. The log of the thickness of the tumor looks to be more normally distributed, so the Cox models will use log thickness. The Cox PH analysis gives the results in the box.

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to detect differences between the treatment groups. The chi-squared test is based on asymptotic approximation, so the p-value should be regarded with caution for small

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takes place in a certain time horizon. If a binary classifier (potentially enhanced with a different likelihood to take more structure of the problem into account) is

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summarizes survival data in terms of the number of events and the proportion surviving at each event time point. The life table for the aml data, created using the R

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Spivak, Andrew L.; Damphousse, Kelly R. (2006). "Who Returns to Prison? A Survival Analysis of Recidivism among Adult Offenders Released in Oklahoma, 1985 – 2004".

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The life table summarizes the events and the proportion surviving at each event time point. The columns in the life table have the following interpretation:

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Nagpal, Chirag (2021). "Deep survival machines: Fully parametric survival regression and representation learning for censored data with competing risks".

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In fact, the hazard rate is usually more informative about the underlying mechanism of failure than the other representations of a lifetime distribution.

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outlined below assumes well-defined events at specific times; other cases may be better treated by models which explicitly account for ambiguous events.

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infection. Although we may know the right-hand side of the duration of interest, we may never know the exact time of exposure to the infectious agent.

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If the event of interest has already happened before the subject is included in the study but it is not known when it occurred, the data is said to be

1088:. Regression models, including the Cox model, generally give more reliable results with normally-distributed variables. For this example we may use a 4987: 6442:

Suresh, K., Severn, C. & Ghosh, D. Survival prediction models: an introduction to discrete-time modeling. BMC Med Res Methodol 22, 207 (2022).

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p=0.013. The p-value corresponding to z=2.5 for sex is p=0.013, indicating that there is a significant difference in survival as a function of sex.

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may not be well-defined, for there may well be mechanical systems in which failure is partial, a matter of degree, or not otherwise localized in

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Singh, Jared; Katzman, L. (2018). "DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network".

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The summary output also gives upper and lower 95% confidence intervals for the hazard ratio: lower 95% bound = 1.15; upper 95% bound = 3.26.

4027:{\displaystyle P(T\leq t_{0}+t\mid T>t_{0})={\frac {P(t_{0}<T\leq t_{0}+t)}{P(T>t_{0})}}={\frac {F(t_{0}+t)-F(t_{0})}{S(t_{0})}}.} 2871:

must be infinite, but is not otherwise constrained; it may be increasing or decreasing, non-monotonic, or discontinuous. An example is the

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quantitative predictors such as gene expression, white blood count, or age. For quantitative predictor variables, an alternative method is

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special case of a Cox PH regression. The Likelihood ratio test has better behavior for small sample sizes, so it is generally preferred.

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The force of mortality is also called the force of failure. It is the probability density function of the distribution of mortality.

2401:{\displaystyle h(t)=\lim _{dt\rightarrow 0}{\frac {\Pr(t\leq T<t+dt)}{dt\cdot S(t)}}={\frac {f(t)}{S(t)}}=-{\frac {S'(t)}{S(t)}}.} 1639: 1018:

summary for the Cox model gives the hazard ratio (HR) for the second group relative to the first group, that is, male versus female.

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for a survival model, in the presence of censored data, is formulated as follows. By definition the likelihood function is the

4363:{\displaystyle {\frac {1}{S(t_{0})}}\int _{0}^{\infty }t\,f(t_{0}+t)\,dt={\frac {1}{S(t_{0})}}\int _{t_{0}}^{\infty }S(t)\,dt,} 3003: 2656:–year old. The hazard rate is also called the failure rate. Hazard rate and failure rate are names used in reliability theory. 1551: 4595:. Right censoring will occur, for example, for those subjects whose birth date is known but who are still alive when they are 2947: 163: 86:

Images of plain-text (content and tables), which include word-processor proofreading markup. Should be converted to wikitext.

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Glennon, Dennis; Nigro, Peter (2005). "Measuring the Default Risk of Small Business Loans: A Survival Analysis Approach".

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It may also happen that subjects with a lifetime less than some threshold may not be observed at all: this is called

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The Cox model assumes that the hazards are proportional. The proportional hazard assumption may be tested using the R

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is known not to have occurred before an observation time and to have occurred before the next observation time.

2038:{\displaystyle s(t)=S'(t)={\frac {d}{dt}}S(t)={\frac {d}{dt}}\int _{t}^{\infty }f(u)\,du={\frac {d}{dt}}=-f(t).} 9116: 8328: 8135: 8024: 7982: 7037: 7018: 6999: 6980: 6961: 5760: 5690: 1300: 148: 8056: 159: 9359: 8318: 7221: 5695: 4662:

censored, and interval censored. These are denoted "unc.", "l.c.", "r.c.", and "i.c." in the equation below.

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axis is the proportion of subjects surviving. At time zero, 100% of the subjects are alive without an event.

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then the derivative, which is the density function of the lifetime distribution, is conventionally denoted

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Cox proportional hazards regression output for melanoma data. Predictor variable is sex 1: female, 2: male.

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lower 95% CI and upper 95% CI are the lower and upper 95% confidence bounds for the proportion surviving.

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must not decrease too quickly, since, by definition, the cumulative hazard has to diverge. For example,

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Finally, the output gives p-values for three alternative tests for overall significance of the model:

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An important application where interval-censored data arises is current status data, where an event

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To answer such questions, it is necessary to define "lifetime". In the case of biological survival,

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In other fields, such as statistical physics, the survival event density function is known as the

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indicates that males have higher risk of death (lower survival rates) than females, in these data.

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survival is the proportion surviving, as determined using the Kaplan–Meier product-limit estimate.

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The age at which a specified proportion of survivors remain can be found by solving the equation

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z = 2.5 = coef/se(coef) = 0.662/0.265. Dividing the coef by its standard error gives the z score.

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Stepanova, Maria; Thomas, Lyn (2002-04-01). "Survival Analysis Methods for Personal Loan Data".

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The survival function is usually assumed to approach zero as age increases without bound (i.e.,

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de Cos Juez, F. J.; García Nieto, P. J.; Martínez Torres, J.; Taboada Castro, J. (2010-10-01).

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Event: Death, disease occurrence, disease recurrence, recovery, or other experience of interest

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is not the hazard function of any survival distribution, because its integral converges to 1.

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Ishwaran, Hemant; Kogalur, Udaya B.; Blackstone, Eugene H.; Lauer, Michael S. (2008-09-01).

1095: 846:(KM) curve. The graph shows the KM plot for the aml data and can be interpreted as follows: 9249: 8824: 8773: 8749: 8711: 8629: 8608: 8560: 8439: 8417: 8386: 8295: 8172: 8123: 8041: 8014: 7970: 7926: 7688: 7464: 7344: 6906: 6667: 5670: 5632: 5562: 5208: 5066: 4958: 4470:). If the survival of different individuals is independent, the number of survivors at age 4415: 4371: 3781: 3680: 3653: 2627: 3486: 3428: 3370: 3274: 2426: 8: 9483: 9396: 9321: 9244: 8925: 8689: 8682: 8644: 8552: 8532: 8504: 8237: 8103: 8098: 8088: 8080: 7898: 7859: 7749: 7739: 7648: 7427: 7383: 7301: 7226: 7128: 6805:

Pollock, Kenneth H.; Winterstein, Scott R.; Bunck, Christine M.; Curtis, Paul D. (1989).

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in mechanical survival problems. In the latter case, the reliability function is denoted

1081: 328: 249: 6910: 6671: 5340:{\displaystyle \Pr(T>T_{i}\mid \theta )=1-F(T_{i}\mid \theta )=S(T_{i}\mid \theta ).} 5198:{\displaystyle \Pr(T<T_{i}\mid \theta )=F(T_{i}\mid \theta )=1-S(T_{i}\mid \theta ).} 2192: 9462: 9410: 9221: 9075: 8971: 8920: 8796: 8693: 8677: 8654: 8431: 8165: 8148: 8108: 8019: 7914: 7876: 7847: 7807: 7767: 7713: 7630: 7316: 7311: 6930: 6834: 6787: 6698: 6655: 6636: 6628: 6417: 6388: 6369: 6305: 6282: 6256: 6140: 6112: 6000: 5992: 5956: 5825: 5805: 5716: 5680: 2925: 2878: 2662: 2607: 2587: 2567: 2408: 2172: 2126: 2106: 2086: 2046: 7059: 6352:

Richards, S. J. (2012). "A handbook of parametric survival models for actuarial use".

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predictions of survival than the Cox PH model. The prediction errors are estimated by

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coef = 0.662 is the estimated logarithm of the hazard ratio for males versus females.

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for analyzing the expected duration of time until one event occurs, such as death in

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Ritschard, Gilbert; Gabadinho, Alexis; Muller, Nicolas S.; Studer, Matthias (2008).

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For an interval censored datum, such that the age at death is known to be less than

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The solid line (similar to a staircase) shows the progression of event occurrences.

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axis is time, from zero (when observation began) to the last observed time point.

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Treatment group: the variable "x" indicates if maintenance chemotherapy was given

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Time is indicated by the variable "time", which is the survival or censoring time

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For right-censored data, such that the age at death is known to be greater than

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Kennedy, Edward H.; Hu, Chen; O’Brien, Barbara; Gross, Samuel R. (2014-05-20).

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https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-022-01679-6

6074: 5810: 5747: 4633: 3742: 7110: 6870: 6853: 6739: 6722: 6581: 6270: 3160:{\displaystyle {\frac {d}{dt}}\Lambda (t)=-{\frac {S'(t)}{S(t)}}=\lambda (t).} 2189:

and we desire the probability that it will not survive for an additional time

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Data are in the R package ISwR. The Cox proportional hazards regression using

930: 371: 6775: 6680: 6656:"Rate of false conviction of criminal defendants who are sentenced to death" 6407: 5063:

For left-censored data, such that the age at death is known to be less than

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Cox models can be extended to deal with variations on the simple analysis.

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To describe the effect of categorical or quantitative variables on survival

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is a hazard function if and only if it satisfies the following properties:

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models relax that assumption. The study of recurring events is relevant in

6616: 3633:{\displaystyle S(t)=\exp={\frac {f(t)}{\lambda (t)}}=1-F(t),\quad t>0.} 2564:

In actuarial science, the hazard rate is the rate of death for lives aged

9349: 9311: 8994: 8895: 8757: 8570: 8537: 8029: 7946: 7941: 7585: 7542: 7522: 7502: 7492: 7261: 5707: 1419: 842:) is theoretically a smooth curve, but it is usually estimated using the 790:

Event (recurrence of aml cancer) is indicated by the variable "status". 0

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System Reliability Theory: Models, Statistical Methods, and Applications

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Cox PH output for melanoma data set with covariate log tumor thickness

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The hazard function can alternatively be represented in terms of the

1089: 285: 277: 7100: 6822: 6807:"Survival Analysis in Telemetry Studies: The Staggered Entry Design" 6729:. Mathematical Models in Medicine, Business & Engineering 2009. 6300:

Nagpal, Chirag (2021). "Deep Cox mixtures for survival regression".

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or when the study ends. We generally encounter right-censored data.

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The name "cumulative hazard function" is derived from the fact that

1842:{\displaystyle S(t)=\Pr(T>t)=\int _{t}^{\infty }f(u)\,du=1-F(t).} 1274: 973: 424: 126: 7864: 7482: 7359: 7354: 7349: 6310: 6261: 4637: 4538: 4491: 2552:{\displaystyle \mu (x)=-{d \over dx}\ln(S(x))={\frac {f(x)}{S(x)}}} 1530: 1219:

The survival tree produced by the analysis is shown in the figure.

1077: 1059: 398: 289: 6389:"Survival analysis in clinical trials: Basics and must know areas" 6190:

An introduction to recursive partitioning using the RPART routines

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Related quantities are defined in terms of the survival function.

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This example uses the melanoma data set from Dalgaard Chapter 14.

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Example: Cox proportional hazards regression analysis for melanoma

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Log-rank test: Testing for differences in survival in the aml data

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Saegusa, Takumi; Di, Chongzhi; Chen, Ying Qing (September 2014).

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S(t): The probability that a subject survives longer than time t.

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Proper Scoring Rules for Survival Analysis, Hiroki Yanagisawa,

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Similarly, a survival event density function can be defined as

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types of models for a given data set is a reasonable strategy.

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se(coef) = 0.265 is the standard error of the log hazard ratio.

830:), is the probability that a subject survives longer than time 312: 6098: 6063:

International Journal of Data Mining, Modelling and Management

6056: 5056:{\displaystyle \Pr(T=T_{i}\mid \theta )=f(T_{i}\mid \theta ).} 3745:

of future lifetime. The probability of death at or before age

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The force of mortality of the survival function is defined as

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Sex is encoded as a numeric vector (1: female, 2: male). The R

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The aml data set sorted by survival time is shown in the box.

