Pseudo-data augmentation for exact conditional likelihood inference in meta-analysis

In meta-analyses of binary outcomes, two-stage methods based on the DerSimonian-Laird-type random-effects model have been widely used, but these methods fix the within-study variances to their asymptotic estimates and rely on normality assumptions of the outcome measures. Such strict and often unrealistic assumptions can yield biased or inefficient inference. Likelihood-based approaches such as the binomial-normal generalized linear mixed model and the hypergeometric-normal (HGN) model alleviate some of these issues but are intrinsically restricted to the odds-ratio scale, limiting interpretability and precluding direct estimation of the risk-ratio-a more clinically meaningful measure. To overcome these limitations, we propose a unified likelihood-based framework that enables direct estimation of the risk-ratio under the HGN formulation. The proposed method introduces a pseudo-data augmentation approach that preserves the conditional likelihood structure of the HGN model while yielding an unbiased estimating function for the log-risk-ratio. Higher-order inference is achieved via jackknife bias and variance corrections, ensuring accurate coverage even in small or sparse datasets. Simulation studies confirm nearly unbiased estimation and well-calibrated confidence intervals across a wide range of conditions. Applications to published meta-analyses demonstrate that this approach yields interpretable, coherent, and computationally tractable inference.