Statistical issues associated with the analysis of binary outcomes in randomised controlled trials when the effect measure of interest is the relative risk.

Abstract

Background: Binary outcomes have traditionally been analysed using logistic regression which estimates odds ratios. A popular alternative is to estimate relative risks using log binomial regression. Due to convergence problems with this model, alternative methods have been proposed for estimating relative risks. Comparisons between methods are limited and guidance on which method(s) should be used in practice is lacking. These methods are often applied to clustered data, despite the absence of evidence supporting their use in this setting. Comparison of methods in the clustered data setting via simulation is difficult. The simulation model requires specification of the random effects variance on the log scale, but the intraclass correlation coefficient (ICC) on the probability scale is the preferred measure of dependence. The relationship between the ICC and the random effects variance has been defined under the logistic model but not the log binomial model. The appropriate method for analysing binary outcomes from perinatal trials which include infants from multiple births is a matter of debate, and relative risks have received little attention in this context. Aim: To investigate statistical issues associated with the analysis of binary outcomes in randomised controlled trials (RCTs) when the effect measure of interest is the relative risk. Specifically, the aims are: • To compare the performance of methods for estimating relative risks in RCTs with independent and clustered observations; • To determine the relationship between the ICC on the probability scale and the between cluster variance on the log scale; • To provide guidance on the analysis of binary outcomes from perinatal trials including infants from multiple births. Methods: Simulation studies are conducted to compare methods for estimating relative risks using independent and clustered data. To determine the ICC in the latter scenario, the relationship between the ICC on the probability scale and the random effects variance on the log scale is derived. Additional simulation studies are conducted to determine how different analytical methods compare in perinatal trials with multiple births. Example datasets are analysed for illustration. Results: Some methods for estimating relative risks are associated with large bias and poor coverage. Others fail to overcome the convergence problems of log binomial regression. Several methods perform well across a wide range of independent and clustered data settings, including modified Poisson regression. When simulating clustered data, the ICC can be determined from the random effects variance on the log scale based on a Taylor series expansion or properties of the lognormal distribution. Failure to account for clustering in perinatal trials including multiple births leads to inflated type I errors and undercoverage, unless both the ICC and the multiple birth rate are low. Conclusion: Relative risks are a useful measure of effect for binary outcomes. Difficulties in estimating relative risks due to convergence problems with log binomial regression can be overcome using one of several alternatives, including the popular modified Poisson regression approach. This method works well for both independent and clustered data. Clustering should be taken into account in the analysis of perinatal trials including multiple births.