Measurement errors in control risk regression: A comparison of correction techniques

Control risk regression is a diffuse approach for meta‐analysis about the effectiveness of a treatment, relating the measure of risk with which the outcome occurs in the treated group to that in the control group. The severity of illness is a source of between‐study heterogeneity that can be difficult to measure. It can be approximated by the rate of events in the control group. Since the estimate is a surrogate for the underlying risk, it is prone to measurement error. Correction methods are necessary to provide reliable inference. This article illustrates the extent of measurement error effects under different scenarios, including departures from the classical normality assumption for the control risk distribution. The performance of different measurement error corrections is examined. Attention will be paid to likelihood‐based structural methods assuming a distribution for the control risk measure and to functional methods avoiding the assumption, namely, a simulation‐based method and two score function methods. Advantages and limits of the approaches are evaluated through simulation. In case of large heterogeneity, structural approaches are preferable to score methods, while score methods perform better for small heterogeneity and small sample size. The simulation‐based approach has a satisfactory behavior whichever the examined scenario, with no convergence issues. The methods are applied to a meta‐analysis about the association between diabetes and risk of Parkinson disease. The study intends to make researchers aware of the measurement error problem occurring in control risk regression and lead them to the use of appropriate correction techniques to prevent fallacious conclusions.