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The goodness of fit of survival models can be assessed using

4413:

In reliability problems, the expected lifetime is called the

331:, and in many areas of social sciences and medical research. 296: 5721:

Lead times for metallic components in the aerospace industry

4410:, that is, at birth, this reduces to the expected lifetime. 1173:: time to progression, or last follow-up free of progression 910:

n.event is the number of subjects who have events at time t.

403:

The following terms are commonly used in survival analyses:

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Kreer, Markus; Kizilersu, Ayse; Thomas, Anthony W. (2022).

5815: 1726:; it is the rate of death or failure events per unit time. 1457:

if there is the possibility of immediate death or failure.

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or may not have an event after the end of observation time.

304: 5659: 5650: 4438:), by definition, the expected number of survivors at age 6333:. Vol. 1 (2nd ed.). Macmillan. pp. 473–474 4034:

Therefore, the probability density of future lifetime is

3677:

is the time remaining until death, given survival to age

1546:, is defined as the complement of the survival function, 311:

or other organ failure) may have the same ambiguity. The

307:. Even in biological problems, some events (for example, 4426:

As the probability of an individual surviving until age

3228:{\displaystyle \Lambda (t)=\int _{0}^{t}\lambda (u)\,du} 252:

and failure in mechanical systems. This topic is called

6956:(Second ed.). Boca Raton: Chapman & Hall/CRC. 1010:

The Cox regression results are interpreted as follows.

6059:"Mining event histories: a social science perspective" 2732:{\displaystyle \forall x\geq 0\left(h(x)\geq 0\right)} 9446: 6970: 6899:

Physica A: Statistical Mechanics and Its Applications

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which is the "accumulation" of the hazard over time.

3175: 3068: 3006: 2950: 2928: 2908: 2881: 2845: 2810: 2747: 2688: 2665: 2630: 2610: 2590: 2570: 2456: 2429: 2220: 2195: 2175: 2149: 2129: 2109: 2089: 2069: 1857: 1744: 1642: 1554: 1362: 1179:: status at last follow-up (1=progressed, 0=censored) 814: 343:

To describe the survival times of members of a group

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Autoregressive conditional heteroskedasticity (ARCH)

6892: 6163:"rpart: Recursive Partitioning and Regression Trees" 2875:

hazard function, which is large for small values of

368:

To compare the survival times of two or more groups

334: 6989: 6187:Atkinson, Elizabeth J.; Therneau, Terry J. (1997). 5598:can be used to estimate the survival function. The 1729:The survival function can be expressed in terms of 1155:

This example of a survival tree analysis uses the R

151:. Unsourced material may be challenged and removed. 8495: 6489: 6433: 5742:Intertrade waiting times of electronically traded 5578: 5551: 5405: 5372: 5339: 5224: 5197: 5082: 5055: 4974: 4947: 4402: 4362: 4189: 4026: 3797: 3770: 3729: 3696: 3669: 3632: 3504: 3475: 3446: 3417: 3388: 3356: 3321: 3292: 3259: 3227: 3159: 3052: 2990: 2934: 2914: 2887: 2863: 2831: 2789: 2731: 2671: 2648: 2616: 2596: 2576: 2551: 2435: 2400: 2204: 2181: 2161: 2135: 2115: 2095: 2075: 2037: 1841: 1710: 1614: 1398: 1159:package "rpart". The example is based on 146 stage 1137: 9489:Mathematical and quantitative methods (economics) 7111:Lifelines, a Python package for survival analysis 6386: 6331:International Encyclopedia of the Social Sciences 6249:IEEE Journal of Biomedical and Health Informatics 4419:, and the expected future lifetime is called the 3643:Quantities derived from the survival distribution 2790:{\displaystyle \int _{0}^{\infty }h(x)dx=\infty } 1150: 974:Cox proportional hazards (PH) regression analysis 904:time gives the time points at which events occur. 425:Example: Acute myelogenous leukemia survival data 9470: 7011:Statistical Models and Methods for Lifetime Data 6971:Elandt-Johnson, Regina; Johnson, Norman (1999). 6761: 6186: 5610: 5422: 5241: 5099: 4991: 4886: 4830: 4774: 4718: 4541:in question. Typically one is interested in the 2258: 2237: 2169:). Suppose that an item has survived for a time 1760: 1570: 1531:Lifetime distribution function and event density 1418:denoting the time of death, and "Pr" stands for 1378: 1255: 1060:Cox model using a covariate in the melanoma data 399:Definitions of common terms in survival analysis 299:is unambiguous, but for mechanical reliability, 8581:Multivariate adaptive regression splines (MARS) 6660:Proceedings of the National Academy of Sciences 6567: 6537: 6024:Journal of the American Statistical Association 5631:Discrete-time survival models are connected to 1711:{\displaystyle f(t)=F'(t)={\frac {d}{dt}}F(t).} 7066:Dr. Therneau's page on the Mayo Clinic website 7027: 7013:(2nd ed.). Hoboken: John Wiley and Sons. 6990:Kalbfleisch, J. D.; Prentice, Ross L. (2002). 6495: 6473:https://apps.dtic.mil/sti/tr/pdf/ADA030940.pdf 6017: 5893: 5891: 4370:where the second expression is obtained using 2053:Hazard function and cumulative hazard function 1460:The survival function must be non-increasing: 1051:Score (log-rank) test = 6.47 on 1 df, p=0.0110 1045:Likelihood ratio test = 6.15 on 1 df, p=0.0131 876: 7136: 6992:The statistical analysis of failure time data 5921: 4647: 6602: 6513: 6496:Kleinbaum, David G.; Klein, Mitchel (2012), 6460:https://www.ms.uky.edu/~mai/research/llz.pdf 6229: 6160: 5589: 3267:, we see that it increases without bound as 2624:years later is the force of mortality for a 1434:in problems of biological survival, and the 1076:In the histograms, the thickness values are 941:Kaplan–Meier graph by treatment group in aml 6954:Modelling Survival Data in Medical Research 6543: 6203: 6161:Therneau, Terry J.; Atkinson, Elizabeth J. 5888: 1426:. The survival function is also called the 1303:. Unsourced material may be challenged and 1119: 339:Survival analysis is used in several ways: 53:Learn how and when to remove these messages 7181: 7143: 7129: 6524:(First ed.), Chapman & Hall/CRC, 6444:https://doi.org/10.1186/s12874-022-01679-6 6302:Machine Learning for Healthcare Conference 2804:The hazard function must be non-negative, 1234: 1226:Survival tree for prostate cancer data set 1197:: diploid/tetraploid/aneuploid DNA pattern 7794: 6869: 6738: 6697: 6679: 6416: 6406: 6309: 6260: 6126: 6116: 5955: 5864: 4350: 4278: 4252: 3483:, and the lifetime distribution function 3218: 3060:or differentiating (with the chain rule) 3053:{\displaystyle \,S(t)=\exp(-\Lambda (t))} 3007: 2951: 1965: 1808: 1615:{\displaystyle F(t)=\Pr(T\leq t)=1-S(t).} 1484:. This property follows directly because 1453:(0) = 1, although it could be less than 1 1323:Learn how and when to remove this message 229:Learn how and when to remove this message 211:Learn how and when to remove this message 109:Learn how and when to remove this message 7116:Survival Analysis in NAG Fortran Library 6548:(First ed.), Chapman and Hall/CRC, 6519: 6351: 6018:Leblanc, Michael; Crowley, John (1993). 5897: 5622: 2998:so transposing signs and exponentiating 2991:{\displaystyle \,\Lambda (t)=-\log S(t)} 1221: 1094: 1067: 1001: 936: 891: 7008: 6951: 6544:Tableman, Mara; Kim, Jong Sung (2003), 6498:Survival analysis: A Self-learning text 5660:Distributions used in survival analysis 5651:Computer software for survival analysis 2103:, is defined as the event rate at time 1191:: early endocrine therapy (1=no, 0=yes) 9471: 9107:Kaplan–Meier estimator (product limit) 7056:"A Package for Survival Analysis in S" 6324: 6299: 6246: 5870: 5781:Chance-constrained portfolio selection 1346:The object of primary interest is the 1264: 1072:Histograms of melanoma tumor thickness 999:R gives the results shown in the box. 9180: 8747: 8494: 7793: 7563: 7180: 7124: 6851: 6020:"Survival Trees by Goodness of Split" 5970: 441:Aml data set sorted by survival time 9417: 9117:Accelerated failure time (AFT) model 7053: 6605:Journal of Money, Credit and Banking 6387:Singh, R.; Mukhopadhyay, K. (2011). 6325:Darity, William A. Jr., ed. (2008). 6204:Ishwaran, Hemant; Kogalur, Udaya B. 6156: 6154: 6094: 6092: 5973:"Regression Trees for Censored Data" 5836:Sequence analysis in social sciences 5686:Exponential-logarithmic distribution 4197:and the expected future lifetime is 1335: 1301:adding citations to reliable sources 1268: 950:with one degree of freedom, and the 149:adding citations to reliable sources 120: 59: 18: 9429: 8712:Analysis of variance (ANOVA, anova) 7564: 6994:. New York: John Wiley & Sons. 6975:. New York: John Wiley & Sons. 6727:Mathematical and Computer Modelling 4982:equal to the age at death, we have 2123:conditional on survival until time 981:Cox proportional hazards regression 382:Cox proportional hazards regression 13: 8807:Cochran–Mantel–Haenszel statistics 7433:Pearson product-moment correlation 7032:. Hoboken: John Wiley & Sons. 6945: 6852:Saleh, Joseph Homer (2019-12-23). 6811:The Journal of Wildlife Management 6485:https://arxiv.org/abs/2305.00621v3 5851:Discrete-time proportional hazards 5638: 4552:= 1/2, or other quantiles such as 4494:of the proportion of survivors is 4333: 4244: 3546: 3403: 3300:tends to zero). This implies that 3245: 3176: 3084: 3035: 2952: 2909: 2855: 2784: 2758: 2689: 1948: 1791: 1086:Symmetric probability distribution 1048:Wald test = 6.24 on 1 df, p=0.0125 815:Kaplan–Meier plot for the aml data 14: 9510: 7072:"Engineering Statistics Handbook" 7047: 7028:Rausand, M.; Hoyland, A. (2004). 6973:Survival Models and Data Analysis 6151: 6089: 3396:, the cumulative hazard function 3271:tends to infinity (assuming that 2832:{\displaystyle \lambda (t)\geq 0} 335:Introduction to survival analysis 34:This article has multiple issues. 9456: 9428: 9416: 9404: 9391: 9390: 9181: 6233:BMC Medical Research Methodology 6105:The Annals of Applied Statistics 1399:{\displaystyle S(t)=\Pr(T>t)} 1273: 125: 64: 23: 9066:Least-squares spectral analysis 6886: 6845: 6798: 6755: 6714: 6647: 6596: 6561: 6477: 6464: 6452: 6380: 6345: 6318: 6293: 6240: 6223: 6197: 5701: 3620: 1138:Tree-structured survival models 136:needs additional citations for 42:or discuss these issues on the 8047:Mean-unbiased minimum-variance 7150: 7093:Survival/Failure Time Analysis 6354:Scandinavian Actuarial Journal 6180: 6050: 6036:10.1080/01621459.1993.10476296 6011: 5964: 5915: 5900:Introductory Statistics with R 5761:Accelerated failure time model 5691:Generalized gamma distribution 5543: 5518: 5509: 5484: 5475: 5425: 5331: 5312: 5303: 5284: 5269: 5244: 5189: 5170: 5155: 5136: 5127: 5102: 5047: 5028: 5019: 4994: 4939: 4889: 4858: 4833: 4802: 4777: 4746: 4721: 4680: 4674: 4347: 4341: 4310: 4297: 4275: 4256: 4228: 4215: 4181: 4168: 4160: 4141: 4126: 4113: 4105: 4092: 4083: 4064: 4015: 4002: 3994: 3981: 3972: 3953: 3938: 3919: 3911: 3873: 3861: 3817: 3614: 3608: 3590: 3584: 3576: 3570: 3558: 3555: 3549: 3540: 3528: 3522: 3499: 3493: 3470: 3464: 3441: 3435: 3412: 3406: 3383: 3377: 3351: 3342: 3316: 3310: 3287: 3281: 3254: 3248: 3215: 3209: 3185: 3179: 3151: 3145: 3133: 3127: 3119: 3113: 3093: 3087: 3047: 3044: 3038: 3029: 3017: 3011: 2985: 2979: 2961: 2955: 2858: 2846: 2820: 2814: 2772: 2766: 2715: 2709: 2643: 2631: 2543: 2537: 2529: 2523: 2511: 2508: 2502: 2496: 2466: 2460: 2415:which is used particularly in 2389: 2383: 2375: 2369: 2346: 2340: 2332: 2326: 2311: 2305: 2288: 2261: 2247: 2230: 2224: 2029: 2023: 2011: 2008: 2002: 1990: 1962: 1956: 1917: 1911: 1887: 1881: 1867: 1861: 1833: 1827: 1805: 1799: 1775: 1763: 1754: 1748: 1702: 1696: 1672: 1666: 1652: 1646: 1606: 1600: 1585: 1573: 1564: 1558: 1540:lifetime distribution function 1393: 1381: 1372: 1366: 1151:Example survival tree analysis 1: 9360:Geographic information system 8576:Simultaneous equations models 7087:interactive learning activity 6522:Event History Analysis with R 5902:(Second ed.), Springer, 5857: 5611:Discrete-time survival models 3737:in the present notation. The 1735:probability density functions 1256:Deep Learning survival models 1203:: % of cells in G2 phase 1166:The variables in stages are: 8543:Coefficient of determination 8154:Uniformly most powerful test 6500:(Third ed.), Springer, 6366:10.1080/03461238.2010.506688 4563: 7: 9112:Proportional hazards models 9056:Spectral density estimation 9038:Vector autoregression (VAR) 8472:Maximum posterior estimator 7704:Randomized controlled trial 7009:Lawless, Jerald F. (2003). 6919:10.1016/j.physa.2021.126456 6764:Justice Research and Policy 6327:"Censoring, Left and Right" 5971:Segal, Mark Robert (1988). 5831:Residence time (statistics) 5821:Proportional hazards models 5753: 3778:, given survival until age 3476:{\displaystyle \lambda (t)} 3418:{\displaystyle \Lambda (t)} 3322:{\displaystyle \lambda (t)} 3260:{\displaystyle \Lambda (t)} 1244:package "randomForestSRC". 