587:
930:, they should be considered alongside other measures for interpretation of the treatment effect, e.g. the ratio of median times (median ratio) at which treatment and control group participants are at some endpoint. If the analogy of a race is applied, the hazard ratio is equivalent to the odds that an individual in the group with the higher hazard reaches the end of the race first. The probability of being first can be derived from the odds, which is the probability of being first divided by the probability of not being first:
47:
So, for a hazardous outcome (e.g., severe disease or death), an HR below 1 indicates that the treatment (e.g., vaccination) is protective against the outcome of interest. In other cases, an HR greater than 1 indicates the treatment is favorable. For example, if the outcome is actually favorable (e.g., accepting a job offer to end a spell of unemployment), an HR greater than 1 indicates that seeking a job is favorable to not seeking one (if "treatment" is defined as seeking a job).
1077:. A statistically important, but practically insignificant effect can produce a large hazard ratio, e.g. a treatment increasing the number of one-year survivors in a population from one in 10,000 to one in 1,000 has a hazard ratio of 10. It is unlikely that such a treatment would have had much impact on the median endpoint time ratio, which likely would have been close to unity, i.e. mortality was largely the same regardless of group membership and
614:(independent variable), e.g. death, remission of disease or contraction of disease. The curve represents the odds of an endpoint having occurred at each point in time (the hazard). The hazard ratio is simply the relationship between the instantaneous hazards in the two groups and represents, in a single number, the magnitude of distance between the Kaplan–Meier plots.
58:(ORs) in that RRs and ORs are cumulative over an entire study, using a defined endpoint, while HRs represent instantaneous risk over the study time period, or some subset thereof. Hazard ratios suffer somewhat less from selection bias with respect to the endpoints chosen and can indicate risks that happen before the endpoint.
46:
vaccination status was associated with significantly decreased risk for the composite of severe COVID-19 or mortality with a HR of 0.20 (95% CI, 0.17–0.22)." In essence, the hazard for the composite outcome was 80% lower among the vaccinated relative to those who were unvaccinated in the same study.
1084:
By contrast, a treatment group in which 50% of infections are resolved after one week (versus 25% in the control) yields a hazard ratio of two. If it takes ten weeks for all cases in the treatment group and half of cases in the control group to resolve, the ten-week hazard ratio remains at two, but
1046:
Treatment effect depends on the underlying disease related to survival function, not just the hazard ratio. Since the hazard ratio does not give us direct time-to-event information, researchers have to report median endpoint times and calculate the median endpoint time ratio by dividing the control
731:
exists between groups. For instance, a particularly risky surgery might result in the survival of a systematically more robust group who would have fared better under any of the competing treatment conditions, making it look as if the risky procedure was better. Follow-up time is also important. A
617:
Hazard ratios do not reflect a time unit of the study. The difference between hazard-based and time-based measures is akin to the difference between the odds of winning a race and the margin of victory. When a study reports one hazard ratio per time period, it is assumed that difference between
573:
is the estimate of treatment effect derived from the regression model. This hazard ratio, that is, the ratio between the predicted hazard for a member of one group and that for a member of the other group, is given by holding everything else constant, i.e. assuming proportionality of the hazard
744:
Hazard ratios are often treated as a ratio of death probabilities. For example, a hazard ratio of 2 is thought to mean that a group has twice the chance of dying than a comparison group. In the Cox-model, this can be shown to translate to the following relationship between group
601:
In its simplest form, the hazard ratio can be interpreted as the chance of an event occurring in the treatment arm divided by the chance of the event occurring in the control arm, or vice versa, of a study. The resolution of these endpoints are usually depicted using
199:
510:
577:
For a continuous explanatory variable, the same interpretation applies to a unit difference. Other HR models have different formulations and the interpretation of the parameter estimates differs accordingly.
1032:
35:
corresponding to the conditions characterised by two distinct levels of a treatment variable of interest. For example, in a clinical study of a drug, the treated population may die at twice the
979:
1421:
917:
812:
1422:
Elaimy, Ameer; Alexander R Mackay, Wayne T Lamoreaux, Robert K Fairbanks, John J Demakas, Barton S Cooke, Benjamin J Peressini, John T Holbrook, Christopher M Lee (5 July 2011).
