Design and Analysis of Clinical Study 12. Meta-analysis

1. Design and Analysis of Clinical Study 12. Meta-analysis Dr. Tuan V. Nguyen Garvan Institute of Medical Research Sydney, Australia

2. Overview • What is meta-analysis • Two types of data • Statistical procedures

3. Why Meta-analysis/Systematic Reviews? • “. . . the mass of new information makes it difficult for practicing physicians to follow the literature in all areas that might be relevant to their practices. New methods to synthesize and present information from widely dispersed publications are needed . . . .”Jerome Kassirer. Clinical trials and meta-analysis: what do they do for us? N Engl J Med 1992; 327:273-4.

4. Why Need Meta-analysis? Information Explosion • 10-fold Increase in Number of Professional Journals • Psychology Journals: 91 (1951) --> 1,175 (1992) • Math Science Journals: 91 (1953) --> 920 (1992) • Biomedical Journals: 2,300 (1940)--> 23,000 (1993)

5. Problem – Conflicting Information • Not only is there more information, but . . . • Not all information is of equal quality • Information does not necessarily = evidence • There is often conflicting information & reports Traditional narrative reviews can be very “impressionistic”

6. Problems With Traditional Literature Reviews Addressed in Meta-analysis • Selective inclusion of studies, often based on the reviewer's own impressionistic view of the quality of the study • Differential subjective weighting of studies in the interpretation of a set of findings • Misleading interpretations of study findings • Failure to examine characteristics of the studies as potential explanations for disparate or inconsistent results across studies • Failure to examine moderating variables in the relationship under examination

7. Rationale for Systematic Reviews • “provide summaries of what we know, and do not know, that are as free from bias as possible.” (Chalmers et al 1999) • “research that uses explicit & transparent methods to synthesise relevant studies, allowing others to comment on, criticise or attempt to replicate the conclusions reached. Systematic reviews follow same set of procedures as any individual study, & are often reported in the same way. . . .” (Petrsino et al 1999)

8. 4 Basic Questions That a SR/MA Tries to Answer • Are the results of the different studies similar? • To the extent that they are similar, what is the best overall estimate of effect? • How precise and robust is this estimate? • Can dissimilarities be explained? Lau J, Ioannidis JPA, Schmid CH. Quantitative Synthesis in Systematic Reviews. Annals of Internal Medicine 1997; 127:820-826.

9. What is a Systematic Review? • Assemble the most complete dataset feasible, with involvement of investigators • Analyse results of eligible studies. Use statistical synthesis of data (meta-analysis) if appropriate & possible • Perform sensitivity analyses, if appropriate & possible (including subgroup analyses) • Prepare a structured report of the review, stating aims, describing materials & methods, & reporting results

10. Cochrane Library • Cochrane Library CD (& WWW) • Cochrane Database of Systematic Reviews (CDSR) • Database of Abstracts of Reviews of Effectiveness (DARE) • Cochrane Central Register of Controlled Trials (CENTRAL) • Cochrane Review Methodology Database • Health Technology Assessment DB (HTA) • NHS Economic/Evaluation Database (NHS EED)

11. Search Strategy – References & Databases • Studies were identified from • Cochrane Airways Group's Special Register of Controlled Trials comprised of references from • MEDLINE (1966-2000) • EMBASE (1980-2000) • CINAHL (1982-2000) • hand searched airways-related journals • PsychINFO • Reference lists from relevant review articles that were identified (ancestry approach

12. Search Strategy - Terms • Congestive Heart Failure OR Heart Failure* AND • clinical trial* OR beta blocker* • placebo* OR trial* OR random* OR double-blind OR double blind OR single-blind OR single blind OR controlled study OR comparative study.

13. Identification of Trials • Potentially relevant studies from literature search and hand searches • Excluded on basis of abstract, e.g., not randomised or controlled clinical trials Articles selected for full text review • Excluded after full text review • Eligible trials

14. Main Outcome Measures • Mortality / death

15. Beta-blocker and Congestive Heart Failure

16. Model of Meta-analysis • For each study • Relative risk • Variance and standard error of logRR • 95% confidence interval of RR • Weight

17. Model of Meta-analysis • For all studies • Overall relative risk • Variance and standard error • 95% confidence interval

18. Meta-analysis: an example

19. Meta-analysis: an example 95% CI of logRR = -0.38 ± 1.96×0.06 = -0.498, -0.265 95% of RR: exp(-0.498) = 0.61 to exp(-0.265) = 0.77

