Performance of cluster-weighted modified Poisson regression for estimating risk ratios in longitudinal data with informative cluster sizes
Jemar R. Bather, Samuel Anyaso-Samuel, Yuyu Chen, Luther Elliott, Alex S. Bennett, Melody S. GoodmanAbstract
Objectives
To evaluate the performance of modified Poisson regression using cluster-weighted generalized estimating equations (MP-CWGEE) for estimating risk ratios in longitudinal data with informative cluster sizes (ICSs).
Methods
Using a comprehensive Monte Carlo simulation study, we evaluated the finite-sample performance of MP-CWGEE relative to five competing approaches: (1) modified Poisson regression using (unweighted) generalized estimating equations (MP-GEE), (2) log-binomial regression using cluster-weighted generalized estimating equations (LB-CWGEE), (3) log-binomial regression using (unweighted) generalized estimating equations (LB-GEE), (4) log-binomial mixed effects model (LB-MM), and (5) Poisson mixed effects model (Pois-MM). We conducted 1,000 simulations across 324 simulation scenarios, spanning different ICS mechanisms, informativeness degrees, sample sizes, exposure effects, within-person correlations, and exposure-covariate associations. Performance metrics included convergence rate, empirical bias, standard error ratio, coverage rate, and empirical Type I error rate. MP-CWGEE’s practical application was demonstrated in a cohort study of 423 people who used illicit opioids in New York City.
Results
MP-CWGEE recovered the individual-averaged marginal risk ratio with negligible bias, near-nominal coverage and Type I error, and perfect convergence across all scenarios, including under high ICS. The unweighted marginal estimators were biased under ICS, and the log-binomial approaches converged less reliably. The Pois-MM performed comparably to MP-CWGEE, but requires a random-effects specification and yields a conditional (cluster-specific) rather than a marginal interpretation.
Conclusions
MP-CWGEE offers a robust modeling approach for estimating risk ratios in longitudinal data with ICSs. Implementation code for R, Stata, and SAS is provided to facilitate wider adoption.