87:
1038:
In the previous example, a hazard ratio of 2 corresponds to a 67% chance of an early death. The hazard ratio does not convey information about how soon the death will occur.
923:). The corresponding death probabilities are 0.8 and 0.96. It should be clear that the hazard ratio is a relative measure of effect and tells us nothing about absolute risk.
858:
380:
1075:
551:
259:
372:
325:
302:
694:
655:
571:
1050:
While the median endpoint ratio is a relative speed measure, the hazard ratio is not. The relationship between treatment effect and the hazard ratio is given as
279:
230:
724:
are all possible causes of change in the hazard rate over time. For instance, a surgical procedure may have high early risk, but excellent long term outcomes.
625:
of the two groups, whereas a hazard ratio other than one indicates difference in hazard rates between groups. The researcher indicates the probability of this
727:
If the hazard ratio between groups remain constant, this is not a problem for interpretation. However, interpretation of hazard ratios become impossible when
1740:
1473:
1367:
1285:
1307:
2032:
2028:
2078:
2036:
2024:
984:
1733:
1382:
736:
rates. The researchers' decision about when to follow up is arbitrary and may lead to very different reported hazard ratios.
2199:
2115:
1980:
1136:
Najjar-Debbiny, R.; Gronich, N.; Weber, G.; Khoury, J.; Amar, M.; Stein, N.; Goldstein, L. H.; Saliba, W. (2 June 2022).
1950:
330:
The hazard ratio is the effect on this hazard rate of a difference, such as group membership (for example, treatment or
606:. These curves relate the proportion of each group where the endpoint has not been reached. The endpoint could be any
1726:
1707:
1631:
1594:
1560:
1530:
1503:
936:
520:
2237:
212:) is the number at risk at the beginning of an interval. A hazard is the probability that a patient fails between
2044:
1305:
39:
of the control population. The hazard ratio would be 2, indicating a higher hazard of death from the treatment.
2082:
1804:
927:
618:
groups was proportional. Hazard ratios become meaningless when this assumption of proportionality is not met.
2230:
1915:
2209:
867:
752:
194:{\displaystyle h(t)=\lim _{\Delta t\to 0}{\frac {{\text{observed events in interval}}\ /N(t)}{\Delta t}},}
2269:
2264:
2173:
2145:
2074:
1828:
1112:
516:
81:
of the number of events per unit time divided by the number at risk, as the time interval approaches 0:
2274:
2223:
1899:
603:
526:
For two groups that differ only in treatment condition, the ratio of the hazard functions is given by
2018:
732:
cancer treatment associated with better remission rates might on follow-up be associated with higher
661:
might then be used to assess the significance of any differences observed in these survival curves.
505:{\displaystyle \log h(t)=f{\big (}h_{0}(t),\alpha +\beta _{1}X_{1}+\cdots +\beta _{k}X_{k}{\big )}.}
1956:
1904:
1784:
697:
665:
821:
712:
The proportional hazards assumption for hazard ratio estimation is strong and often unreasonable.
2002:
1872:
1850:
1819:
1794:
1777:
1424:"Multimodality treatment of brain metastases: an institutional survival analysis of 275 patients"
713:
1495:
Clinical Trials: Study Design, Endpoints and
Biomarkers, Drug Safety, and FDA and ICH Guidelines
1306:
L. Douglas Case; Gretchen
Kimmick, Electra D. Paskett, Kurt Lohmana, Robert Tucker (June 2002).
1053:
529:
235:
2153:
1990:
1911:
673:
1345:
668:
and researchers provide a 95% confidence interval for the hazard ratio, e.g. derived from the
341:
307:
284:
2259:
1994:
1881:
1789:
1753:
1467:
1361:
1279:
1086:
1078:
1718:
679:
640:
621:
If the proportional hazard assumption holds, a hazard ratio of one means equivalence in the
556:
1960:
1138:"Effectiveness of Paxlovid in Reducing Severe COVID-19 and Mortality in High Risk Patients"
1107:
67:
8:
1867:
1799:
626:
335:
78:
2120:
2070:
1885:
1814:
1772:
1673:
1648:
1450:
1423:
1337:
1209:
1162:
1137:
669:
607:
590:
586:
331:
264:
215:
1262:
1237:
42:
For example, a scientific paper might use an HR to state something such as: "Adequate
2194:
2158:
2125:
2050:
1972:
1749:
1703:
1678:
1627:
1590:
1556:
1526:
1499:
1455:
1329:
1267:
1205:
1167:
1098:
746:
20:
1397:
1341:
1253:
1235:
1213:
1968:
1889:
1843:
1838:
1668:
1660:
1445:
1435:
1319:
1257:
1249:
1201:
1157:
1149:
1324:
2163:
1986:
1941:
1697:
1664:
1621:
1584:
1550:
1520:
1493:
1236:
Spruance, Spotswood; Julia E. Reid, Michael Grace, Matthew Samore (August 2004).
