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Combinatorial meta-analysis

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A jackknife method was applied to meta-analytic data some years later but it does not appear that specialized software was developed for the task. Other commentators have also called for related methods, apparently unaware of the original work. More recent work by a software porting team at Brown
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Gee's original software for performing jackknife and combinatorial meta analysis was based on older meta-analytic macros written in the SAS programming language. It was the basis of one report in the area of arthritis treatment. While this software was shared with colleagues informally, it was not
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A further implication of this is that arguments over inclusion or exclusion of studies may be moot when the distribution of all possible results is taken into account. A useful tool developed by Gee (reference to come when published) is the "PPES" plot (standing for "Probability of Positive Effect
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Bellamy, N., Campbell, J. and Gee, T. (2005). Can study selection, variable management and time period influence observed effect sizes in systematic reviews of hyaluronan/hylan products?. In: R. Altman, Poster presentations. 10th World Congress on Osteoarthritis, Massachusetts, U.S.A., (S71-S71).
311:. Where a clear effect is present, this plot should asymptote to near 1.0 fairly rapidly. With this, it is possible then that, for instance, disputes over the inclusion or exclusion of two or three studies out of a dozen or more may be framed in the context of a plot that shows a clear effect for 348:
garbage by a critic, it does offer a way of examining the extent to which those studies may have changed a result. Similarly, it offers no direct solution to the problem of which method to choose for combination or weighting. What it does offer, as noted above, is triangulation, where agreements
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It is also possible through CMA to examine the relationship of covariates with effect sizes. For example, if industry funding is suspected as a source of bias, then the proportion of studies in a given subset that were industry funded can be computed and plotted directly against the effect size
203:) is the study of the behaviour of statistical properties of combinations of studies from a meta-analytic dataset (typically in social science research). In an article that develops the notion of "gravity" in the context of meta-analysis, Travis Gee proposed that the 254:
Where it is computationally feasible to obtain all possible combinations, the resulting distribution of statistics is termed "exact CMA." Where the number of possible combinations is prohibitively large, it is termed "approximate CMA."
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Marek Lukacik, MDa, Ronald L. Thomas, PhDb, Jacob V. Aranda, MD, PhDbA Meta-analysis of the Effects of Oral Zinc in the Treatment of Acute and Persistent Diarrhea, Pediatrics Vol. 121 No. 2 February 1, 2008, pp. 326 -336 (doi:
299:. This can be adapted to a "PMES" plot (standing for "Probability of Minimal Effect Size"), where the proportion of studies exceeding some minimal effect size (e.g., SMD = 0.10) is taken for each value of 262:
of adopting a single method and computing a single result, and allows significant triangulation to occur, by computing different indices for each combination and examining whether they all tell the same story.
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method to identify the number of intercepts that may be present in the dataset by looking at which studies are included in the local minima that may be obtained through recombination.
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estimate. If average age in the various studies was itself fairly variable, then the mean of these means across studies in a given combination can be obtained, and similarly plotted.
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CMA makes it possible to study the relative behaviour of different statistics under combinatorial conditions. This differs from the standard approach in
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Size", assuming differences are scaled such that larger in a positive direction is desired). For each subset of combinations, where studies are taken
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in that article could be extended to examine all possible combinations of studies (where practical) or random subsets of studies (where the
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at a time, the proportion of results that show a positive effect size (either WMD or SMD will work) is taken, and this is plotted against
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Olkin I, Dahabreh IJ, Trikalinos TA. GOSH - A graphical display of study heterogeneity. Research Synthesis Methods. 2012;3(3):214-223.
