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Quantitative Synthesis I Prepared for: The Agency for Healthcare Research and Quality (AHRQ) Training Modules for Systematic Reviews Methods Guide www.ahrq.gov Systematic Review Process Overview Example: Meta Meta-Analysis Analysis Data Set BetaBeta -Blockers after Myocardial Infarction - Secondary Prevention N === 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Study ============ Reynolds Wilhelmsson Ahlmark Multctr. Int Baber Rehnqvist Norweg.Multr Taylor BHAT Julian Hansteen Manger Cats Rehnqvist q ASPS EIS LITRG Herlitz Year ==== 1972 1974 1974 1977 1980 1980 1981 1982 1982 98 1982 1982 1983 1983 1983 1984 1987 1988 Experiment Control Obs Tot Obs Tot ====== ====== ====== ====== 3 38 3 39 7 114 14 116 5 69 11 93 102 1533 127 1520 28 355 27 365 4 59 6 52 98 945 152 939 60 632 48 471 138 38 1916 9 6 188 88 1921 9 64 873 52 583 25 278 37 282 9 291 16 293 25 154 31 147 45 263 47 266 57 858 45 883 86 1195 93 1200 169 698 179 697 Odds Ratio ===== 1.03 0.48 0.58 0.78 1.07 0.56 0.60 0.92 0. 0.72 0.81 0.65 0.55 0.73 0.96 1.33 0.92 0.92 95% CI Low High ===== ===== 0.19 5.45 0.18 1.23 0.19 1.76 0.60 1.03 0.62 1.86 0.15 2.10 0.46 0.79 0.62 1.38 0.5 0.57 0.90 0.55 1.18 0.38 1.12 0.24 1.27 0.40 1.30 0.61 1.51 0.89 1.98 0.68 1.25 0.73 1.18 Combining Effect Estimates What is the average (overall) treatment‐control diff difference in blood pressure? i bl d ? Study N Mean difference (mm Hg) A 554 ‐6.2 ‐6.9 to ‐5.5 B 304 ‐7.7 ‐10.2 to ‐5.2 C 39 ‐0.1 ‐6.5 to 6.3 95% Confidence Interval Simple Average What is the average (overall) treatment‐control diff difference in blood pressure? i bl d ? (‐6.2) 6.2) + ((‐ (‐7.7) 7.7) + ((‐ (‐0.1) 4 7 mm Hg = ‐4.7 mm Hg 3 Study y N M Mean difference mmHg g A 554 ‐6.2 ‐6.9 to ‐5.5 B 304 ‐7.7 ‐10.2 to ‐5.2 C 39 ‐0.1 ‐6.5 to 6.3 95% CI Weighted Average What is the average (overall) treatment‐control diff difference in blood pressure? i bl d ? (554 x -6.2) (554 x 6.2) 6.2) + (304 x (304 x -7.7) 7.7) 7.7) + (39 x (39 x -0.1) 0.1) 6.4 mm Hg 6 4 mm Hg = -6.4 mm Hg 554 + 304 + 39 Study y N M Mean difference mmHg g A 554 ‐6.2 ‐6.9 to ‐5.5 B 304 ‐7.7 77 ‐10.2 to ‐5.2 10 2 t 5 2 C 39 ‐0.1 k 95% CI ‐6.5 to 6.3 X w x i 1 k i i w i 1 i General Formula: Weighted Average Effect Size (d+) k d i 1 k wid i i 1 Where: di = effect size of the ith study wi = weight of the ith study k = number of studies wi Calculation of Weights Generallyy is the inverse of the variance of treatment effect (that captures both study size and precision)) Different formula for odds ratio, risk ratio, and risk difference Readily available in books and software Heterogeneity (Diversity) Is it reasonable? Are the characteristics and effects of studies sufficiently similar to estimate an average effect? Types of heterogeneity: Clinical diversity Methodological diversity Statistical heterogeneity Clinical Diversity Are the studies of similar treatments, populations, settings, design, et cetera, such that an average effect would be clinically meaningful? Example: A Meta-analysis With a Large Degree of Clinical Diversity 25 randomized controlled trials compared endoscopic hemostasis with standard therapy for bleeding peptic ulcer. 5 different types of treatment were used: monopolar electrode, bipolar electrode, argon laser, neodymium-YAG laser, and sclerosant injection. 4 different conditions were treated: active bleeding, g, a nonspurting blood vessel, no blood vessels seen, and undesignated. 