717:
2189:
2110:
2062:
1855:
1767:
728:
634:
1041:
2253:
2168:
2135:
2130:
1117:
658:
51:
1894:
1682:
1459:
1440:
1333:
1271:
1171:
1103:
1153:
2204:
2058:
1931:
1921:
721:
630:
622:
74:
32:
1522:
Intuitive
Biostatistics: A Nonmathematical Guide to Statistical Thinking
2006:
1998:
1964:
1926:
1833:
1186:
701:
594:
55:
338:
that treat the logarithm of the HR as a function of a baseline hazard
2066:
2054:
1308:"Interpreting Measures of Treatment Effect in Cancer Clinical Trials"
611:
2100:
1548:
43:
2105:
733:
1135:
1582:
523:, and the exponential, Gompertz and Weibull parametric models.
818:
is the hazard ratio). Therefore, with a hazard ratio of 2, if
1748:
664:
Conventionally, probabilities lower than 0.05 are considered
66:
Regression models are used to obtain hazard ratios and their
1187:"New Methods for Analyzing Labor Force Structural Dynamics"
1042:
The hazard ratio, treatment effect and time-based endpoints
1027:{\displaystyle P={\frac {\mathit {HR}}{1+{\mathit {HR}}}}}
1016:
1000:
945:
1047:
group median value by the treatment group median value.
593:
illustrating overall survival based on volume of brain
707:
1623:
Sas
Survival Analysis Techniques for Medical Research
1056:
987:
939:
870:
824:
755:
682:
643:
559:
532:
383:
344:
310:
287:
267:
238:
218:
90:
374:and a linear combination of explanatory variables:
1069:
1026:
973:
911:
852:
806:
688:
649:
565:
545:
504:
366:
319:
296:
273:
253:
224:
193:
2251:
739:
629:difference being due to chance by reporting the
107:
974:{\displaystyle {\mathit {HR}}={\frac {P}{1-P}}}
1549:Geoffrey R. Norman; David L. Streiner (2008).
1734:
1525:. Oxford University Press. pp. 210–218.
494:
410:
1472:: CS1 maint: multiple names: authors list (
1366:: CS1 maint: multiple names: authors list (
1284:: CS1 maint: multiple names: authors list (
1184:
61:
261:, given that they have survived up to time
1741:
1727:
1583:David G. Kleinbaum; Mitchel Klein (2005).
1231:
1229:
1227:
1225:
1223:
1672:
1615:
1613:
1576:
1449:
1439:
1323:
1261:
1161:
1085:the median endpoint time ratio is ten, a
2033:Preventable fraction among the unexposed
2029:Attributable fraction for the population
1544:
1542:
1518:
1390:Journal of the Royal Statistical Society
585:
2037:Preventable fraction for the population
2025:Attributable fraction among the exposed
1640:
1586:Survival Analysis: A Self-Learning Text
1512:
1487:
1485:
1483:
1220:
2252:
1699:Biostatistical Methods in Epidemiology
1695:
1689:
1646:
1619:
1610:
1301:
1299:
1297:
1295:
1722:
1655:. The Changing Face of Epidemiology.
1539:
1491:
1415:
1242:Antimicrobial Agents and Chemotherapy
912:{\displaystyle S_{1}(t)=0.2^{2}=0.04}
807:{\displaystyle S_{1}(t)=S_{0}(t)^{r}}
704:(one) in their confidence intervals.
2200:Correlation does not imply causation
2116:Animal testing on non-human primates
1498:. Academic Press. pp. 165–168.
1480:
1216:– via Elsevier Science Direct.
