1. 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

2. Homogeneity Testing

3. Computation of the Homogeneity Q Statistic

4. 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

5. Gerald

6. 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

7. 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

8. 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

9. Formulae for CI and PI
CI =
PI =

10. Gerald (exercise) then Fatima

11. MA with subgroups

12. Demonstration

13. 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)

14. 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