Statistical tests for heterogeneity of clusters and composite endpoints

Clinical trials and epidemiological cohort studies often group similar diseases together into a composite endpoint, to increase statistical power. A common example is to use a 3-digit code from the International Classification of Diseases (ICD), to represent a collection of several 4-digit coded diseases. More recently, data-driven studies are using associations with risk factors to cluster diseases, leading this article to reconsider the assumptions needed to study a composite endpoint of several potentially distinct diseases. An important assumption is that the (possibly multivariate) associations are the same for all diseases in a composite endpoint (not heterogeneous). Therefore, multivariate measures of heterogeneity from meta-analysis are considered, including multi-variate versions of the I2 and Q statistics. Whereas meta-analysis offers tools to test heterogeneity of clustering studies, clustering models suggest an alternative heterogeneity test, of whether the data are better described by one, or more, clusters of elements with the same mean. The assumptions needed to model composite endpoints with a proportional hazards model are also considered. It is found that the model can fail if one or more diseases in the composite endpoint have different associations. Tests of the proportional hazards assumption can help identify when this occurs. It is emphasised that in multi-stage diseases such as cancer, some germline genetic variants can strongly modify the baseline hazard function and cannot be adjusted for, but must instead be used to stratify the data.