Slide 1AgendaMeta-RegressionFixed-Effect ModelFixed-Effect ModelFixed-Effect Model ANOVA TableRandom-Effects ModelRandom-Effects ModelRandom-Effects Model FitProportion of Covariate Explained Variance Variance Explained by CovariateToday’s First In-Class ActivityComplex Data StructuresIndependent Subgroups within a StudyCombining Across SubgroupsCombining Across SubgroupsMultiple Outcomes or Time-Points within a StudyCombining Outcomes or Time-PointsCombining Outcomes or Time-PointsCombining Outcomes or Time-PointsComparing Outcomes or Time-Points within a StudyComparing Outcomes or Time-PointsMultiple Comparisons within a StudyToday’s Second In-Class ActivityEVAL 6970: Meta-AnalysisMeta-Regression and Complex Data StructuresDr. Chris L. S. CorynSpring 2011Agenda•Meta-regression–In-class activity•Complex data structures–In-class activityMeta-Regression•Used to estimate the impact/influence of categorical and/or continuous covariates (moderators) on effect sizes or to predict effect sizes in studies with specific characteristics•A ratio of 10:1 (studies to covariates) is recommendedFixed-Effect ModelRegression of Latitude on Log risk ratioLatitudeLog risk ratio8.80 13.84 18.88 23.92 28.96 34.00 39.04 44.08 49.12 54.16 59.200.600.340.08-0.18-0.44-0.70-0.96-1.22-1.48-1.74-2.00Fixed-Effect ModelANOVA informationFixed-Effect Model ANOVA TableModel ()121.49992 1 0.00000Residual ()30.73309 11 0.00121Total () 152.23301 12 0.00000121.49992 1 0.0000030.73309 11 0.00121152.23301 12 0.00000• , means that the total variance is greater than would be expected based on within-study error• , means that the relationship between the covariate and the effect is greater than would be expected by chance• , means that even with the covariate in the model, some of the between-studies variance is unexplainedRandom-Effects ModelRegression of Latitude on Log risk ratioLatitudeLog risk ratio8.80 13.84 18.88 23.92 28.96 34.00 39.04 44.08 49.12 54.16 59.200.600.340.08-0.18-0.44-0.70-0.96-1.22-1.48-1.74-2.00Random-Effects ModelRandom-Effects Model Fit•Tests of the model–Simultaneous test that all coefficients (excluding intercept) are zero–Goodness of fit test that all unexplained variance is zero=CHIDIST(,)•?Proportion of Covariate Explained Variance•In meta-analysis, the total variance includes both variance within studies and between studies•Study-level covariates explain only the between-studies portion of the variance�2=1−(������������2������2)Calculating ?������2 Use the fixed-effect meta-analysis results(not meta-regression results)Calculating ?������������2 Results from random-effectsmeta-regression usingmethod of momentsVariance Explained by CovariateToday’s First In-Class Activity•From the “BCG Meta-Regression.CMA” data set –Using a risk ratio as the effect size, conduct a random-effects meta-regression (with method of moments) regressing latitude on the risk ratio–Write the regression equation, calculate the -test to estimate the impact of the slope, compute the LL and UL of , and calculate (see pages 196-202)–Interpret and explain the results•?Complex Data Structures•Main categories of complex data structures–Independent subgroups within a study–Multiple outcomes or time-points within a study–Multiple comparisons within a study•The first two are (relatively) easily handled in Comprehensive Meta-Analysis 2.0Independent Subgroups within a Study•When two or more independent subgroups (each of which contribute unique information) are reported within the same study, the options are1. Compare effects between subgroups•For two subgroups, -test•For two or more subgroups, -test based on ANOVA•-test for heterogeneity 2. Compute a summary effect for all subgroups combined•?Combining Across Subgroups•Option 1a (effect size is computed within subgroups)–Treat each subgroup as a separate study•Interest is in between-subgroup variation•Option 1b (effect size is computed within studies)–Compute a composite score and use the composite score for each study as the unit of analysis•Interest is in between-study variationCombining Across Subgroups•Option 2 (ignore subgroup membership)–Collapse across subgroups to compute a summary effect size and variance–Subgroup membership is considered unimportant and is ignored (and its variance is not part of the summary effect size or standard error)–Essentially a main effect meta-analysisMultiple Outcomes or Time-Points within a Study•When a study reports data on more than one outcome, or over more than one time-point, where outcomes or time-points are based on the same participants (i.e., dependent), the options are1. Compute a composite effect size accounting for the correlation between outcomes or time-points2. Compute a difference between outcomes or time-points accounting for the correlation between outcomes or time-pointsCombining Outcomes or Time-Points•The effect size for two outcomes or time-points is computed as•With variance of the combined mean´� =12(�1=�2) �´�=14(��1+��2+2 �√��1√��2)Combining Outcomes or Time-Points•For more than two outcomes or time-points•With variance of ´� =1�(∑����) �´�=(1�)2(∑�=1���+∑�≠ �(���√��1√��2))Combining Outcomes or Time-Points•The problem is that often is not known (e.g., not reported in a study)•If is unknown, the only solution is to use a plausible value or range of values (sensitivity)–Similarity (or dissimilarity) of outcomes–Time elapsed between time-points and stability of relative scores over time•By default, Comprehensive Meta-Analysis 2.0 sets to 1.00 (which may overestimate the variance and underestimate precision)•?Comparing Outcomes or Time-Points within a Study•The effect size for the difference between two outcomes or time-points is computed as•With variance�����=�1−�2 �����=��1+��2− 2�√��1√��2Comparing Outcomes or Time-Points•As before, the problem is that often is not known (e.g., not reported in a study)•If is unknown, the only solution is to use a plausible value or range of values (sensitivity)•By default, Comprehensive Meta-Analysis 2.0 sets to 0.00 (which may overestimate the variance and underestimate precision of the difference)•?Multiple Comparisons within a
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