1626:. SAS Institute. pp. 111–150.
1383:"Regression-Models and Life-Tables"
1380:
1292:
708:The proportional hazards assumption
334:, male or female), as estimated by
13:
1552:Biostatistics: The Bare Essentials
1428:World Journal of Surgical Oncology
1374:
1013:
997:
942:
515:Such models are generally classed
311:
288:
245:
179:
151:
111:
14:
2286:
1238:"Hazard Ratio in Clinical Trials"
581:
519:models; the best known being the
1647:Hernán, Miguel (January 2010).
1254:10.1128/AAC.48.8.2787-2792.2004
1185:Flinn, C.; Heckman, J. (1982).
517:proportional hazards regression
2083:Pre- and post-test probability
1805:Patient and public involvement
1649:"The Hazards of Hazard Ratios"
1555:. PMPH-USA. pp. 283–287.
1178:
1129:
926:While hazard ratios allow for
887:
881:
841:
835:
795:
788:
772:
766:
521:Cox proportional hazards model
431:
425:
399:
393:
361:
355:
174:
168:
157:
136:
117:
100:
94:
1:
1325:10.1634/theoncologist.7-3-181
1123:
740:The hazard ratio and survival
700:hazard ratios cannot include
2210:Sex as a biological variable
1665:10.1097/EDE.0b013e3181c1ea43
1396:(2): 187–220. Archived from
1206:10.1016/0304-4076(82)90097-5
1142:Clinical Infectious Diseases
853:{\displaystyle S_{0}(t)=0.2}
604:Kaplan–Meier survival curves
7:
2174:Intention-to-treat analysis
2146:Analysis of clinical trials
2075:Specificity and sensitivity
1829:Randomized controlled trial
1113:Proportional hazards models
1092:
130:observed events in interval
10:
2291:
1070:{\displaystyle e^{\beta }}
657:from the Cox-model or the
546:{\displaystyle e^{\beta }}
254:{\displaystyle t+\Delta t}
50:Hazard ratios differ from
2218:
2183:Interpretation of results
2182:
2144:
2093:
2043:
2017:
1979:
1949:
1940:
1916:Nested case–control study
1866:
1813:
1760:
1702:. John Wiley & Sons.
1519:Motulsky, Harvey (2010).
698:Statistically significant
62:Definition and derivation
1785:Academic clinical trials
1696:Newman, Stephan (2003).
1589:(2 ed.). Springer.
1079:clinically insignificant
367:{\displaystyle h_{0}(t)}
320:{\displaystyle \Delta t}
297:{\displaystyle \Delta t}
2003:Relative risk reduction
1851:Adaptive clinical trial
1795:Evidence-based medicine
1778:Adaptive clinical trial
1194:Journal of Econometrics
1991:Number needed to treat
1441:10.1186/1477-7819-9-69
1392:. B (Methodological).
1087:clinically significant
1071:
1028:
975:
913:
860:(20% survived at time
854:
808:
690:
689:{\displaystyle \beta }
674:regression coefficient
651:
650:{\displaystyle \beta }
598:
597:. Elaimy et al. (2011)
567:
566:{\displaystyle \beta }
547:
506:
368:
321:
298:
275:
255:
226:
195:
31:) is the ratio of the
1995:Number needed to harm
1882:Cross-sectional study
1834:Scientific experiment
1790:Clinical study design
1620:Cantor, Alan (2003).
1072:
1029:
976:
914:
855:
809:
691:
652:
637:. For instance, the
633:associated with some
589:
568:
548:
507:
369:
322:
299:
276:
256:
227:
196:
1961:Cumulative incidence
1054:
985:
937:
868:
822:
753:
680:
641:
610:associated with the
557:
530:
381:
342:
308:
285:
265:
236:
216:
88:
68:confidence intervals
1868:Observational study
1800:Real world evidence
1754:experimental design
1492:Brody, Tom (2011).
1381:Cox, D. R. (1972).
