A comparison of analytic approaches for individual patient data meta-analyses with binary outcomes

Background: Individual patient data meta-analyses (IPD-MA) are often performed using a one-stage approach-a form of generalized linear mixed model (GLMM) for binary outcomes. We compare (i) one-stage to two-stage approaches (ii) the performance of two estimation procedures (Penalized Quasi-likelihood-PQL and Adaptive Gaussian Hermite Quadrature-AGHQ) for GLMMs with binary outcomes within the one-stage approach and (iii) using stratified study-effect or random study-effects. Methods: We compare the different approaches via a simulation study, in terms of bias, mean-squared error (MSE), coverage and numerical convergence, of the pooled treatment effect (beta(1)) and between-study heterogeneity of the treatment effect (tau(2)(1)). We varied the prevalence of the outcome, sample size, number of studies and variances and correlation of the random effects. Results: The two-stage and one-stage methods produced approximately unbiased beta(1) estimates. PQL performed better than AGHQ for estimating t12 with respect to MSE, but performed comparably with AGHQ in estimating the bias of beta(1) and of tau(2)(1). The random study-effects model outperformed the stratified study-effects model in small size MA. Conclusion: The one-stage approach is recommended over the two-stage method for small size MA. There was no meaningful difference between the PQL and AGHQ procedures. Though the random-intercept and stratified-intercept approaches can suffer from their underlining assumptions, fitting GLMM with a random-intercept are less prone to misfit and has good convergence rate.