Statistical models of publication basis in meta-analysis.

Abstract

Objectives: To review, apply and compare existing publication bias methodology. To extend the selection model methods that adjust combined estimates and to develop models to adjust for publication bias and heterogeneity simultaneously. ' Methods: Methodologies that test for the existence of publication bias, estimate the number of missing studies, and adjust combined estimates for publication bias are reviewed. Parametric weighted distribution methodology is developed further. The existing family of distributions is extended to include a logistic function. Weight functions previously limited to modelling selection based on two-tailed p-values have been restructured for one-tailed p-values. The selection mechanism model has been developed to incorporate both p-values and precision. The model for effect size has been developed to incorporate linear predictors, so heterogeneity and publication bias can be modelled simultaneously. Data: Two systematic reviews taken from the Cochrane Library and simulation studies. Results: Methods that test for the existence of publication bias or estimate the number of missing studies are limited by the strength of their assumptions and low power. Weighted distributions offer the only way to directly assess the impact of publication bias. In data sets in which there is heterogeneity or the true treatment effect is null, modelling the selection mechanism on p-values only can lead to over-adjusted estimates and considerable variability between estimates with wide confidence intervals. Extending the selection model to include precision reduces this. It is then possible to include other covariates such as study quality or type. The effect-size model can be extended in a similar way to include linear predictors. Combination of these two models allows simultaneous consideration of the influence of publication bias and heterogeneity. Conclusions: Weighted distributions offer a flexible approach to modelling publication bias. Inclusion of precision in the selection model reduces sensitivity of the model to the shape of the selection model improving consistency of results. No selection model should be used on its own but in conjunction with others to allow a sensitivity approach