1348:on 24 December 2019
1154:10.1093/cid/ciac443
2270:Statistical ratios
2265:Medical statistics
2154:Risk–benefit ratio
2121:First-in-man study
2071:Case fatality rate
1912:Case–control study
1886:Longitudinal study
1067:
1024:
971:
928:hypothesis testing
909:
850:
804:
747:survival functions
686:
670:standard deviation
647:
608:dependent variable
599:
591:Kaplan-Meier curve
563:
543:
502:
364:
317:
294:
271:
251:
222:
191:
124:
73:The instantaneous
37:rate per unit time
2275:Survival analysis
2247:
2246:
2195:Survivorship bias
2159:Systematic review
2126:Multicenter trial
2089:
2088:
2079:Likelihood-ratios
2051:Clinical endpoint
2019:Population impact
1973:Period prevalence
1750:Clinical research
1099:Survival analysis
1022:
969:
672:of the Cox-model
336:regression models
327:approaches zero.
274:{\displaystyle t}
225:{\displaystyle t}
186:
135:
131:
106:
21:survival analysis
2282:
2094:Trial/test types
1969:Point prevalence
1947:
1946:
1890:Ecological study
1873:EBM II-2 to II-3
1844:Open-label trial
1839:Blind experiment
1815:Controlled study
1743:
1736:
1729:
1720:
1719:
1714:
1713:
1693:
1687:
1686:
1676:
1644:
1638:
1637:
1617:
1608:
1607:
1605:
1603:
1580:
1574:
1573:
1571:
1569:
1546:
1537:
1536:
1516:
1510:
1509:
1489:
1478:
1477:
1471:
1463:
1453:
1443:
1419:
1413:
1412:
1410:
1408:
1402:
1387:
1378:
1372:
1371:
1365:
1357:
1355:
1353:
1344:. Archived from
1327:
1303:
1290:
1289:
1283:
1275:
1265:
1248:(8): 2787–2792.
1233:
1218:
1217:
1191:
1182:
1176:
1175:
1165:
1148:(3): e342–e349.
1133:
1076:
1074:
1073:
1068:
1066:
1065:
1033:
1031:
1030:
1025:
1023:
1021:
1020:
1019:
1003:
995:
980:
978:
977:
972:
970:
968:
954:
949:
948:
919:(4% survived at
918:
916:
915:
910:
902:
901:
880:
879:
859:
857:
856:
851:
834:
833:
813:
811:
810:
805:
803:
802:
787:
786:
765:
764:
695:
693:
692:
687:
656:
654:
653:
648:
572:
570:
569:
564:
552:
550:
549:
544:
542:
541:
511:
509:
508:
503:
498:
497:
491:
490:
481:
480:
462:
461:
452:
451:
424:
423:
414:
413:
373:
371:
370:
365:
354:
353:
326:
324:
323:
318:
303:
301:
300:
295:
280:
278:
277:
272:
260:
258:
257:
252:
231:
229:
228:
223:
200:
198:
197:
192:
187:
185:
177:
164:
133:
132:
129:
126:
123:
38:
2290:
2289:
2285:
2284:
2283:
2281:
2280:
2279:
2250:
2249:
2248:
2243:
2214:
2178:
2140:
2085:
2039:
2013:
1987:Risk difference
1975:
1936:
1870:
1862:
1817:
1809:
1773:Trial protocols
1756:
1747:
1717:
1710:
1694:
1690:
1645:
1641:
1634:
1618:
1611:
1601:
1599:
1597:
1581:
1577:
1567:
1565:
1563:
1547:
1540:
1533:
1517:
1513:
1506:
1490:
1481:
1465:
1464:
1420:
1416:
1406:
1404:
1403:on 20 June 2013
1400:
1385:
1379:
1375:
1359:
1358:
1351:
1349:
1304:
1293:
1277:
1276:
1234:
1221:
1189:
1183:
1179:
1134:
1130:
1126:
1095:
1061:
1057:
1055:
1052:
1051:
1044:
1012:
1011:
1004:
996:
994:
986:
983:
982:
958:
953:
941:
940:
938:
935:
934:
