The population risk as an explanatory variable in research synthesis of clinical trials

The population risk, for example the control group mortality rate, is an aggregate measurement of many important attributes of a clinical trial, such as the general health of the patients treated and the experience of the staff performing the trial. Plotting measurements of the population risk against the treatment effect estimates for a group of clinical trials may reveal an apparent association, suggesting that differences in the population risk might explain heterogeneity in the results of clinical trials. In this paper we consider using estimates of population risk to explain treatment effect heterogeneity, and show that using these estimates as fixed covariates will result in bias. This bias depends on the treatment effect and population risk definitions chosen, and the magnitude of measurement errors. To account for the effect of measurement error, we represent clinical trials in a bivariate two-level hierarchical model, and show how to estimate the parameters of the model by both maximum likelihood and Bayes procedures. We use two examples to demonstrate the method.