896:Life table for the aml data 877:Life table for the aml data 84:. The specific problem is: 10: 9515: 8872:Multivariate distributions 7292:Average absolute deviation 6075:10.1504/IJDMMM.2008.022538 5871:Miller, Rupert G. (1997), 5766:Bayesian survival analysis 5696:Hypertabastic distribution 4955:For uncensored data, with 4648:Fitting parameters to data 2900:cumulative hazard function 1339: 431:Acute Myelogenous Leukemia 386:Parametric survival models 9386: 9340: 9277: 9230: 9193: 9189: 9176: 9148: 9130: 9097: 9088: 9046: 8993: 8954: 8903: 8894: 8860:Structural equation model 8815: 8772: 8768: 8743: 8702: 8668: 8622: 8589: 8551: 8518: 8514: 8490: 8430: 8339: 8258: 8222: 8213: 8196:Score/Lagrange multiplier 8181: 8134: 8079: 8005: 7996: 7806: 7802: 7789: 7748: 7722: 7674: 7629: 7611:Sample size determination 7576: 7572: 7559: 7463: 7418: 7392: 7374: 7330: 7282: 7202: 7193: 7189: 7176: 7158: 6871:10.1057/s41599-019-0366-y 6740:10.1016/j.mcm.2010.03.017 6582:10.1287/opre.50.2.277.426 6546:Survival Analysis Using S 6271:10.1109/JBHI.2021.3052441 6101:"Random survival forests" 5875:, John Wiley & Sons, 5736:Time-to-violent death of 5730:Survival distribution of 5676:Log-logistic distribution 5602:can be used to provide a 5590:Non-parametric estimation 2902:, conventionally denoted 2604:, the force of mortality 2423:, where it is denoted by 2063:, conventionally denoted 1542:, conventionally denoted 1508:below) are well-defined. 1350:, conventionally denoted 9355:Environmental statistics 8877:Elliptical distributions 8670:Generalized linear model 8599:Simple linear regression 8369:Hodges–Lehmann estimator 7826:Probability distribution 7735:Stochastic approximation 7297:Coefficient of variation 7083:Survival analysis applet 6520:Brostrom, Göran (2012), 5898:Dalgaard, Peter (2008), 5666:Exponential distribution 4579:for the true event time 4575:If only the lower limit 3739:expected future lifetime 3357:{\displaystyle \exp(-t)} 2915:{\displaystyle \Lambda } 2839:, and its integral over 2076:{\displaystyle \lambda } 1731:probability distribution 1722:is sometimes called the 1120:Extensions to Cox models 954:is calculated using the 948:Chi-squared distribution 917:(survival in the table). 794:= no event (censored), 1 9494:Mathematics in medicine 9015:Cross-correlation (XCF) 8623:Non-standard predictors 8057:Lehmann–Scheffé theorem 7730:Adaptive clinical trial 6952:Collett, David (2003). 6858:Palgrave Communications 6776:10.3818/jrp.8.2.2006.57 6681:10.1073/pnas.1306417111 6408:10.4103/2229-3485.86872 5791:Frequency of exceedance 5406:{\displaystyle T_{i,l}} 5373:{\displaystyle T_{i,r}} 4659:conditional probability 4403:{\displaystyle t_{0}=0} 3771:{\displaystyle t_{0}+t} 3730:{\displaystyle T-t_{0}} 3238:From the definition of 2162:{\displaystyle T\geq t} 1235:Survival random forests 392:Survival random forests 262:reliability engineering 9411:Mathematics portal 9232:Engineering statistics 9140:Nelson–Aalen estimator 8717:Analysis of covariance 8604:Ordinary least squares 8528:Pearson product-moment 7932:Statistical functional 7843:Empirical distribution 7676:Controlled experiments 7405:Frequency distribution 7183:Descriptive statistics 7106:Survival Analysis in R 5796:Kaplan–Meier estimator 5776:Censoring (statistics) 5628: 5600:Nelson–Aalen estimator 5596:Kaplan–Meier estimator 5580: 5553: 5407: 5374: 5341: 5226: 5199: 5084: 5057: 4976: 4949: 4421:mean residual lifetime 4404: 4364: 4191: 4028: 3799: 3772: 3731: 3698: 3671: 3634: 3506: 3477: 3454:, the hazard function 3448: 3419: 3390: 3367:The survival function 3358: 3323: 3294: 3261: 3229: 3161: 3054: 2992: 2936: 2916: 2889: 2865: 2833: 2791: 2733: 2673: 2650: 2618: 2598: 2578: 2553: 2437: 2402: 2206: 2183: 2163: 2137: 2117: 2097: 2077: 2039: 1843: 1712: 1616: 1400: 1354:, which is defined as 1227: 1215:: Gleason grade (3-10) 1100: 1073: 1007: 942: 897: 872:censored observations. 429:This example uses the 282:event history analysis 9327:Population statistics 9269:System identification 9003:Autocorrelation (ACF) 8931:Exponential smoothing 8845:Discriminant analysis 8840:Canonical correlation 8704:Partition of variance 8566:Regression validation 8410:(Jonckheere–Terpstra) 8309:Likelihood-ratio test 7998:Frequentist inference 7910:Location–scale family 7831:Sampling distribution 7796:Statistical inference 7763:Cross-sectional study 7750:Observational studies 7709:Randomized experiment 7538:Stem-and-leaf display 7340:Central limit theorem 6617:10.1353/mcb.2005.0051 5713:False conviction rate 5626: 5581: 5579:{\displaystyle T_{i}} 5554: 5408: 5375: 5342: 5227: 5225:{\displaystyle T_{i}} 5200: 5085: 5083:{\displaystyle T_{i}} 5058: 4977: 4975:{\displaystyle T_{i}} 4950: 4476:binomial distribution 4405: 4365: 4192: 4029: 3800: 3798:{\displaystyle t_{0}} 3773: 3732: 3699: 3697:{\displaystyle t_{0}} 3672: 3670:{\displaystyle t_{0}} 3635: 3507: 3478: 3449: 3420: 3391: 3359: 3324: 3295: 3262: 3230: 3162: 3055: 2993: 2937: 2917: 2890: 2866: 2834: 2792: 2734: 2674: 2651: 2649:{\displaystyle (x+t)} 2619: 2599: 2579: 2554: 2438: 2403: 2207: 2184: 2164: 2138: 2118: 2098: 2078: 2040: 1844: 1713: 1617: 1432:survivorship function 1401: 1250:bootstrap re-sampling 1225: 1098: 1071: 1005: 940: 895: 9250:Probabilistic design 8835:Principal components 8678:Exponential families 8630:Nonlinear regression 8609:General linear model 8571:Mixed effects models 8561:Errors and residuals 8538:Confounding variable 8440:Bayesian probability 8418:Van der Waerden test 8408:Ordered alternative 8173:Multiple comparisons 8052:Rao–Blackwellization 8015:Estimating equations 7971:Statistical distance 7689:Factorial experiment 7222:Arithmetic-Geometric 5732:radio-tagged animals 5671:Weibull distribution 5633:empirical likelihood 5563: 5419: 5384: 5351: 5238: 5209: 5096: 5067: 4988: 4959: 4668: 4416:mean time to failure 4381: 4372:integration by parts 4203: 4040: 3811: 3782: 3749: 3708: 3681: 3654: 3516: 3512:are related through 3505:{\displaystyle F(t)} 3487: 3458: 3447:{\displaystyle f(t)} 3429: 3400: 3389:{\displaystyle S(t)} 3371: 3333: 3304: 3293:{\displaystyle S(t)} 3275: 3242: 3173: 3066: 3004: 2948: 2926: 2906: 2879: 2843: 2808: 2745: 2686: 2663: 2628: 2608: 2588: 2568: 2454: 2447:is another synonym. 2436:{\displaystyle \mu } 2427: 2218: 2193: 2173: 2147: 2127: 2107: 2087: 2067: 1855: 1742: 1640: 1552: 1449:Usually one assumes 1436:reliability function 1360: 1297:improve this section 889:software, is shown. 798:= event (recurrence) 258:reliability analysis 250:biological organisms 145:improve this article 91:improve this article 80:to meet Knowledge's 16:Branch of statistics 9322:Official statistics 9245:Methods engineering 8926:Seasonal adjustment 8694:Poisson regressions 8614:Bayesian regression 8553:Regression analysis 8533:Partial correlation 8505:Regression analysis 8104:Prediction interval 8099:Likelihood interval 8089:Confidence interval 8081:Interval estimation 8042:Unbiased estimators 7860:Model specification 7740:Up-and-down designs 7428:Partial correlation 7384:Index of dispersion 7302:Interquartile range 6911:2022PhyA..58726456K 6672:2014PNAS..111.7230G 6570:Operations Research 5771:Cell survival curve 5726:criminal recidivism 4655:likelihood function 4583:is known such that 4337: 4248: 3205: 2762: 2143:or later (that is, 1952: 1795: 1265:General formulation 1209:: tumor grade (1-4) 442: 352:Kaplan–Meier curves 329:systems reliability 160:"Survival analysis" 9342:Spatial statistics 9222:Medical statistics 9122:First hitting time 9076:Whittle likelihood 8727:Degrees of freedom 8722:Multivariate ANOVA 8655:Heteroscedasticity 8467:Bayesian estimator 8432:Bayesian inference 8281:Kolmogorov–Smirnov 8166:Randomization test 8136:Testing hypotheses 8109:Tolerance interval 8020:Maximum likelihood 7915:Exponential family 7848:Density estimation 7808:Statistical theory 7768:Natural experiment 7714:Scientific control 7631:Survey methodology 7317:Standard deviation 6193:. Mayo Foundation. 6128:10.1214/08-AOAS169 5940:10.1111/biom.12185 5826:Reliability theory 5806:Maximum likelihood 5717:sentenced to death 5681:Gamma distribution 5629: 5576: 5549: 5403: 5370: 5337: 5222: 5195: 5080: 5053: 4972: 4945: 4885: 4829: 4773: 4717: 4608:interval censoring 4442:out of an initial 4400: 4360: 4316: 4234: 4187: 4024: 3795: 3768: 3727: 3694: 3667: 3630: 3502: 3473: 3444: 3415: 3386: 3354: 3319: 3290: 3257: 3225: 3191: 3157: 3050: 2988: 2932: 2912: 2885: 2861: 2829: 2787: 2748: 2729: 2669: 2646: 2614: 2594: 2584:. For a life aged 2574: 2549: 2433: 2409:Force of mortality 2398: 2254: 2205:{\displaystyle dt} 2202: 2179: 2159: 2133: 2113: 2093: 2073: 2047:first passage time 2035: 1938: 1839: 1781: 1708: 1612: 1396: 1228: 1185:: age at diagnosis 1101: 1080:and do not have a 1074: 1008: 943: 898: 440: 274:duration modelling 254:reliability theory 9479:Survival analysis 9444: 9443: 9382: 9381: 9378: 9377: 9317:National accounts 9287:Actuarial science 9279:Social statistics 9172: 9171: 9168: 9167: 9164: 9163: 9099:Survival function 9084: 9083: 8946:Granger causality 8787:Contingency table 8762:Survival analysis 8739: 8738: 8735: 8734: 8591:Linear regression 8486: 8485: 8482: 8481: 8457:Credible interval 8426: 8425: 8209: 8208: 8025:Method of moments 7894:Parametric family 7855:Statistical model 7785: 7784: 7781: 7780: 7699:Random assignment 7621:Statistical power 7555: 7554: 7551: 7550: 7400:Contingency table 7370: 7369: 7237:Generalized/power 7054:Therneau, Terry. 6666:(20): 7230–7235. 6394:Perspect Clin Res 5873:Survival analysis 5841:Survival function 5380:and greater than 4861: 4805: 4749: 4686: 4597:lost to follow-up 4591:, this is called 4314: 4232: 4185: 4130: 4056: 4019: 3942: 3594: 3137: 3082: 2935:{\displaystyle H} 2888:{\displaystyle t} 2672:{\displaystyle h} 2617:{\displaystyle t} 2597:{\displaystyle x} 2577:{\displaystyle x} 2547: 2488: 2421:actuarial science 2393: 2350: 2315: 2236: 2182:{\displaystyle t} 2136:{\displaystyle t} 2116:{\displaystyle t} 2096:{\displaystyle h} 1988: 1936: 1906: 1691: 1428:survivor function 1348:survival function 1342:Survival function 1336:Survival function 1333: 1332: 1325: 1116:textbooks cited. 