897:
893:
875:
871:
869:
866:
865:
829:
825:
823:
820:
819:
798:
794:
782:
778:
760:
756:
754:
751:
750:
742:
718:adverse effects
710:
681:
678:
677:
642:
639:
638:
584:
558:
555:
554:
537:
533:
531:
528:
527:
493:
492:
486:
482:
476:
472:
457:
453:
447:
443:
419:
415:
409:
408:
382:
379:
378:
349:
345:
343:
340:
339:
309:
306:
305:
286:
283:
282:
266:
263:
262:
237:
234:
233:
217:
214:
213:
178:
160:
128:
127:
125:
110:
89:
86:
85:
64:
36:
17:
12:
11:
5:
2288:
2278:
2277:
2272:
2267:
2262:
2245:
2244:
2242:
2241:
2238:List of topics
2234:
2227:
2219:
2216:
2215:
2213:
2212:
2207:
2202:
2197:
2192:
2190:Selection bias
2186:
2184:
2180:
2179:
2177:
2176:
2171:
2166:
2161:
2156:
2150:
2148:
2142:
2141:
2139:
2138:
2133:
2128:
2123:
2118:
2113:
2111:Animal testing
2108:
2103:
2097:
2095:
2091:
2090:
2087:
2086:
2063:Mortality rate
2049:
2047:
2041:
2040:
2023:
2021:
2015:
2014:
1985:
1983:
1977:
1976:
1955:
1953:
1944:
1938:
1937:
1935:
1934:
1929:
1924:
1919:
1909:
1908:
1907:
1902:
1892:
1878:
1876:
1864:
1863:
1861:
1860:
1859:
1858:
1856:Platform trial
1848:
1847:
1846:
1841:
1836:
1825:
1823:
1811:
1810:
1808:
1807:
1802:
1797:
1792:
1787:
1782:
1781:
1780:
1775:
1768:Clinical trial
1764:
1762:
1758:
1757:
1746:
1745:
1738:
1731:
1723:
1716:
1715:
1708:
1688:
1639:
1632:
1609:
1595:
1575:
1561:
1538:
1531:
1511:
1504:
1479:
1414:
1373:
1318:(3): 181–187.
1312:The Oncologist
1291:
1219:
1200:(1): 115–168.
1177:
1127:
1125:
1122:
1121:
1120:
1115:
1110:
1101:
1094:
1091:
1064:
1060:
1043:
1040:
1036:
1035:
1018:
1015:
1010:
1007:
1002:
999:
993:
990:
981:; conversely,
967:
964:
961:
957:
952:
947:
944:
908:
905:
900:
896:
892:
889:
886:
883:
878:
874:
849:
846:
843:
840:
837:
832:
828:
801:
797:
793:
790:
785:
781:
777:
774:
771:
768:
763:
759:
741:
738:
729:selection bias
709:
706:
685:
646:
635:test statistic
583:
582:Interpretation
580:
562:
540:
536:
513:
512:
501:
496:
489:
485:
479:
475:
471:
468:
465:
460:
456:
450:
446:
442:
439:
436:
433:
430:
427:
422:
418:
412:
407:
404:
401:
398:
395:
392:
389:
386:
363:
360:
357:
352:
348:
316:
313:
293:
290:
270:
250:
247:
244:
241:
221:
202:
201:
190:
184:
181:
176:
173:
170:
167:
163:
159:
156:
153:
150:
147:
144:
141:
138:
122:
119:
116:
113:
109:
105:
102:
99:
96:
93:
63:
60:
52:relative risks
15:
9:
6:
4:
3:
2:
2287:
2276:
2273:
2271:
2268:
2266:
2263:
2261:
2258:
2257:
2255:
2240:
2239:
2235:
2233:
2232:
2228:
2226:
2225:
2221:
2220:
2217:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2187:
2185:
2181:
2175:
2172:
2170:
2169:Meta-analysis
2167:
2165:
2162:
2160:
2157:
2155:
2152:
2151:
2149:
2147:
2143:
2137:
2136:Vaccine trial
2134:
2132:
2131:Seeding trial
2129:
2127:
2124:
2122:
2119:
2117:
2114:
2112:
2109:
2107:
2104:
2102:
2099:
2098:
2096:
2092:
2084:
2080:
2076:
2072:
2068:
2064:
2060:
2056:
2052:
2048:
2046:
2042:
2038:
2034:
2030:
2026:
2022:
2020:
2016:
2012:
2008:
2004:
2000:
1996:
1992:
1988:
1984:
1982:
1978:
1974:
1970:
1966:
1962:
1958:
1954:
1952:
1948:
1945:
1943:
1939:
1933:
1930:
1928:
1925:
1923:
1920:
1917:
1913:
1910:
1906:
1903:
1901:
1900:Retrospective
1898:
1897:
1896:
1893:
1891:
1887:
1883:
1880:
1879:
1877:
1874:
1869:
1865:
1857:
1854:
1853:
1852:
1849:
1845:
1842:
1840:
1837:
1835:
1832:
1831:
1830:
1827:
1826:
1824:
1821:
1820:EBM I to II-1
1816:
1812:
1806:
1803:
1801:
1798:
1796:
1793:
1791:
1788:
1786:
1783:
1779:
1776:
1774:
1771:
1770:
1769:
1766:
1765:
1763:
1759:
1755:
1751:
1744:
1739:
1737:
1732:
1730:
1725:
1724:
1721:
1711:
1709:9780471461609
1705:
1701:
1700:
1692:
1684:
1680:
1675:
1670:
1666:
1662:
1658:
1654:
1650:
1643:
1635:
1633:9781590471357
1629:
1625:
1624:
1616:
1614:
1598:
1596:9780387239187
1592:
1588:
1587:
1579:
1564:
1562:9781550093476
1558:
1554:
1553:
1545:
1543:
1534:
1532:9780199730063
1528:
1524:
1523:
1515:
1507:
1505:9780123919137
1501:
1497:
1496:
1488:
1486:
1484:
1475:
1469:
1461:
1457:
1452:
1447:
1442:
1437:
1433:
1429:
1425:
1418:
1399:
1395:
1391:
1384:
1377:
1369:
1363:
1347:
1343:
1339:
1335:
1331:
1326:
1321:
1317:
1313:
1309:
1302:
1300:
1298:
1296:
1287:
1281:
1273:
1269:
1264:
1259:
1255:
1251:
1247:
1243:
1239:
1232:
1230:
1228:
1226:
1224:
1215:
1211:
1207:
1203:
1199:
1195:
1188:
1181:
1173:
1169:
1164:
1159:
1155:
1151:
1147:
1143:
1139:
1132:
1128:
1119:
1118:Relative risk
1116:
1114:
1111:
1109:
1105:
1102:
1100:
1097:
1096:
1090:
1088:
1082:
1080:
1062:
1058:
1048:
1039:
1008:
1005:
991:
988:
965:
962:
959:
955:
950:
933:
932:
931:
929:
924:
922:
906:
903:
898:
894:
890:
884:
876:
872:
863:
847:
844:
838:
830:
826:
817:
799:
791:
783:
779:
775:
769:
761:
757:
748:
737:
735:
730:
725:
723:
719:
715:
714:Complications
705:
703:
699:
683:
675:
671:
667:
662:
660:
659:log-rank test
644:
636:
632:
628:
624:
619:
615:
613:
609:
605:
596:
592:
588:
579:
575:
560:
538:
534:
524:
522:
518:
499:
487:
483:
477:
473:
469:
466:
463:
458:
454:
448:
444:
440:
437:
434:
428:
420:
416:
405:
402:
396:
390:
387:
384:
377:
376:
375:
358:
350:
346:
337:
333:
328:
314:
291:
281:, divided by
268:
248:
242:
239:
219:
211:
207:
188:
182:
171:
165:
161:
154:
148:
145:
142:
139:
120:
114:
103:
97:
91:
84:
83:
82:
80:
76:
71:
69:
59:
57:
53:
48:
45:
40:
34:
30:
26:
22:
16:Medical ratio
2260:Epidemiology
2236:
2229:
2222:
2011:Hazard ratio
2010:
1895:Cohort study
1698:
1691:
1659:(1): 13–15.
1656:
1653:Epidemiology
1652:
1642:
1622:
1600:. Retrieved
1585:
1578:
1566:. Retrieved
1551:
1521:
1514:
1494:
1468:cite journal
1431:
1427:
1417:
1405:. Retrieved
1398:the original
1393:
1389:
1376:
1362:cite journal
1350:. Retrieved
1346:the original
1315:
1311:
1280:cite journal
1245:
1241:
1197:
1193:
1180:
1145:
1141:
1131:
1104:Failure rate
1089:difference.