3 different outcomes were assessed: emergency g y overall mortality, y and recurrent bleeding. g surgery, Sacks HS, et al. JAMA 1990;264:494-9. Methodological Diversity Are the studies of similar design g and conduct such that an average effect would be clinically meaningful? Statistical Heterogeneity Is the observed variabilityy of effects g greater than that expected by chance alone? Two statistical measures are commonly used to assess statistical heterogeneity: Cochran’ss Q Cochran Q-statistics statistics I2 index Example: A Fixed Effect Model Suppose that we have a container t i with ith a very llarge number of black and white balls. The ratio of white to black balls is predetermined and fi d fixed. We wish to estimate this ratio. ratio Now, imagine that the container represents a clinical condition and the balls represent outcomes. Random Sampling From a Container With a Fixed Number of White and Black Balls (Equal Sample Size) Random Sampling From a Container With a Fixed Number of Black and White Balls (Different Sample Size) Different Containers With Different Proportions of Black and White Balls (Random Effects Model) Random Sampling From Containers To Get an Overall Estimate of the Proportion of Black and White Balls Statistical Models of Combining 2x2 Tables Fixed effect model: assumes a common treatment effect. For inverse variance weighted method, the precision of the estimate determines the importance of the study. The Peto and Mantel-Haenzel methods are noninverse variance weighted fixed effect models. Random effects model: in contrast to the fixed fi ed effect model, accounts for within-study variation. The most popular random effects model in use is the DerSimonian and Laird inverse variance weighted method, which calculates the sum of the within-study variation and the among-study variation. Random effects model can also be implemented with Bayesian methods. methods Example Meta-analysis Where Fixed and the Random Effects Models Yield Identical Results Example Meta-analysis Where Results from Fixed and Random Effects Models Will Differ Gross PA, et al. Inn Intern Med 1995;123:518-27. Reprinted with permission from the American College of Physicians. Weights of the Fixed Effect and Random Effects Models Fixed Effect Weight R d Random Eff Effects t W Weight i ht 1 wi vi 1 w vi v * * i where: vi = within studyy variance v* = between study variance Commonly Used Statistical Methods for Combining 2x2 Tables Odds Ratio Risk Ratio Risk Difference Fixed Effect • Mante • Mantel‐Haenszel • Inverse variance Model • l‐Haenszel Peto • Inverse variance weighted g weighted • Exact E t • Inverse variance weighted Random • DerSimonian • DerSimonian • DerSimonian Effects and Laird and Laird and Laird Model Dealing With Heterogeneity Lau J, L J ett al. l Ann A Intern I t Med M d 1997;127:820-6. 1997 127 820 6 Reprinted R i t d with ith permission i i from f the th American A i College C ll off Physicians. Summary: Statistical Models of Combining 2x2 Tables Most meta-analyses of clinical trials combine treatment effects (risk ratio, ratio odds ratio ratio, risk difference) across studies to produce a common estimate, by using either a fixed effect or random effects ff model. d l In practice, the results from using these two models are similar when there is little or no heterogeneity. heterogeneity When heterogeneity is present, the random effects model generally produces a more conservative result (smaller Z-score) with a similar estimate but also a wider confidence interval; however, there are rare exceptions of extreme heterogeneity where the random effects model may yield counterintuitive results. Caveats Manyy assumptions p are made in meta-analyses, y so care is needed in the conduct and interpretation. Most meta meta-analyses analyses are retrospective exercises, exercises suffering from all the problems of being an observational design. design Researchers cannot make up missing information or fix poorly collected, collected analyzed analyzed, or reported data. Key Messages Basic meta-analyses can be easily carried out with readily dil available il bl statistical i i l software. f Relative measures are more likely to be h homogeneous across studies t di and d are generally ll preferred. The random effects model is the appropriate statistical model in most instances. The decision to conduct a meta-analysis meta analysis should be based on: a a well well-formulated formulated question, appreciation of the heterogeneity of the data, and understanding of how the results will be used.