1078:positively skewed 821:survival function 784: 783: 418:Survival function 357:Survival function 270:duration analysis 242:Survival analysis 239: 238: 231: 221: 220: 213: 195: 119: 118: 111: 82:quality standards 73:This article may 57: 9506: 9461: 9460: 9452: 9432: 9431: 9420: 9419: 9409: 9408: 9394: 9393: 9297:Crime statistics 9191: 9190: 9178: 9177: 9095: 9094: 9061:Fourier analysis 9048:Frequency domain 9028: 8975: 8941:Structural break 8901: 8900: 8850:Cluster analysis 8797:Log-linear model 8770: 8769: 8745: 8744: 8686: 8660:Homoscedasticity 8516: 8515: 8492: 8491: 8411: 8403: 8395: 8394:(Kruskal–Wallis) 8379: 8364: 8319:Cross validation 8304: 8286:Anderson–Darling 8233: 8220: 8219: 8191:Likelihood-ratio 8183:Parametric tests 8161:Permutation test 8144:1- & 2-tails 8035:Minimum distance 8007:Point estimation 8003: 8002: 7954:Optimal decision 7905: 7804: 7803: 7791: 7790: 7773:Quasi-experiment 7723:Adaptive designs 7574: 7573: 7561: 7560: 7438:Rank correlation 7200: 7199: 7191: 7190: 7178: 7177: 7145: 7138: 7131: 7122: 7121: 7075: 7063: 7058:. Archived from 7043: 7024: 7005: 6986: 6967: 6939: 6938: 6890: 6884: 6883: 6873: 6849: 6843: 6842: 6802: 6796: 6795: 6759: 6753: 6752: 6742: 6733:(7): 1177–1184. 6718: 6712: 6711: 6701: 6683: 6651: 6645: 6644: 6600: 6594: 6593: 6565: 6559: 6558: 6541: 6535: 6534: 6517: 6511: 6510: 6493: 6487: 6481: 6475: 6468: 6462: 6456: 6450: 6440: 6431: 6430: 6420: 6410: 6384: 6378: 6377: 6349: 6343: 6342: 6340: 6338: 6322: 6316: 6315: 6313: 6297: 6291: 6290: 6264: 6255:(8): 3163–3175. 6244: 6238: 6237: 6227: 6221: 6220: 6218: 6216: 6201: 6195: 6194: 6184: 6178: 6177: 6175: 6173: 6158: 6149: 6148: 6130: 6120: 6096: 6087: 6086: 6054: 6048: 6047: 6030:(422): 457–467. 6015: 6009: 6008: 5968: 5962: 5961: 5959: 5919: 5913: 5912: 5895: 5886: 5885: 5868: 5585: 5583: 5582: 5577: 5575: 5574: 5558: 5556: 5555: 5550: 5536: 5535: 5502: 5501: 5468: 5467: 5443: 5442: 5412: 5410: 5409: 5404: 5402: 5401: 5379: 5377: 5376: 5371: 5369: 5368: 5346: 5344: 5343: 5338: 5324: 5323: 5296: 5295: 5262: 5261: 5231: 5229: 5228: 5223: 5221: 5220: 5204: 5202: 5201: 5196: 5182: 5181: 5148: 5147: 5120: 5119: 5089: 5087: 5086: 5081: 5079: 5078: 5062: 5060: 5059: 5054: 5040: 5039: 5012: 5011: 4981: 4979: 4978: 4973: 4971: 4970: 4954: 4952: 4951: 4946: 4932: 4931: 4907: 4906: 4884: 4851: 4850: 4828: 4795: 4794: 4772: 4739: 4738: 4716: 4700: 4699: 4478:with parameters 4409: 4407: 4406: 4401: 4393: 4392: 4369: 4367: 4366: 4361: 4336: 4331: 4330: 4329: 4315: 4313: 4309: 4308: 4289: 4268: 4267: 4247: 4242: 4233: 4231: 4227: 4226: 4207: 4196: 4194: 4193: 4188: 4186: 4184: 4180: 4179: 4163: 4153: 4152: 4136: 4131: 4129: 4125: 4124: 4108: 4104: 4103: 4076: 4075: 4059: 4057: 4055: 4044: 4033: 4031: 4030: 4025: 4020: 4018: 4014: 4013: 3997: 3993: 3992: 3965: 3964: 3948: 3943: 3941: 3937: 3936: 3914: 3904: 3903: 3885: 3884: 3868: 3860: 3859: 3835: 3834: 3804: 3802: 3801: 3796: 3794: 3793: 3777: 3775: 3774: 3769: 3761: 3760: 3736: 3734: 3733: 3728: 3726: 3725: 3703: 3701: 3700: 3695: 3693: 3692: 3676: 3674: 3673: 3668: 3666: 3665: 3650:at a given time 3639: 3637: 3636: 3631: 3595: 3593: 3579: 3565: 3511: 3509: 3508: 3503: 3482: 3480: 3479: 3474: 3453: 3451: 3450: 3445: 3424: 3422: 3421: 3416: 3395: 3393: 3392: 3387: 3363: 3361: 3360: 3355: 3328: 3326: 3325: 3320: 3299: 3297: 3296: 3291: 3266: 3264: 3263: 3258: 3234: 3232: 3231: 3226: 3204: 3199: 3166: 3164: 3163: 3158: 3138: 3136: 3122: 3112: 3103: 3083: 3081: 3070: 3059: 3057: 3056: 3051: 2997: 2995: 2994: 2989: 2941: 2939: 2938: 2933: 2921: 2919: 2918: 2913: 2894: 2892: 2891: 2886: 2870: 2868: 2867: 2864:{\displaystyle } 2862: 2838: 2836: 2835: 2830: 2796: 2794: 2793: 2788: 2761: 2756: 2738: 2736: 2735: 2730: 2728: 2724: 2678: 2676: 2675: 2670: 2655: 2653: 2652: 2647: 2623: 2621: 2620: 2615: 2603: 2601: 2600: 2595: 2583: 2581: 2580: 2575: 2558: 2556: 2555: 2550: 2548: 2546: 2532: 2518: 2489: 2487: 2476: 2442: 2440: 2439: 2434: 2411:is a synonym of 2407: 2405: 2404: 2399: 2394: 2392: 2378: 2368: 2359: 2351: 2349: 2335: 2321: 2316: 2314: 2291: 2256: 2253: 2211: 2209: 2208: 2203: 2188: 2186: 2185: 2180: 2168: 2166: 2165: 2160: 2142: 2140: 2139: 2134: 2122: 2120: 2119: 2114: 2102: 2100: 2099: 2094: 2082: 2080: 2079: 2074: 2044: 2042: 2041: 2036: 1989: 1987: 1976: 1951: 1946: 1937: 1935: 1924: 1907: 1905: 1894: 1880: 1848: 1846: 1845: 1840: 1794: 1789: 1717: 1715: 1714: 1709: 1692: 1690: 1679: 1665: 1621: 1619: 1618: 1613: 1456: 1405: 1403: 1402: 1397: 1328: 1321: 1317: 1314: 1308: 1277: 1269: 1243: 1162: 1158: 1114: 1017: 998: 956:Chi-squared test 888: 809: 797: 793: 443: 439: 234: 227: 216: 209: 205: 202: 196: 194: 153: 129: 121: 114: 107: 103: 100: 94: 68: 67: 60: 49: 27: 26: 19: 9514: 9513: 9509: 9508: 9507: 9505: 9504: 9503: 9469: 9468: 9467: 9455: 9447: 9445: 9440: 9403: 9374: 9336: 9273: 9259:quality control 9226: 9208:Clinical trials 9185: 9160: 9144: 9132:Hazard function 9126: 9080: 9042: 9026: 8989: 8985:Breusch–Godfrey 8973: 8950: 8890: 8865:Factor analysis 8811: 8792:Graphical model 8764: 8731: 8698: 8684: 8664: 8618: 8585: 8547: 8510: 8509: 8478: 8422: 8409: 8401: 8393: 8377: 8362: 8341:Rank statistics 8335: 8314:Model selection 8302: 8260:Goodness of fit 8254: 8231: 8205: 8177: 8130: 8075: 8064:Median unbiased 7992: 7903: 7836:Order statistic 7798: 7777: 7744: 7718: 7670: 7625: 7568: 7566:Data collection 7547: 7459: 7414: 7388: 7366: 7326: 7278: 7195:Continuous data 7185: 7172: 7154: 7149: 7074:. NIST/SEMATEK. 7070: 7050: 7040: 7021: 7002: 6983: 6964: 6948: 6946:Further reading 6943: 6942: 6891: 6887: 6850: 6846: 6823:10.2307/3801296 6803: 6799: 6760: 6756: 6719: 6715: 6652: 6648: 6601: 6597: 6566: 6562: 6556: 6542: 6538: 6532: 6518: 6514: 6508: 6494: 6490: 6482: 6478: 6469: 6465: 6457: 6453: 6441: 6434: 6385: 6381: 6350: 6346: 6336: 6334: 6323: 6319: 6298: 6294: 6245: 6241: 6228: 6224: 6214: 6212: 6202: 6198: 6185: 6181: 6171: 6169: 6159: 6152: 6097: 6090: 6055: 6051: 6016: 6012: 5989:10.2307/2531894 5969: 5965: 5920: 5916: 5910: 5896: 5889: 5883: 5869: 5865: 5860: 5855: 5756: 5704: 5662: 5653: 5641: 5639:Goodness of fit 5613: 5592: 5570: 5566: 5564: 5561: 5560: 5525: 5521: 5491: 5487: 5457: 5453: 5432: 5428: 5420: 5417: 5416: 5391: 5387: 5385: 5382: 5381: 5358: 5354: 5352: 5349: 5348: 5319: 5315: 5291: 5287: 5257: 5253: 5239: 5236: 5235: 5216: 5212: 5210: 5207: 5206: 5177: 5173: 5143: 5139: 5115: 5111: 5097: 5094: 5093: 5074: 5070: 5068: 5065: 5064: 5035: 5031: 5007: 5003: 4989: 4986: 4985: 4966: 4962: 4960: 4957: 4956: 4921: 4917: 4896: 4892: 4865: 4846: 4842: 4809: 4790: 4786: 4753: 4734: 4730: 4695: 4691: 4690: 4669: 4666: 4665: 4650: 4593:right censoring 4566: 4388: 4384: 4382: 4379: 4378: 4332: 4325: 4321: 4320: 4304: 4300: 4293: 4288: 4263: 4259: 4243: 4238: 4222: 4218: 4211: 4206: 4204: 4201: 4200: 4175: 4171: 4164: 4148: 4144: 4137: 4135: 4120: 4116: 4109: 4099: 4095: 4071: 4067: 4060: 4058: 4048: 4043: 4041: 4038: 4037: 4009: 4005: 3998: 3988: 3984: 3960: 3956: 3949: 3947: 3932: 3928: 3915: 3899: 3895: 3880: 3876: 3869: 3867: 3855: 3851: 3830: 3826: 3812: 3809: 3808: 3789: 3785: 3783: 3780: 3779: 3756: 3752: 3750: 3747: 3746: 3721: 3717: 3709: 3706: 3705: 3688: 3684: 3682: 3679: 3678: 3661: 3657: 3655: 3652: 3651: 3648:Future lifetime 3645: 3580: 3566: 3564: 3517: 3514: 3513: 3488: 3485: 3484: 3459: 3456: 3455: 3430: 3427: 3426: 3401: 3398: 3397: 3372: 3369: 3368: 3334: 3331: 3330: 3305: 3302: 3301: 3276: 3273: 3272: 3243: 3240: 3239: 3200: 3195: 3174: 3171: 3170: 3123: 3105: 3104: 3102: 3074: 3069: 3067: 3064: 3063: 3005: 3002: 3001: 2949: 2946: 2945: 2927: 2924: 2923: 2907: 2904: 2903: 2880: 2877: 2876: 2844: 2841: 2840: 2809: 2806: 2805: 2757: 2752: 2746: 2743: 2742: 2705: 2701: 2687: 2684: 2683: 2664: 2661: 2660: 2629: 2626: 2625: 2609: 2606: 2605: 2589: 2586: 2585: 2569: 2566: 2565: 2533: 2519: 2517: 2480: 2475: 2455: 2452: 2451: 2428: 2425: 2424: 2413:hazard function 2379: 2361: 2360: 2358: 2336: 2322: 2320: 2292: 2257: 2255: 2240: 2219: 2216: 2215: 2194: 2191: 2190: 2174: 2171: 2170: 2148: 2145: 2144: 2128: 2125: 2124: 2108: 2105: 2104: 2088: 2085: 2084: 2068: 2065: 2064: 2060:hazard function 2055: 1980: 1975: 1947: 1942: 1928: 1923: 1898: 1893: 1873: 1856: 1853: 1852: 1790: 1785: 1743: 1740: 1739: 1683: 1678: 1658: 1641: 1638: 1637: 1553: 1550: 1549: 1533: 1525:carbon isotopes 1454: 1416:random variable 1361: 1358: 1357: 1344: 1338: 1329: 1318: 1312: 1309: 1294: 1278: 1267: 1258: 1241: 1237: 1160: 1156: 1153: 1140: 1122: 1112: 1062: 1015: 996: 990: 976: 927: 886: 879: 817: 807: 795: 791: 427: 401: 362:Hazard function 337: 321:Recurring event 244:is a branch of 235: 224: 223: 222: 217: 206: 200: 197: 154: 152: 142: 130: 115: 104: 98: 95: 88: 69: 65: 28: 24: 17: 12: 11: 5: 9512: 9502: 9501: 9496: 9491: 9486: 9481: 9466: 9465: 9442: 9441: 9439: 9438: 9426: 9414: 9400: 9387: 9384: 9383: 9380: 9379: 9376: 9375: 9373: 9372: 9367: 9362: 9357: 9352: 9346: 9344: 9338: 9337: 9335: 9334: 9329: 9324: 9319: 9314: 9309: 9304: 9299: 9294: 9289: 9283: 9281: 9275: 9274: 9272: 9271: 9266: 9261: 9252: 9247: 9242: 9236: 9234: 9228: 9227: 9225: 9224: 9219: 9214: 9205: 9203:Bioinformatics 9199: 9197: 9187: 9186: 9174: 9173: 9170: 9169: 9166: 9165: 9162: 9161: 9159: 9158: 9152: 9150: 9146: 9145: 9143: 9142: 9136: 9134: 9128: 9127: 9125: 9124: 9119: 9114: 9109: 9103: 9101: 9092: 9086: 9085: 9082: 9081: 9079: 9078: 9073: 9068: 9063: 9058: 9052: 9050: 9044: 9043: 9041: 9040: 9035: 9030: 9022: 9017: 9012: 9011: 9010: 9008:partial (PACF) 8999: 8997: 8991: 8990: 8988: 8987: 8982: 8977: 8969: 8964: 8958: 8956: 8955:Specific tests 8952: 8951: 8949: 8948: 8943: 8938: 8933: 8928: 8923: 8918: 8913: 8907: 8905: 8898: 8892: 8891: 8889: 8888: 8887: 8886: 8885: 8884: 8869: 8868: 8867: 8857: 8855:Classification 8852: 8847: 8842: 8837: 8832: 8827: 8821: 8819: 8813: 8812: 8810: 8809: 8804: 8802:McNemar's test 8799: 8794: 8789: 8784: 8778: 8776: 8766: 8765: 8741: 8740: 8737: 8736: 8733: 8732: 8730: 8729: 8724: 8719: 8714: 8708: 8706: 8700: 8699: 8697: 8696: 8680: 8674: 8672: 8666: 8665: 8663: 8662: 8657: 8652: 8647: 8642: 8640:Semiparametric 8637: 8632: 8626: 8624: 8620: 8619: 8617: 8616: 8611: 8606: 8601: 8595: 8593: 8587: 8586: 8584: 8583: 8578: 8573: 8568: 8563: 8557: 8555: 8549: 8548: 8546: 8545: 8540: 8535: 8530: 8524: 8522: 8512: 8511: 8508: 8507: 8502: 8496: 8488: 8487: 8484: 8483: 8480: 8479: 8477: 8476: 8475: 8474: 8464: 8459: 8454: 8453: 8452: 8447: 8436: 8434: 8428: 8427: 8424: 8423: 8421: 8420: 8415: 8414: 8413: 8405: 8397: 8381: 8378:(Mann–Whitney) 8373: 8372: 