1083:
1049:
1045:
1037:
925:
920:
861:
815:
743:
726:
722:late effects
711:
663:
620:
616:
600:
576:
525:
514:
329:
209:
205:
203:
72:
65:
49:
41:
33:hazard rates
28:
25:hazard ratio
24:
18:
2205:Null result
2164:Replication
2059:Infectivity
1981:Association
1932:Case report
1922:Case series
1905:Prospective
1108:Hazard rate
666:significant
631:probability
623:hazard rate
574:functions.
75:hazard rate
56:odds ratios
2254:Categories
2007:Odds ratio
1999:Risk ratio
1965:Prevalence
1951:Occurrence
1927:Case study
1602:7 December
1568:7 December
1434:(69): 69.
1407:5 December
1352:7 December
1124:References
595:metastases
54:(RRs) and
2067:Morbidity
2055:Virulence
1957:Incidence
1063:β
963:−
684:β
645:β
612:covariate
561:β
539:β
474:β
467:⋯
445:β
438:α
388:
312:Δ
289:Δ
246:Δ
180:Δ
152:Δ
118:→
112:Δ
2231:Glossary
2224:Category
2101:In vitro
1942:Measures
1761:Overview
1683:20010207
1460:21729314
1342:46520247
1334:12065789
1272:15273082
1214:16100294
1172:35653428
1093:See also
553:, where
44:COVID-19
2106:In vivo
1674:3653612
1451:3148547
1163:9214014
814:(where
734:relapse
676:, i.e.
332:control
77:is the
1706:
1681:
1671:
1630:
1593:
1559:
1529:
1502:
1458:
1448:
1340:
1332:
1270:
1263:478551
1260:
1212:
1170:
1160:
627:sample
204:where
134:
23:, the
2045:Other
1401:(PDF)
1386:(PDF)
1338:S2CID
1210:S2CID
1190:(PDF)
702:unity
304:, as
79:limit
1884:vs.
1752:and
1704:ISBN
1679:PMID
1628:ISBN
1604:2012
1591:ISBN
1570:2012
1557:ISBN
1527:ISBN
1500:ISBN
1474:link
1456:PMID
1409:2012
1368:link
1354:2012
1330:PMID
1286:link
1268:PMID
1168:PMID
1106:and
907:0.04
720:and
232:and
1669:PMC
1661:doi
1446:PMC
1436:doi
1320:doi
1258:PMC
1250:doi
1202:doi
1158:PMC
1150:doi
895:0.2
864:),
848:0.2
696:.
385:log
108:lim
19:In
2256::
2081:,
2077:,
2073:,
2069:,
2065:,
2061:,
2057:,
2053:,
2035:,
2031:,
2027:,
2009:,
2005:,
2001:,
1997:,
1993:,
1989:,
1971:,
1967:,
1963:,
1959:,
1888:,
1677:.
1667:.
1657:21
1651:.
1612:^
1541:^
1482:^
1470:}}
1466:{{
1454:.
1444:.
1430:.
1426:.
1394:34
1388:.
1364:}}
1360:{{
1336:.
1328:.
1314:.
1310:.
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1282:}}
1278:{{
1266:.
1256:.
1246:48
1244:.
1240:.
1222:^
1208:.
1198:18
1196:.
1192:.
1166:.
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1146:76
1144:.
1140:.
1081:.
749::
716:,
70:.
29:HR
1918:)
1914:(
1875:)
1871:(
1822:)
1818:(
1742:e
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1728:v
1712:.
1685:.
1663::
1636:.
1606:.
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1508:.
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1462:.
1438::
1432:9
1411:.
1370:)
1356:.
1322::
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1288:)
1274:.
1252::
1204::
1174:.
1152::
1059:e
1034:.
1017:R
1014:H
1009:+
1006:1
1001:R
998:H
992:=
989:P
966:P
960:1
956:P
951:=
946:R
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921:t
904:=
899:2
891:=
888:)
885:t
882:(
877:1
873:S
862:t
845:=
842:)
839:t
836:(
831:0
827:S
816:r
800:r
796:)
792:t
789:(
784:0
780:S
776:=
773:)
770:t
767:(
762:1
758:S
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500:.
495:)
488:k
484:X
478:k
470:+
464:+
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411:(
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351:0
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206:N
189:,
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166:N
162:/
158:]
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121:0
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104:=
101:)
98:t
95:(
92:h
27:(
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