A model-based correction for outcome reporting bias in meta-analysis

It is often suspected (or known) that outcomes published in medical trials are selectively reported. A systematic review for a particular outcome of interest can only include studies where that outcome was reported and so may omit, for example, a study that has considered several outcome measures but only reports those giving significant results. Using the methodology of the Outcome Reporting Bias (ORB) in Trials study of (Kirkham and others, 2010. The impact of outcome reporting bias in randomised controlled trials on a cohort of systematic reviews. British Medical Journal 340, c365), we suggest a likelihood-based model for estimating the effect of ORB on confidence intervals and p-values in meta-analysis. Correcting for bias has the effect of moving estimated treatment effects toward the null and hence more cautious assessments of significance. The bias can be very substantial, sometimes sufficient to completely overturn previous claims of significance. We re-analyze two contrasting examples, and derive a simple fixed effects approximation that can be used to give an initial estimate of the effect of ORB in practice.