8371: 8358: 8357: 8356: 8345: 8343: 8337: 8336: 8334: 8333: 8332: 8331: 8326: 8321: 8311: 8306: 8303:(Shapiro–Wilk) 8298: 8293: 8288: 8283: 8278: 8270: 8264: 8262: 8256: 8255: 8253: 8252: 8244: 8235: 8223: 8217: 8215:Specific tests 8211: 8210: 8207: 8206: 8204: 8203: 8198: 8193: 8187: 8185: 8179: 8178: 8176: 8175: 8170: 8169: 8168: 8158: 8157: 8156: 8146: 8140: 8138: 8132: 8131: 8129: 8128: 8127: 8126: 8121: 8111: 8106: 8101: 8096: 8091: 8085: 8083: 8077: 8076: 8074: 8073: 8068: 8067: 8066: 8061: 8060: 8059: 8054: 8039: 8038: 8037: 8032: 8027: 8022: 8011: 8009: 8000: 7994: 7993: 7991: 7990: 7985: 7980: 7979: 7978: 7968: 7963: 7962: 7961: 7951: 7950: 7949: 7944: 7939: 7929: 7924: 7919: 7918: 7917: 7912: 7907: 7891: 7890: 7889: 7884: 7879: 7869: 7868: 7867: 7862: 7852: 7851: 7850: 7840: 7839: 7838: 7828: 7823: 7818: 7812: 7810: 7800: 7799: 7787: 7786: 7783: 7782: 7779: 7778: 7776: 7775: 7770: 7765: 7760: 7754: 7752: 7746: 7745: 7743: 7742: 7737: 7732: 7726: 7724: 7720: 7719: 7717: 7716: 7711: 7706: 7701: 7696: 7691: 7686: 7680: 7678: 7672: 7671: 7669: 7668: 7666:Standard error 7663: 7658: 7653: 7652: 7651: 7646: 7635: 7633: 7627: 7626: 7624: 7623: 7618: 7613: 7608: 7603: 7598: 7596:Optimal design 7593: 7588: 7582: 7580: 7570: 7569: 7557: 7556: 7553: 7552: 7549: 7548: 7546: 7545: 7540: 7535: 7530: 7525: 7520: 7515: 7510: 7505: 7500: 7495: 7490: 7485: 7480: 7475: 7469: 7467: 7461: 7460: 7458: 7457: 7452: 7451: 7450: 7445: 7435: 7430: 7424: 7422: 7416: 7415: 7413: 7412: 7407: 7402: 7396: 7394: 7393:Summary tables 7390: 7389: 7387: 7386: 7380: 7378: 7372: 7371: 7368: 7367: 7365: 7364: 7363: 7362: 7357: 7352: 7342: 7336: 7334: 7328: 7327: 7325: 7324: 7319: 7314: 7309: 7304: 7299: 7294: 7288: 7286: 7280: 7279: 7277: 7276: 7271: 7266: 7265: 7264: 7259: 7254: 7249: 7244: 7239: 7234: 7229: 7227:Contraharmonic 7224: 7219: 7208: 7206: 7197: 7187: 7186: 7174: 7173: 7171: 7170: 7165: 7159: 7156: 7155: 7148: 7147: 7140: 7133: 7125: 7119: 7118: 7113: 7108: 7103: 7090: 7076: 7068: 7062:on 2006-09-07. 7049: 7048:External links 7046: 7045: 7044: 7038: 7025: 7019: 7006: 7000: 6987: 6981: 6968: 6962: 6947: 6944: 6941: 6940: 6885: 6844: 6797: 6754: 6713: 6646: 6611:(5): 923–947. 6595: 6576:(2): 277–289. 6560: 6555:978-1584884088 6554: 6536: 6531:978-1439831649 6530: 6512: 6507:978-1441966452 6506: 6488: 6476: 6463: 6451: 6432: 6401:(4): 145–148. 6379: 6360:(4): 233–257. 6344: 6317: 6292: 6239: 6222: 6196: 6179: 6150: 6088: 6049: 6010: 5963: 5934:(3): 619–628. 5914: 5909:978-0387790534 5908: 5887: 5881: 5862: 5861: 5859: 5856: 5854: 5853: 5848: 5843: 5838: 5833: 5828: 5823: 5818: 5813: 5811:Mortality rate 5808: 5803: 5798: 5793: 5788: 5783: 5778: 5773: 5768: 5763: 5757: 5755: 5752: 5751: 5750: 5748:stock exchange 5740: 5738:Roman emperors 5734: 5728: 5724:Predictors of 5722: 5719: 5710: 5703: 5700: 5699: 5698: 5693: 5688: 5683: 5678: 5673: 5668: 5661: 5658: 5652: 5649: 5640: 5637: 5612: 5609: 5604:non-parametric 5591: 5588: 5573: 5569: 5548: 5545: 5542: 5539: 5534: 5531: 5528: 5524: 5520: 5517: 5514: 5511: 5508: 5505: 5500: 5497: 5494: 5490: 5486: 5483: 5480: 5477: 5474: 5471: 5466: 5463: 5460: 5456: 5452: 5449: 5446: 5441: 5438: 5435: 5431: 5427: 5424: 5400: 5397: 5394: 5390: 5367: 5364: 5361: 5357: 5336: 5333: 5330: 5327: 5322: 5318: 5314: 5311: 5308: 5305: 5302: 5299: 5294: 5290: 5286: 5283: 5280: 5277: 5274: 5271: 5268: 5265: 5260: 5256: 5252: 5249: 5246: 5243: 5219: 5215: 5194: 5191: 5188: 5185: 5180: 5176: 5172: 5169: 5166: 5163: 5160: 5157: 5154: 5151: 5146: 5142: 5138: 5135: 5132: 5129: 5126: 5123: 5118: 5114: 5110: 5107: 5104: 5101: 5077: 5073: 5052: 5049: 5046: 5043: 5038: 5034: 5030: 5027: 5024: 5021: 5018: 5015: 5010: 5006: 5002: 4999: 4996: 4993: 4969: 4965: 4944: 4941: 4938: 4935: 4930: 4927: 4924: 4920: 4916: 4913: 4910: 4905: 4902: 4899: 4895: 4891: 4888: 4883: 4880: 4877: 4874: 4871: 4868: 4864: 4860: 4857: 4854: 4849: 4845: 4841: 4838: 4835: 4832: 4827: 4824: 4821: 4818: 4815: 4812: 4808: 4804: 4801: 4798: 4793: 4789: 4785: 4782: 4779: 4776: 4771: 4768: 4765: 4762: 4759: 4756: 4752: 4748: 4745: 4742: 4737: 4733: 4729: 4726: 4723: 4720: 4715: 4712: 4709: 4706: 4703: 4698: 4694: 4689: 4685: 4682: 4679: 4676: 4673: 4649: 4646: 4634:life insurance 4630:actuarial work 4565: 4562: 4399: 4396: 4391: 4387: 4359: 4356: 4353: 4349: 4346: 4343: 4340: 4335: 4328: 4324: 4319: 4312: 4307: 4303: 4299: 4296: 4292: 4287: 4284: 4281: 4277: 4274: 4271: 4266: 4262: 4258: 4255: 4251: 4246: 4241: 4237: 4230: 4225: 4221: 4217: 4214: 4210: 4183: 4178: 4174: 4170: 4167: 4162: 4159: 4156: 4151: 4147: 4143: 4140: 4134: 4128: 4123: 4119: 4115: 4112: 4107: 4102: 4098: 4094: 4091: 4088: 4085: 4082: 4079: 4074: 4070: 4066: 4063: 4054: 4051: 4047: 4023: 4017: 4012: 4008: 4004: 4001: 3996: 3991: 3987: 3983: 3980: 3977: 3974: 3971: 3968: 3963: 3959: 3955: 3952: 3946: 3940: 3935: 3931: 3927: 3924: 3921: 3918: 3913: 3910: 3907: 3902: 3898: 3894: 3891: 3888: 3883: 3879: 3875: 3872: 3866: 3863: 3858: 3854: 3850: 3847: 3844: 3841: 3838: 3833: 3829: 3825: 3822: 3819: 3816: 3792: 3788: 3767: 3764: 3759: 3755: 3743:expected value 3724: 3720: 3716: 3713: 3704:. Thus, it is 3691: 3687: 3664: 3660: 3644: 3641: 3629: 3626: 3623: 3619: 3616: 3613: 3610: 3607: 3604: 3601: 3598: 3592: 3589: 3586: 3583: 3578: 3575: 3572: 3569: 3563: 3560: 3557: 3554: 3551: 3548: 3545: 3542: 3539: 3536: 3533: 3530: 3527: 3524: 3521: 3501: 3498: 3495: 3492: 3472: 3469: 3466: 3463: 3443: 3440: 3437: 3434: 3425:, the density 3414: 3411: 3408: 3405: 3385: 3382: 3379: 3376: 3353: 3350: 3347: 3344: 3341: 3338: 3318: 3315: 3312: 3309: 3289: 3286: 3283: 3280: 3256: 3253: 3250: 3247: 3224: 3221: 3217: 3214: 3211: 3208: 3203: 3198: 3194: 3190: 3187: 3184: 3181: 3178: 3156: 3153: 3150: 3147: 3144: 3141: 3135: 3132: 3129: 3126: 3121: 3118: 3115: 3111: 3108: 3101: 3098: 3095: 3092: 3089: 3086: 3080: 3077: 3073: 3049: 3046: 3043: 3040: 3037: 3034: 3031: 3028: 3025: 3022: 3019: 3016: 3013: 3010: 2987: 2984: 2981: 2978: 2975: 2972: 2969: 2966: 2963: 2960: 2957: 2954: 2931: 2911: 2884: 2860: 2857: 2854: 2851: 2848: 2828: 2825: 2822: 2819: 2816: 2813: 2799: 2798: 2786: 2783: 2780: 2777: 2774: 2771: 2768: 2765: 2760: 2755: 2751: 2740: 2727: 2723: 2720: 2717: 2714: 2711: 2708: 2704: 2700: 2697: 2694: 2691: 2668: 2645: 2642: 2639: 2636: 2633: 2613: 2593: 2573: 2545: 2542: 2539: 2536: 2531: 2528: 2525: 2522: 2516: 2513: 2510: 2507: 2504: 2501: 2498: 2495: 2492: 2486: 2483: 2479: 2474: 2471: 2468: 2465: 2462: 2459: 2432: 2397: 2391: 2388: 2385: 2382: 2377: 2374: 2371: 2367: 2364: 2357: 2354: 2348: 2345: 2342: 2339: 2334: 2331: 2328: 2325: 2319: 2313: 2310: 2307: 2304: 2301: 2298: 2295: 2290: 2287: 2284: 2281: 2278: 2275: 2272: 2269: 2266: 2263: 2260: 2252: 2249: 2246: 2243: 2239: 2235: 2232: 2229: 2226: 2223: 2201: 2198: 2178: 2158: 2155: 2152: 2132: 2112: 2092: 2072: 2054: 2051: 2034: 2031: 2028: 2025: 2022: 2019: 2016: 2013: 2010: 2007: 2004: 2001: 1998: 1995: 1992: 1986: 1983: 1979: 1974: 1971: 1968: 1964: 1961: 1958: 1955: 1950: 1945: 1941: 1934: 1931: 1927: 1922: 1919: 1916: 1913: 1910: 1904: 1901: 1897: 1892: 1889: 1886: 1883: 1879: 1876: 1872: 1869: 1866: 1863: 1860: 1838: 1835: 1832: 1829: 1826: 1823: 1820: 1817: 1814: 1811: 1807: 1804: 1801: 1798: 1793: 1788: 1784: 1780: 1777: 1774: 1771: 1768: 1765: 1762: 1759: 1756: 1753: 1750: 1747: 1707: 1704: 1701: 1698: 1695: 1689: 1686: 1682: 1677: 1674: 1671: 1668: 1664: 1661: 1657: 1654: 1651: 1648: 1645: 1628:differentiable 1611: 1608: 1605: 1602: 1599: 1596: 1593: 1590: 1587: 1584: 1581: 1578: 1575: 1572: 1569: 1566: 1563: 1560: 1557: 1532: 1529: 1410:is some time, 1395: 1392: 1389: 1386: 1383: 1380: 1377: 1374: 1371: 1368: 1365: 1340:Main article: 1337: 1334: 1331: 1330: 1281: 1279: 1272: 1266: 1263: 1257: 1254: 1236: 1233: 1217: 1216: 1210: 1204: 1198: 1192: 1186: 1180: 1174: 1152: 1149: 1139: 1136: 1135: 1134: 1130: 1121: 1118: 1061: 1058: 1053: 1052: 1049: 1046: 1036: 1035: 1032: 1029: 1026: 1022: 1019: 989: 986: 975: 972: 926: 923: 922: 921: 918: 914: 911: 908: 905: 878: 875: 874: 873: 869: 865: 862: 855: 816: 813: 803: 802: 799: 788: 782: 781: 778: 775: 772: 768: 767: 764: 761: 758: 754: 753: 752:Nonmaintained 750: 747: 744: 740: 739: 736: 733: 730: 726: 725: 724:Nonmaintained 722: 719: 716: 712: 711: 708: 705: 702: 698: 697: 696:Nonmaintained 694: 691: 688: 684: 683: 680: 677: 674: 670: 669: 668:Nonmaintained 666: 663: 660: 656: 655: 652: 649: 646: 642: 641: 640:Nonmaintained 638: 635: 632: 628: 627: 626:Nonmaintained 624: 621: 618: 614: 613: 610: 607: 604: 600: 599: 596: 593: 590: 586: 585: 584:Nonmaintained 582: 579: 576: 572: 571: 568: 565: 562: 558: 557: 554: 551: 548: 544: 543: 542:Nonmaintained 540: 537: 534: 530: 529: 526: 523: 520: 516: 515: 514:Nonmaintained 512: 509: 506: 502: 501: 500:Nonmaintained 498: 495: 492: 488: 487: 486:Nonmaintained 484: 481: 478: 474: 473: 472:Nonmaintained 470: 467: 464: 460: 459: 456: 453: 447: 426: 423: 422: 421: 415: 411: 408: 400: 397: 396: 395: 394: 393: 390: 389:Survival trees 387: 384: 376: 375: 374: 366: 365: 364: 359: 354: 349: 336: 333: 325:repeated event 237: 236: 219: 218: 133: 131: 124: 117: 116: 99:September 2019 72: 70: 63: 58: 32: 31: 29: 22: 15: 9: 6: 4: 3: 2: 9511: 9500: 9497: 9495: 9492: 9490: 9487: 9485: 9482: 9480: 9477: 9476: 9474: 9464: 9459: 9454: 9453: 9450: 9437: 9436: 9427: 9425: 9424: 9415: 9413: 9412: 9407: 9401: 9399: 9398: 9389: 9388: 9385: 9371: 9368: 9366: 9365:Geostatistics 9363: 9361: 9358: 9356: 9353: 9351: 9348: 9347: 9345: 9343: 9339: 9333: 9332:Psychometrics 9330: 9328: 9325: 9323: 9320: 9318: 9315: 9313: 9310: 9308: 9305: 9303: 9300: 9298: 9295: 9293: 9290: 9288: 9285: 9284: 9282: 9280: 9276: 9270: 9267: 9265: 9262: 9260: 9256: 9253: 9251: 9248: 9246: 9243: 9241: 9238: 9237: 9235: 9233: 9229: 9223: 9220: 9218: 9215: 9213: 9209: 9206: 9204: 9201: 9200: 9198: 9196: 9195:Biostatistics 9192: 9188: 9184: 9179: 9175: 9157: 9156:Log-rank test 9154: 9153: 9151: 9147: 9141: 9138: 9137: 9135: 9133: 9129: 9123: 9120: 9118: 9115: 9113: 9110: 9108: 9105: 9104: 9102: 9100: 9096: 9093: 9091: 9087: 9077: 9074: 9072: 9069: 9067: 9064: 9062: 9059: 9057: 9054: 9053: 9051: 9049: 9045: 9039: 9036: 9034: 9031: 9029: 9027:(Box–Jenkins) 9023: 9021: 9018: 9016: 9013: 9009: 9006: 9005: 9004: 9001: 9000: 8998: 8996: 