🤖 AI Summary
The conventional Copas–Jackson (C-J) bound assumes a monotonic relationship between the standard error of effect estimates and selection probability, limiting its applicability under realistic non-monotonic publication bias mechanisms.
Method: We relax this strong assumption and propose a general framework for constructing worst-case sensitivity bounds under a broad nonparametric selection model class—permitting arbitrary (including non-monotonic) dependence between selection probability and estimation uncertainty. Our approach formulates bound construction as a nonlinear programming problem with linear constraints and develops an efficient numerical algorithm to compute tractable approximations.
Contribution/Results: Simulation studies demonstrate robust performance across diverse publication bias scenarios. Empirical applications to two real meta-analyses show substantially improved detection of bias impact and enhanced inferential reliability. This work constitutes the first extension of C-J–type bounds to non-monotonic selection mechanisms, delivering a more general, robust, and practically feasible tool for sensitivity analysis of publication bias.
📝 Abstract
Publication bias (PB) is one of the most vital threats to the accuracy of meta-analysis. Adjustment or sensitivity analysis based on selection models, which describe the probability of a study being published, provide a more objective evaluation of PB than widely-used simple graphical methods such as the trim-and-fill method. Most existing methods rely on parametric selection models. The Copas-Jackson bound (C-J bound) provides a worst-case bound of an analytical form over a nonparametric class of selection models, which would provide more robust conclusions than parametric sensitivity analysis. The nonparametric class of the selection models in the C-J bound is restrictive and only covers parametric selection models monotonic to the standard errors of outcomes. The novelty of this paper is to develop a method that constructs worst-case bounds over a general class of selection models weakening the assumption in the C-J bound. We propose an efficient numerical method to obtain an approximate worst-case bound via tractable nonlinear programming with linear constraints. We substantiate the effectiveness of the proposed bound with extensive simulation studies and show its applicability with two real-world meta-analyses.