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between methods may be obtained, and disagreements between methods understood across the range of possible combinations of studies.
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estimates. It is observed that this is a special case of the more general approach of CMA which computes results for
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published. A later meta-analysis applied the concept in the context of the treatment of diarrhea.
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Gee, T. (2005) "Capturing study influence: The concept of 'gravity' in meta-analysis",
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An implication of this is that where multiple random intercepts exist, the
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within certain combinations will be minimized. CMA can thus be used as a
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of the situation made it computationally infeasible).
332:University has implemented the concept in STATA. 476: 364: 362: 359: 84:. There might be a discussion about this on 50:Learn how and when to remove these messages 184:Learn how and when to remove this message 166:Learn how and when to remove this message 104:Learn how and when to remove this message 129:This article includes a list of general 477: 370:Counselling, Psychotherapy, and Health 115: 56: 15: 13: 322: 315:combination of 7 or more studies. 135:it lacks sufficient corresponding 14: 496: 31:This article has multiple issues. 120: 61: 20: 266: 227:objects (studies) are combined 39:or discuss these issues on the 457: 448: 418: 404: 394: 384: 335: 1: 352: 7: 197:Combinatorial meta-analysis 10: 501: 243:studies taken 1, 2, 3 ... 218: 223:In the original article, 401:10.1542/peds.2007-0921) 150:more precise citations. 430:ije.oxfordjournals.org 307: − 1, 291: − 1, 247: − 1, 233:jackknife estimation 74:confusing or unclear 436:on 10 November 2016 340:CMA does not solve 82:clarify the article 467:. 19 October 2012. 378:2006-08-19 at the 205:jackknife methods 194: 193: 186: 176: 175: 168: 114: 113: 106: 54: 492: 469: 468: 461: 455: 452: 446: 445: 443: 441: 432:. Archived from 422: 416: 415: 408: 402: 398: 392: 388: 382: 366: 235:), resulting in 189: 182: 171: 164: 160: 157: 151: 146:this article by 137:inline citations 124: 123: 116: 109: 102: 98: 95: 89: 65: 64: 57: 46: 24: 23: 16: 500: 499: 495: 494: 493: 491: 490: 489: 475: 474: 473: 472: 463: 462: 458: 453: 449: 439: 437: 424: 423: 419: 410: 409: 405: 399: 395: 391:8-11 Dec, 2005. 389: 385: 380:Wayback Machine 367: 360: 355: 338: 325: 323:Implementations 269: 221: 190: 179: 178: 177: 172: 161: 155: 152: 142:Please help to 141: 125: 121: 110: 99: 93: 90: 79: 66: 62: 25: 21: 12: 11: 5: 498: 488: 487: 471: 470: 456: 447: 417: 403: 393: 383: 372:, 1(1), 52–75 357: 356: 354: 351: 337: 334: 324: 321: 268: 265: 231:-1 at a time ( 220: 217: 192: 191: 174: 173: 128: 126: 119: 112: 111: 69: 67: 60: 55: 29: 28: 26: 19: 9: 6: 4: 3: 2: 497: 486: 485:Meta-analysis 483: 482: 480: 466: 460: 451: 435: 431: 427: 421: 413: 407: 397: 387: 381: 377: 374: 371: 365: 363: 358: 350: 347: 343: 342:meta-analysis 333: 329: 320: 316: 314: 310: 306: 302: 298: 294: 290: 286: 280: 278: 274: 273:heterogeneity 264: 261: 260:meta-analysis 256: 252: 250: 246: 242: 238: 234: 230: 226: 216: 214: 213:combinatorics 210: 209:meta-analysis 206: 202: 198: 188: 185: 170: 167: 159: 156:February 2010 149: 145: 139: 138: 132: 127: 118: 117: 108: 105: 97: 87: 86:the talk page 83: 77: 75: 70:This article 68: 59: 58: 53: 51: 44: 43: 38: 37: 32: 27: 18: 17: 459: 450: 438:. Retrieved 434:the original 429: 420: 406: 396: 386: 369: 345: 339: 330: 326: 317: 312: 308: 304: 303:= 1, 2, ... 300: 296: 292: 288: 287:= 1, 2, ... 284: 281: 270: 267:Implications 257: 253: 248: 244: 240: 236: 228: 224: 222: 200: 196: 195: 180: 162: 153: 134: 100: 91: 80:Please help 71: 47: 40: 34: 33:Please help 30: 336:Limitations 277:data mining 251:at a time. 207:applied to 148:introducing 440:17 January 353:References 131:references 94:March 2007 76:to readers 36:improve it 42:talk page 479:Category 376:Archived 219:Concept 144:improve 72:may be 346:deemed 133:, but 442:2022 313:any 201:CMA 481:: 428:. 361:^ 45:. 444:. 414:. 309:k 305:k 301:j 297:j 293:k 289:k 285:j 249:k 245:k 241:k 237:k 229:k 225:k 199:( 187:) 181:( 169:) 163:( 158:) 154:( 140:. 107:) 101:( 96:) 92:( 88:. 78:. 52:) 48:(

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improve it
talk page
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confusing or unclear
clarify the article
the talk page
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references
inline citations
improve
introducing
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jackknife methods
meta-analysis
combinatorics
jackknife estimation
meta-analysis
heterogeneity
data mining
meta-analysis



Archived
Wayback Machine
"Statistics Roundtable: The Trusty Jackknife | ASQ"
"Commentary: Heterogeneity in meta-analysis should be expected and appropriately quantified"
the original
"ALLSUBSETS: Stata module to perform all subsets (Combinatorial) meta-analysis in a set of studies"

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