8992: 8986: 8983: 8981: 8980:Durbin–Watson 8978: 8976: 8970: 8968: 8965: 8963: 8962:Dickey–Fuller 8960: 8959: 8957: 8953: 8947: 8944: 8942: 8939: 8937: 8936:Cointegration 8934: 8932: 8929: 8927: 8924: 8922: 8919: 8917: 8914: 8912: 8911:Decomposition 8909: 8908: 8906: 8902: 8899: 8897: 8893: 8883: 8880: 8879: 8878: 8875: 8874: 8873: 8870: 8866: 8863: 8862: 8861: 8858: 8856: 8853: 8851: 8848: 8846: 8843: 8841: 8838: 8836: 8833: 8831: 8828: 8826: 8823: 8822: 8820: 8818: 8814: 8808: 8805: 8803: 8800: 8798: 8795: 8793: 8790: 8788: 8785: 8783: 8782:Cohen's kappa 8780: 8779: 8777: 8775: 8771: 8767: 8763: 8759: 8755: 8751: 8746: 8742: 8728: 8725: 8723: 8720: 8718: 8715: 8713: 8710: 8709: 8707: 8705: 8701: 8695: 8691: 8687: 8681: 8679: 8676: 8675: 8673: 8671: 8667: 8661: 8658: 8656: 8653: 8651: 8648: 8646: 8643: 8641: 8638: 8636: 8635:Nonparametric 8633: 8631: 8628: 8627: 8625: 8621: 8615: 8612: 8610: 8607: 8605: 8602: 8600: 8597: 8596: 8594: 8592: 8588: 8582: 8579: 8577: 8574: 8572: 8569: 8567: 8564: 8562: 8559: 8558: 8556: 8554: 8550: 8544: 8541: 8539: 8536: 8534: 8531: 8529: 8526: 8525: 8523: 8521: 8517: 8513: 8506: 8503: 8501: 8498: 8497: 8493: 8489: 8473: 8470: 8469: 8468: 8465: 8463: 8460: 8458: 8455: 8451: 8448: 8446: 8443: 8442: 8441: 8438: 8437: 8435: 8433: 8429: 8419: 8416: 8412: 8406: 8404: 8398: 8396: 8390: 8389: 8388: 8385: 8384:Nonparametric 8382: 8380: 8374: 8370: 8367: 8366: 8365: 8359: 8355: 8354:Sample median 8352: 8351: 8350: 8347: 8346: 8344: 8342: 8338: 8330: 8327: 8325: 8322: 8320: 8317: 8316: 8315: 8312: 8310: 8307: 8305: 8299: 8297: 8294: 8292: 8289: 8287: 8284: 8282: 8279: 8277: 8275: 8271: 8269: 8266: 8265: 8263: 8261: 8257: 8251: 8249: 8245: 8243: 8241: 8236: 8234: 8229: 8225: 8224: 8221: 8218: 8216: 8212: 8202: 8199: 8197: 8194: 8192: 8189: 8188: 8186: 8184: 8180: 8174: 8171: 8167: 8164: 8163: 8162: 8159: 8155: 8152: 8151: 8150: 8147: 8145: 8142: 8141: 8139: 8137: 8133: 8125: 8122: 8120: 8117: 8116: 8115: 8112: 8110: 8107: 8105: 8102: 8100: 8097: 8095: 8092: 8090: 8087: 8086: 8084: 8082: 8078: 8072: 8069: 8065: 8062: 8058: 8055: 8053: 8050: 8049: 8048: 8045: 8044: 8043: 8040: 8036: 8033: 8031: 8028: 8026: 8023: 8021: 8018: 8017: 8016: 8013: 8012: 8010: 8008: 8004: 8001: 7999: 7995: 7989: 7986: 7984: 7981: 7977: 7974: 7973: 7972: 7969: 7967: 7964: 7960: 7959:loss function 7957: 7956: 7955: 7952: 7948: 7945: 7943: 7940: 7938: 7935: 7934: 7933: 7930: 7928: 7925: 7923: 7920: 7916: 7913: 7911: 7908: 7906: 7900: 7897: 7896: 7895: 7892: 7888: 7885: 7883: 7880: 7878: 7875: 7874: 7873: 7870: 7866: 7863: 7861: 7858: 7857: 7856: 7853: 7849: 7846: 7845: 7844: 7841: 7837: 7834: 7833: 7832: 7829: 7827: 7824: 7822: 7819: 7817: 7814: 7813: 7811: 7809: 7805: 7801: 7797: 7792: 7788: 7774: 7771: 7769: 7766: 7764: 7761: 7759: 7756: 7755: 7753: 7751: 7747: 7741: 7738: 7736: 7733: 7731: 7728: 7727: 7725: 7721: 7715: 7712: 7710: 7707: 7705: 7702: 7700: 7697: 7695: 7692: 7690: 7687: 7685: 7682: 7681: 7679: 7677: 7673: 7667: 7664: 7662: 7661:Questionnaire 7659: 7657: 7654: 7650: 7647: 7645: 7642: 7641: 7640: 7637: 7636: 7634: 7632: 7628: 7622: 7619: 7617: 7614: 7612: 7609: 7607: 7604: 7602: 7599: 7597: 7594: 7592: 7589: 7587: 7584: 7583: 7581: 7579: 7575: 7571: 7567: 7562: 7558: 7544: 7541: 7539: 7536: 7534: 7531: 7529: 7526: 7524: 7521: 7519: 7516: 7514: 7511: 7509: 7506: 7504: 7501: 7499: 7496: 7494: 7491: 7489: 7488:Control chart 7486: 7484: 7481: 7479: 7476: 7474: 7471: 7470: 7468: 7466: 7462: 7456: 7453: 7449: 7446: 7444: 7441: 7440: 7439: 7436: 7434: 7431: 7429: 7426: 7425: 7423: 7421: 7417: 7411: 7408: 7406: 7403: 7401: 7398: 7397: 7395: 7391: 7385: 7382: 7381: 7379: 7377: 7373: 7361: 7358: 7356: 7353: 7351: 7348: 7347: 7346: 7343: 7341: 7338: 7337: 7335: 7333: 7329: 7323: 7320: 7318: 7315: 7313: 7310: 7308: 7305: 7303: 7300: 7298: 7295: 7293: 7290: 7289: 7287: 7285: 7281: 7275: 7272: 7270: 7267: 7263: 7260: 7258: 7255: 7253: 7250: 7248: 7245: 7243: 7240: 7238: 7235: 7233: 7230: 7228: 7225: 7223: 7220: 7218: 7215: 7214: 7213: 7210: 7209: 7207: 7205: 7201: 7198: 7196: 7192: 7188: 7184: 7179: 7175: 7169: 7166: 7164: 7161: 7160: 7157: 7153: 7146: 7141: 7139: 7134: 7132: 7127: 7126: 7123: 7117: 7114: 7112: 7109: 7107: 7104: 7102: 7101:Textbook Page 7098: 7094: 7091: 7088: 7084: 7080: 7077: 7073: 7069: 7067: 7061: 7057: 7052: 7051: 7041: 7035: 7031: 7026: 7022: 7016: 7012: 7007: 7003: 6997: 6993: 6988: 6984: 6978: 6974: 6969: 6965: 6959: 6955: 6950: 6949: 6936: 6932: 6928: 6924: 6920: 6916: 6912: 6908: 6905:(1): 126456. 6904: 6900: 6896: 6889: 6881: 6877: 6872: 6867: 6863: 6859: 6855: 6848: 6840: 6836: 6832: 6828: 6824: 6820: 6816: 6812: 6808: 6801: 6793: 6789: 6785: 6781: 6777: 6773: 6769: 6765: 6758: 6750: 6746: 6741: 6736: 6732: 6728: 6724: 6717: 6709: 6705: 6700: 6695: 6691: 6687: 6682: 6677: 6673: 6669: 6665: 6661: 6657: 6650: 6642: 6638: 6634: 6630: 6626: 6622: 6618: 6614: 6610: 6606: 6599: 6591: 6587: 6583: 6579: 6575: 6571: 6564: 6557: 6551: 6547: 6540: 6533: 6527: 6523: 6516: 6509: 6503: 6499: 6492: 6486: 6480: 6474: 6467: 6461: 6455: 6449: 6445: 6439: 6437: 6428: 6424: 6419: 6414: 6409: 6404: 6400: 6396: 6395: 6390: 6383: 6375: 6371: 6367: 6363: 6359: 6355: 6348: 6332: 6328: 6321: 6312: 6307: 6303: 6296: 6288: 6284: 6280: 6276: 6272: 6268: 6263: 6258: 6254: 6250: 6243: 6235: 6234: 6226: 6211: 6207: 6200: 6192: 6191: 6183: 6168: 6164: 6157: 6155: 6146: 6142: 6138: 6134: 6129: 6124: 6119: 6114: 6110: 6106: 6102: 6095: 6093: 6084: 6080: 6076: 6072: 6068: 6064: 6060: 6053: 6045: 6041: 6037: 6033: 6029: 6025: 6021: 6014: 6006: 6002: 5998: 5994: 5990: 5986: 5982: 5978: 5974: 5967: 5958: 5953: 5949: 5945: 5941: 5937: 5933: 5929: 5925: 5918: 5911: 5905: 5901: 5894: 5892: 5884: 5882:0-471-25218-2 5878: 5874: 5867: 5863: 5852: 5849: 5847: 5846:Survival rate 5844: 5842: 5839: 5837: 5834: 5832: 5829: 5827: 5824: 5822: 5819: 5817: 5814: 5812: 5809: 5807: 5804: 5802: 5799: 5797: 5794: 5792: 5789: 5787: 5784: 5782: 5779: 5777: 5774: 5772: 5769: 5767: 5764: 5762: 5759: 5758: 5749: 5745: 5741: 5739: 5735: 5733: 5729: 5727: 5723: 5720: 5718: 5714: 5711: 5709: 5706: 5705: 5697: 5694: 5692: 5689: 5687: 5684: 5682: 5679: 5677: 5674: 5672: 5669: 5667: 5664: 5663: 5657: 5648: 5646: 5645:scoring rules 5636: 5634: 5625: 5621: 5619: 5608: 5605: 5601: 5597: 5587: 5571: 5567: 5546: 5540: 5537: 5532: 5529: 5526: 5522: 5515: 5512: 5506: 5503: 5498: 5495: 5492: 5488: 5481: 5478: 5472: 5469: 5464: 5461: 5458: 5454: 5450: 5447: 5444: 5439: 5436: 5433: 5429: 5414: 5398: 5395: 5392: 5388: 5365: 5362: 5359: 5355: 5334: 5328: 5325: 5320: 5316: 5309: 5306: 5300: 5297: 5292: 5288: 5281: 5278: 5275: 5272: 5266: 5263: 5258: 5254: 5250: 5247: 5233: 5217: 5213: 5192: 5186: 5183: 5178: 5174: 5167: 5164: 5161: 5158: 5152: 5149: 5144: 5140: 5133: 5130: 5124: 5121: 5116: 5112: 5108: 5105: 5091: 5075: 5071: 5050: 5044: 5041: 5036: 5032: 5025: 5022: 5016: 5013: 5008: 5004: 5000: 4997: 4983: 4967: 4963: 4942: 4936: 4933: 4928: 4925: 4922: 4918: 4914: 4911: 4908: 4903: 4900: 4897: 4893: 4881: 4878: 4875: 4872: 4869: 4866: 4862: 4855: 4852: 4847: 4843: 4839: 4836: 4825: 4822: 4819: 4816: 4813: 4810: 4806: 4799: 4796: 4791: 4787: 4783: 4780: 4769: 4766: 4763: 4760: 4757: 4754: 4750: 4743: 4740: 4735: 4731: 4727: 4724: 4713: 4710: 4707: 4704: 4701: 4696: 4692: 4687: 4683: 4677: 4671: 4663: 4660: 4656: 4645: 4641: 4639: 4635: 4631: 4626: 4625:delayed entry 4622: 4621: 4615: 4611: 4609: 4605: 4604:left-censored 4600: 4598: 4594: 4590: 4586: 4582: 4578: 4573: 4570: 4561: 4559: 4555: 4551: 4547: 4545: 4540: 4536: 4532: 4528: 4524: 4520: 4515: 4513: 4509: 4505: 4501: 4497: 4493: 4489: 4485: 4481: 4477: 4473: 4469: 4465: 4461: 4457: 4453: 4449: 4445: 4441: 4437: 4433: 4429: 4424: 4422: 4418: 4417: 4411: 4397: 4394: 4389: 4385: 4375: 4373: 4357: 4354: 4351: 4344: 4338: 4326: 4322: 4317: 4305: 4301: 4294: 4290: 4285: 4282: 4279: 4272: 4269: 4264: 4260: 4253: 4249: 4239: 4235: 4223: 4219: 4212: 4208: 4198: 4176: 4172: 4165: 4157: 4154: 4149: 4145: 4138: 4132: 4121: 4117: 4110: 4100: 4096: 4089: 4086: 4080: 4077: 4072: 4068: 4061: 4052: 4049: 4045: 4035: 4021: 4010: 4006: 3999: 3989: 3985: 3978: 3975: 3969: 3966: 3961: 3957: 3950: 3944: 3933: 3929: 3925: 3922: 3916: 3908: 3905: 3900: 3896: 3892: 3889: 3886: 3881: 3877: 3870: 3864: 3856: 3852: 3848: 3845: 3842: 3839: 3836: 3831: 3827: 3823: 3820: 3814: 3806: 3790: 3786: 3765: 3762: 3757: 3753: 3744: 3740: 3722: 3718: 3714: 3711: 3689: 3685: 3662: 3658: 3649: 3640: 3627: 3624: 3621: 3617: 3611: 3605: 3602: 3599: 3596: 3587: 3581: 3573: 3567: 3561: 3552: 3543: 3537: 3534: 3531: 3525: 3519: 3496: 3490: 3467: 3461: 3438: 3432: 3409: 3380: 3374: 3365: 3348: 3345: 3339: 3336: 3313: 3307: 3284: 3278: 3270: 3251: 3236: 3222: 3219: 3212: 3206: 3201: 3196: 3192: 3188: 3182: 3168: 3154: 3148: 3142: 3139: 3130: 3124: 3116: 3109: 3106: 3099: 3096: 3090: 3078: 3075: 3071: 3061: 3041: 3032: 3026: 3023: 3020: 3014: 3008: 2999: 2982: 2976: 2973: 2970: 2967: 2964: 2958: 2943: 2929: 2901: 2896: 2882: 2874: 2873:bathtub curve 2852: 2849: 2826: 2823: 2817: 2811: 2802: 2781: 2778: 2775: 2769: 2763: 2753: 2749: 2741: 2725: 2721: 2718: 2712: 2706: 2702: 2698: 2695: 2692: 2682: 2681: 2680: 2666: 2659:Any function 2657: 2640: 2637: 2634: 2611: 2591: 2571: 2562: 2559: 2540: 2534: 2526: 2520: 2514: 2505: 2499: 2493: 2490: 2484: 2481: 2477: 2472: 2469: 2463: 2457: 2448: 2446: 2430: 2422: 2418: 2414: 2410: 2395: 2386: 2380: 2372: 2365: 2362: 2355: 2352: 2343: 2337: 2329: 2323: 2317: 2308: 2302: 2299: 2296: 2293: 2285: 2282: 2279: 2276: 2273: 2270: 2267: 2264: 2250: 2244: 2241: 2233: 2227: 2221: 2213: 2199: 2196: 2176: 2156: 2153: 2150: 2130: 2110: 2090: 2070: 2062: 2061: 2050: 2048: 2032: 2026: 2020: 2017: 2014: 2005: 1999: 1996: 1993: 1984: 1981: 1977: 1972: 1969: 1966: 1959: 1953: 1943: 1939: 1932: 1929: 1925: 1920: 1914: 1908: 1902: 1899: 1895: 1890: 1884: 1877: 1874: 1870: 1864: 1858: 1850: 1836: 1830: 1824: 1821: 1818: 1815: 1812: 1809: 1802: 1796: 1786: 1782: 1778: 1772: 1769: 1766: 1757: 1751: 1745: 1737: 1736: 1732: 1727: 1725: 1724:event density 1721: 1718:The function 1705: 1699: 1693: 1687: 1684: 1680: 1675: 1669: 1662: 1659: 1655: 1649: 1643: 1635: 1633: 1629: 1625: 1609: 1603: 1597: 1594: 1591: 1588: 1582: 1579: 1576: 1567: 1561: 1555: 1547: 1545: 1541: 1536: 