ABSTRACT
The differential efficacy of treatments across studies may relate to inter-study differences in participant, study, and design factors. Some of these differences may be related to differences in the average underlying risk among study participants. When information about these sources of between-study heterogeneity are unavailable, it may be possible to use the proportion of events in the control or reference group as a surrogate for the underlying risk to partly explain this heterogeneity. This relationship can be modeled by regressing the treatment effect or the treatment risk on the control risk. A complication arises because the control risk can only be estimated and is thus measured with error. In addition, when the treatment effect is the dependent variable, it is correlated with the control risk. Two classes of methods for modeling this correlated measurement error are discussed: structural approaches that model both the observed and true treatment and control risks (and may allow for non-normality of the control risks); and functional approaches (corrected score, conditional score, and SIMEX) that leave the distribution of the control risks unspecified.
