Adjusting for publication bias: a multiple imputation approach

Article type
Authors
Carpenter J, Rücker G, Schwarzer G
Abstract
Background: Meta-analysis seeks to combine information from various sources to arrive at a precise, unbiased estimate of an intervention effect. This effort is compromised if the information available to the analyst is subject to unknown selection bias. Considerable effort has therefore gone into methods for (i) detecting selection bias and (ii) correcting the estimate in the presence of bias. Objectives: We show how a recent proposal for sensitivity analysis after multiple imputation [1] can be applied to this problem. Methods: First, possible missing trials are imputed assuming there is no publication bias. Then, the imputed studies are re-weighted, so they represent unpublished studies - missed because of publication bias. The weights are adjusted until the original and weighted imputed studies together show no evidence of publication bias. Then, using these weights, an estimate of intervention effect, adjusted for publication bias, is calculated. Conclusions: Our proposal is attractive as it (i) allows a range of publication bias models, (ii) can be used with any of the tests for publication bias in the literature, and (iii) the results can be displayed on a funnel plot. We illustrate our approach with some meta-analyses where there is a suggetion of publication bias, and compare it with ‘Trim and Fill’ and the Copas selection model. Reference: [1] Carpenter JR, Kenward M and White I (2007) Sensitivity analysis after multiple imputation under missing at random: a weighting approach. Statistical Methods in Medical Research 16: 259-275.