H676 Week 4 – Heterogeneity & Subgroup Analysis (incl. Meta-Regression) Gerald - P&R Chapter 7 (to 217) and TEXT Chapters 15 & 16 Brian - TEXT Chapter 17 Exercises Subgroup (Moderator) Analysis Fatima – P&R Chapter 7 (218 to 226), DeCoster Chapter 9, and TEXT Chapter 19 BREAK Video + Demonstration re categorical moderator variable analysis Meta-Regression Brian – TEXT Chapters 20 & 21 Demonstration

Homogeneity Testing

Computation of the Homogeneity Q Statistic

Alternatives to Q – I2 &T2 T2 = variance of ESs I2 = proportion of dispersion due to true differences between studies T2 = estimate of between-study variance

Gerald

Prediction Intervals – Chapter 17 Confidence Interval (CI) and associated statistics the central tendency (estimated mean) and spread of the data being analyzed Prediction Interval (PI) the interval within which we would expect 95% of new cases (studies) to fall PI is always larger than CI

CI = M +/- tdf * SQRT (T2 + VM) Calculation of PI CI = M +/- tdf * SQRT (T2 + VM) Where M = the sample mean T2 = variance of effect sizes (across studies) VM = variance of the sample mean tdf = the t-value corresponding to alpha = .05 for df degrees of freedom

Another way of comparing CI and PI CI quantifies the accuracy of the sample mean It reflects only error around the mean With an infinite N, CI approaches zero 95% chance that the mean lies within the CI PI addresses the actual dispersion of effect sizes It incorporates true dispersion as well as error With an infinite N, PI approaches the actual dispersion of true ESs 95% of the observed values lie within the PIs CI and PI are not interchangeable

Formulae for CI and PI CI = PI =

Gerald (exercise) then Fatima

MA with subgroups https://www.youtube.com/watch?v=Y7X5ZbfJgDI&feature=youtu.be

Demonstration

Meta-Regression Just like regular multiple regression, using moderator variables to predict ES Using example in the book Order by size of ES (Risk Ratio) Substantial variation in RR and Hypothesis that latitude was related to RR Order by latitude and run meta-regression Random-effects model more appropriate Use R2 to quantify magnitude of the relationship (analogous to regular R2)

Some technical considerations Several methods for estimating T2 Method of Moments, Maximum Likelihood, Restricted Maximum Likelihook Knap-Hartung method for random-effects models Both accessible under “Computational options” tab when have results table open Adjust for multiple comparisons when necessary Use appropriate software that include the weighting formulae Analyses of subgroups and meta-regression are observational, not experimental (no random assignment) – so not causal Statistical power is often low