1528: 1526: 1522: 1518: 1514: 1509: 1507: 1503: 1499: 1495: 1491: 1487: 1483: 1479: 1475: 1471: 1467: 1463: 1458: 1452: 1447: 1445: 1441: 1437: 1433: 1429: 1425: 1421: 1417: 1413: 1409: 1390: 1387: 1384: 1375: 1369: 1363: 1355: 1353: 1349: 1343: 1327: 1324: 1316: 1306: 1302: 1298: 1292: 1291: 1287: 1282:This section 1280: 1276: 1271: 1270: 1262: 1253: 1251: 1245: 1232: 1224: 1220: 1214: 1211: 1208: 1205: 1202: 1199: 1196: 1193: 1190: 1187: 1184: 1181: 1178: 1175: 1172: 1169: 1168: 1167: 1164: 1148: 1144: 1131: 1127: 1126: 1125: 1117: 1109: 1105: 1097: 1093: 1091: 1087: 1083: 1079: 1070: 1066: 1057: 1050: 1047: 1044: 1043: 1042: 1039: 1033: 1030: 1027: 1023: 1020: 1013: 1012: 1011: 1004: 1000: 993: 985: 982: 971: 969: 965: 959: 957: 953: 949: 939: 935: 934:in the data. 932: 931:log-rank test 919: 915: 912: 909: 906: 903: 902: 901: 894: 890: 884: 870: 866: 863: 860: 856: 853: 849: 848: 847: 845: 841: 837: 833: 829: 825: 822: 812: 800: 789: 786: 785: 779: 776: 773: 770: 769: 765: 762: 759: 756: 755: 751: 748: 745: 742: 741: 737: 734: 731: 728: 727: 723: 720: 717: 714: 713: 709: 706: 703: 700: 699: 695: 692: 689: 686: 685: 681: 678: 675: 672: 671: 667: 664: 661: 658: 657: 653: 650: 647: 644: 643: 639: 636: 633: 630: 629: 625: 622: 619: 616: 615: 611: 608: 605: 602: 601: 597: 594: 591: 588: 587: 583: 580: 577: 574: 573: 569: 566: 563: 560: 559: 555: 552: 549: 546: 545: 541: 538: 535: 532: 531: 527: 524: 521: 518: 517: 513: 510: 507: 504: 503: 499: 496: 493: 490: 489: 485: 482: 479: 476: 475: 471: 468: 465: 462: 461: 457: 454: 452: 448: 445: 444: 438: 435: 432: 419: 416: 412: 409: 406: 405: 404: 391: 388: 385: 383: 380: 379: 377: 373: 372:Log-rank test 370: 369: 367: 363: 360: 358: 355: 353: 350: 348: 345: 344: 342: 341: 340: 332: 330: 326: 322: 316: 314: 310: 306: 302: 298: 293: 291: 287: 283: 279: 275: 271: 267: 263: 259: 255: 251: 247: 243: 233: 230: 215: 212: 204: 193: 190: 186: 183: 179: 176: 172: 169: 165: 162: – 161: 157: 156:Find sources: 150: 146: 140: 139: 134:This article 132: 128: 123: 122: 113: 110: 102: 92: 87: 83: 79: 78: 71: 62: 61: 56: 54: 47: 46: 41: 40: 35: 30: 21: 20: 9433: 9421: 9402: 9395: 9307:Econometrics 9257: / 9240:Chemometrics 9217:Epidemiology 9210: / 9183:Applications 9089: 9025:ARIMA model 8972:Q-statistic 8921:Stationarity 8817:Multivariate 8761: 8760: / 8756: / 8754:Multivariate 8752: / 8692: / 8688: / 8462:Bayes factor 8361:Signed rank 8273: 8247: 8239: 8227: 7922:Completeness 7758:Cohort study 7656:Opinion poll 7591:Missing data 7578:Study design 7533:Scatter plot 7455:Scatter plot 7448:Spearman's ρ 7410:Grouped data 7060:the original 7029: 7010: 6991: 6972: 6953: 6902: 6898: 6888: 6861: 6857: 6847: 6814: 6810: 6800: 6770:(2): 57–88. 6767: 6763: 6757: 6730: 6726: 6716: 6663: 6659: 6649: 6608: 6604: 6598: 6573: 6569: 6563: 6545: 6539: 6521: 6515: 6497: 6491: 6479: 6466: 6454: 6398: 6392: 6382: 6357: 6353: 6347: 6335:. Retrieved 6330: 6320: 6301: 6295: 6252: 6248: 6242: 6231: 6225: 6215:November 12, 6213:. Retrieved 6209: 6199: 6189: 6182: 6172:November 12, 6170:. Retrieved 6166: 6108: 6104: 6066: 6062: 6052: 6027: 6023: 6013: 5983:(1): 35–47. 5980: 5976: 5966: 5931: 5927: 5917: 5899: 5872: 5866: 5801:Logrank test 5786:Failure rate 5702:Applications 5654: 5642: 5630: 5614: 5593: 5415: 5234: 5092: 4984: 4664: 4651: 4642: 4624: 4619: 4616: 4612: 4607: 4603: 4601: 4592: 4588: 4584: 4580: 4576: 4574: 4567: 4557: 4553: 4549: 4548:, for which 4542: 4534: 4530: 4526: 4522: 4518: 4516: 4511: 4507: 4503: 4499: 4495: 4487: 4483: 4479: 4471: 4467: 4463: 4459: 4455: 4451: 4450:newborns is 4447: 4439: 4435: 4431: 4430:or later is 4427: 4425: 4420: 4414: 4412: 4376: 4199: 4036: 3807: 3738: 3647: 3646: 3366: 3268: 3237: 3169: 3062: 3000: 2944: 2899: 2897: 2803: 2800: 2658: 2563: 2560: 2449: 2444: 2412: 2214: 2058: 2056: 1851: 1738: 1728: 1723: 1719: 1636: 1631: 1623: 1548: 1543: 1539: 1537: 1534: 1520: 1516: 1512: 1510: 1505: 1501: 1497: 1493: 1489: 1485: 1481: 1477: 1473: 1469: 1465: 1461: 1459: 1450: 1448: 1443: 1439: 1435: 1431: 1427: 1423: 1411: 1407: 1356: 1351: 1347: 1345: 1319: 1310: 1295:Please help 1283: 1259: 1246: 1238: 1229: 1218: 1212: 1206: 1200: 1194: 1188: 1182: 1176: 1170: 1165: 1154: 1145: 1141: 1123: 1110: 1106: 1102: 1075: 1063: 1054: 1040: 1037: 1009: 994: 991: 977: 968:sample sizes 960: 944: 928: 899: 880: 858: 851: 844:Kaplan–Meier 839: 835: 831: 827: 823: 818: 804: 450: 446:observation 436: 428: 402: 338: 324: 320: 317: 309:heart attack 294: 281: 273: 269: 257: 253: 241: 240: 225: 207: 198: 188: 181: 174: 167: 155: 143:Please help 138:verification 135: 105: 96: 89:Please help 85: 74: 50: 43: 37: 36:Please help 33: 9463:Mathematics 9435:WikiProject 9350:Cartography 9312:Jurimetrics 9264:Reliability 8995:Time domain 8974:(Ljung–Box) 8896:Time-series 8774:Categorical 8758:Time-series 8750:Categorical 8685:(Bernoulli) 8520:Correlation 8500:Correlation 8296:Jarque–Bera 8268:Chi-squared 8030:M-estimator 7983:Asymptotics 7927:Sufficiency 7694:Interaction 7606:Replication 7586:Effect size 7543:Violin plot 7523:Radar chart 7503:Forest plot 7493:Correlogram 7443:Kendall's τ 6817:(1): 7–15. 5715:of inmates 5708:Credit risk 4490:), and the 2445:hazard rate 2443:. The term 1420:probability 1133:covariates. 1090:logarithmic 780:Maintained 766:Maintained 738:Maintained 710:Maintained 682:Maintained 654:Maintained 612:Maintained 598:Maintained 570:Maintained 556:Maintained 528:Maintained 347:Life tables 266:engineering 93:if you can. 9484:Senescence 9473:Categories 9302:Demography 9020:ARMA model 8825:Regression 8402:(Friedman) 8363:(Wilcoxon) 8301:Normality 8291:Lilliefors 8238:Student's 8114:Resampling 7988:Robustness 7976:divergence 7966:Efficiency 7904:(monotone) 7899:Likelihood 7816:Population 7649:Stratified 7601:Population 7420:Dependence 7376:Count data 7307:Percentile 7284:Dispersion 7217:Arithmetic 7152:Statistics 7097:Statistics 7039:047147133X 7020:0471372153 7001:047136357X 6982:0471349925 6963:1584883251 6864:(1): 1–7. 6337:6 November 6311:2101.06536 6262:2003.01176 5977:Biometrics 5928:Biometrics 5858:References 5618:calibrated 5413:, we have 5232:, we have 5090:, we have 4620:truncation 4556:= 0.90 or 4444:population 3805:, is just 2417:demography 1313:April 2021 883:life table 246:statistics 201:April 2021 171:newspapers 39:improve it 8683:Logistic 8450:posterior 8376:Rank sum 8124:Jackknife 8119:Bootstrap 7937:Bootstrap 7872:Parameter 7821:Statistic 7616:Statistic 7528:Run chart 7513:Pie chart 7508:Histogram 7498:Fan chart 7473:Bar chart 7355:L-moments 7242:Geometric 6935:244198364 6927:0378-4371 6880:2055-1045 6831:0022-541X 6792:144566819 6784:1525-1071 6749:0895-7177 6690:0027-8424 6641:154615623 6625:0022-2879 6590:0030-364X 6374:119577304 6287:211817982 6137:1932-6157 6118:0811.1645 6083:1759-1163 6069:(1): 68. 6044:0162-1459 5948:0006-341X 5541:θ 5538:∣ 5513:− 5507:θ 5504:∣ 5473:θ 5470:∣ 5329:θ 5326:∣ 5301:θ 5298:∣ 5279:− 5267:θ 5264:∣ 5187:θ 5184:∣ 5165:− 5153:θ 5150:∣ 5125:θ 5122:∣ 5045:θ 5042:∣ 5017:θ 5014:∣ 4937:θ 4934:∣ 4870:∈ 4863:∏ 4856:θ 4853:∣ 4814:∈ 4807:∏ 4800:θ 4797:∣ 4758:∈ 4751:∏ 4744:θ 4741:∣ 4702:∈ 4688:∏ 4678:θ 4569:Censoring 4564:Censoring 4334:∞ 4318:∫ 4245:∞ 4236:∫ 4087:− 3976:− 3893:≤ 3843:∣ 3824:≤ 3715:− 3603:− 3582:λ 3547:Λ 3544:− 3538:⁡ 3462:λ 3404:Λ 3346:− 3340:⁡ 3308:λ 3246:Λ 3207:λ 3193:∫ 3177:Λ 3143:λ 3100:− 3085:Λ 3036:Λ 3033:− 3027:⁡ 2974:⁡ 2968:− 2953:Λ 2910:Λ 2856:∞ 2824:≥ 2812:λ 2785:∞ 2759:∞ 2750:∫ 2719:≥ 2696:≥ 2690:∀ 2494:⁡ 2473:− 2458:μ 2431:μ 2356:− 2300:⋅ 2268:≤ 2248:→ 2154:≥ 2071:λ 2049:density. 2018:− 1997:− 1949:∞ 1940:∫ 1822:− 1792:∞ 1783:∫ 1595:− 1580:≤ 1519:) → 0 as 1284:does not 286:sociology 278:economics 45:talk page 9499:Survival 9397:Category 9090:Survival 8967:Johansen 8690:Binomial 8645:Isotonic 8232:(normal) 7877:location 7684:Blocking 7639:Sampling 7518:Q–Q plot 7483:Box plot 7465:Graphics 7360:Skewness 7350:Kurtosis 7322:Variance 7252:Heronian 7247:Harmonic 6708:24778209 6427:22145125 6279:33460387 6005:60974957 5754:See also 4638:pensions 4560:= 0.99. 4546:lifetime 4539:quantile 4533:, where 4492:variance 3110:′ 2366:′ 1878:′ 1663:′ 1492:implies 1082:Gaussian 451:(weeks) 290:survival 75:require 9423:Commons 9370:Kriging 9255:Process 9212:studies 9071:Wavelet 8904:General 8071:Plug-in 7865:L space 7644:Cluster 7345:Moments 7163:Outline 6907:Bibcode 6839:3801296 6699:4034186 6668:Bibcode 6633:3839153 6418:3227332 6145:2003897 5997:2531894 5957:4247822 4537:is the 4502:) × (1- 3741:is the 1305:removed 1290:sources 1213:gleason 1104:death. 1084:-like, 952:p-value 868:points. 455:status 301:failure 185:scholar 77:cleanup 9449:Portal 9292:Census 8882:Normal 8830:Manova 8650:Robust 8400:2-way 8392:1-way 8230:-test 7901: 7478:Biplot 7269:Median 7262:Lehmer 7204:Center 7036: 7017: 6998: 6979: 6960: 6933: 6925: 6878: 6837: 6829: 6790: 6782: 6747: 6706: 6696: 6688: 6639: 6631: 6623: 6588: 6552: 6528: 6504: 6425: 6415: 6372: 6285: 6277: 6143: 6135: 6081: 6042: 6003: 5995: 5954: 5946: 5906: 5879: 5744:shares 4544:median 4474:has a 1455: 1406:where 1242: 1195:ploidy 1177:pgstat 1171:pgtime 1161: 1157: 1113: 1016: 997: 887: 808: 796: 792: 313:theory 280:, and 187: 180: 173: 166: 158: 8916:Trend 8445:prior 8387:anova 8276:-test 8250:-test 8242:-test 8149:Power 8094:Pivot 7887:shape 7882:scale 7332:Shape 7312:Range 7257:Heinz 7232:Cubic 7168:Index 6931:S2CID 6835:JSTOR 6788:S2CID 6637:S2CID 6629:JSTOR 6370:S2CID 6306:arXiv 6283:S2CID 6257:arXiv 6141:S2CID 6113:arXiv 6111:(3). 6001:S2CID 5993:JSTOR 5746:on a 4587:> 1476:) if 1414:is a 1207:grade 964:power 449:time 297:death 192:JSTOR 178:books 9149:Test 8349:Sign 8201:Wald 7274:Mode 7212:Mean 7085:and 7079:SOCR 7064:via 7034:ISBN 7015:ISBN 6996:ISBN 6977:ISBN 6958:ISBN 6923:ISSN 6876:ISSN 6827:ISSN 6780:ISSN 6745:ISSN 6704:PMID 6686:ISSN 6621:ISSN 6586:ISSN 6550:ISBN 6526:ISBN 6502:ISBN 6423:PMID 6358:2012 6339:2016 6275:PMID 6217:2021 6210:CRAN 6174:2021 6167:CRAN 6133:ISSN 6079:ISSN 6040:ISSN 5944:ISSN 5904:ISBN 5877:ISBN 5816:MTBF 5594:The 5451:< 5445:< 5251:> 5109:< 4915:< 4909:< 4840:> 4784:< 4636:and 4632:for 4529:for 4525:) = 4482:and 4377:For 3926:> 3887:< 3849:> 3625:> 2419:and 2274:< 2057:The 1770:> 1733:and 1538:The 1504:and 1496:> 1488:> 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