Inference for meta-analysis with a suspected temporal trend

There is sometimes a clear evidence of a strong secular trend in the treatment effect of studies included in a meta-analysis. In such cases, estimating the present-day treatment effect by meta-regression is both reasonable and straightforward. We however consider the more common situation where a secular trend is suspected, but is not strongly statistically significant. Typically, this lack of significance is due to the small number of studies included in the analysis, so that a meta-regression could give wild point estimates. We introduce an empirical Bayes meta-analysis methodology, which shrinks the secular trend toward zero. This has the effect that treatment effects are adjusted for trend, but where the evidence from data is weak, wild results are not obtained. We explore several frequentist approaches and a fully Bayesian method is also implemented. A measure of trend analogous to I(2) is described, and exact significance tests for trend are given. Our preferred method is one based on penalized or h-likelihood, which is computationally simple, and allows invariance of predictions to the (arbitrary) choice of time origin. We suggest that a trendless standard random effects meta-analysis should routinely be supplemented with an h-likelihood analysis as a sensitivity analysis.