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

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.

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 (β ₁) and between-study heterogeneity of the treatment effect (τ ₁² ). We varied the prevalence of the outcome, sample size, number of studies and variances and correlation of the random effects.

The two-stage and one-stage methods produced approximately unbiased β ₁ estimates. PQL performed better than AGHQ for estimating τ ₁² with respect to MSE, but performed comparably with AGHQ in estimating the bias of β ₁ and of τ ₁² . The random study-effects model outperformed the stratified study-effects model in small size MA.

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.