20. Meta-analysis using R library(meta) n1 <- c(25.9.194.25.105.320.33.261.133.232.1327.1990.214) d1 <- c(5.1.23.1.4.53.3.12.6.2.156.145.8) n2 <- c(25.16.189.25.34.321.16.84.145.134.1320.2001.212) d2 <- c(6.2.21.2.2.67.2.13.11.5.228.217.17) bb <- data.frame(n1.d1.n2.d2) res <- metabin(d1.n1.d2.n2.data=bb.sm=”RR”.meth=”I”) res plot(res. lwd=3)

21. Meta-analysis using R > res RR 95%-CI %W(fixed) %W(random) 1 0.8333 [0.2918; 2.3799] 1.26 1.26 2 0.8889 [0.0930; 8.4951] 0.27 0.27 3 1.0670 [0.6116; 1.8617] 4.47 4.47 4 0.5000 [0.0484; 5.1677] 0.25 0.25 5 0.6476 [0.1240; 3.3814] 0.51 0.51 6 0.7935 [0.5731; 1.0986] 13.08 13.08 7 0.7273 [0.1346; 3.9282] 0.49 0.49 8 0.2971 [0.1410; 0.6258] 2.49 2.49 9 0.5947 [0.2262; 1.5632] 1.48 1.48 10 0.2310 [0.0454; 1.1744] 0.52 0.52 11 0.6806 [0.5635; 0.8221] 38.81 38.81 12 0.6719 [0.5496; 0.8214] 34.31 34.31 13 0.4662 [0.2056; 1.0570] 2.07 2.07 Number of trials combined: 13 RR 95%-CI z p.value Fixed effects model 0.6821 [0.6064; 0.7672] -6.3741 < 0.0001 Random effects model 0.6821 [0.6064; 0.7672] -6.3741 < 0.0001 Quantifying heterogeneity: tau^2 = 0; H = 1 [1; 1.45]; I^2 = 0% [0%; 52.6%] Test of heterogeneity: Q d.f. p.value 11 12 0.5292

22. Forest Plot

23. An Inverted Funnel Plot to Detect Publication Bias

24. An Inverted Funnel Plot to Detect Publication Bias

25. Heterogeneity • Common, to be expected, not the exception • Should do test for homogeneity, but . . . interpret heterogeneity cautiously in spirit of exploratory data analysis • Exploring sources of heterogeneity can lead to insights about modification of apparent associations by various aspects of • Study design • Exposure measurements • Study populations

26. Heterogeneity • Relations discovered in process of exploring heterogeneity may be useful in planning & carrying out new studies • Excluding outliers solely on basis of disagreement with other studies can lead to seriously biased summary estimates (avoid) • Easier to interpret sources of heterogeneity when identified in advance of data analysis (not when suggested only by data)

27. Fixed & Random Effects • Fixed effects models assume that an intervention has a single true effect • Random effects models assume that an effect may vary across studies

28. Random Effects • Assumes sample of studies randomly drawn from population of studies • This is NOT typically true because: • All trials are included • Trials are systematically (e.g., conveniently) sampled and not randomly sampled

29. Random Effects • Primary value of M-A is in search for predictors of between-study heterogeneity • Random-effects summary is last resort only when predictors or causes of between-study heterogeneity cannot be identified • Random-effects can conceal fact that summary estimate or fitted model is poor summary of the data Sander Greenland. Am J Epidemiol 1994;140;290-6.

30. Random Effects • Sometimes needed, but more sensitive to publication bias than fixed-effects • Random effects weights vary less across studies than fixed-effects weights • W = 1/v versus w = 1/(v + t2) • Leads to reduced variation in weights • Thus smaller studies given larger relative weights when random effects models used • Thus influenced more strongly by any tendency NOT to publish small statistically insignificant studies  biased estimate, spuriously strong associations

31. Random Effects • Fixed effects weights vs. random effects weights • W = 1/v versus w = 1/(v + t2) • Identical when there is little or no between study variation • When differ, confidence intervals are larger for random-effects than fixed effects • Smaller studies given larger relative weights in random effects models & > influence • Conversely, influence of larger studies is less • May result in type II (beta error), e.g., Finding no significant difference when one truly exists

32. Methodologic Choices & Their Implications in Dealing With Heterogeneous Data in a Meta-analysis Lau J, Ioannidis JPA, Schmid CH. Quantitative Synthesis in Systematic Reviews. Annals of Internal Medicine 1997; 127:820-826.