A nonparametric test for the association between longitudinal covariates and censored survival data

Many biomedical studies focus on the association between a longitudinal measurement and a time-to-event outcome while quantifying this association by means of a longitudinal-survival joint model. In this article we propose using the LLR test — a longitudinal extension of the log-rank test statistic given by Peto and Peto (1972) — to provide evidence of a plausible association between a time-to-event outcome (right- or interval-censored) and a time-dependent covariate. As joint model methods are complex and hard to interpret, it is wise to conduct a preliminary test such as LLR for checking the association between both processes. The LLR statistic can be expressed in the form of a weighted difference of hazards, yielding a broad class of weighted log-rank test statistics known as LWLR¿, which allow a specific emphasis along the time axis of the effects of the time-dependent covariate on the survival. The asymptotic distribution of LLR is derived by means of a permutation approach under the assumption that the censoring mechanism is independent of the survival time and the longitudinal covariate. A simulation study is conducted to evaluate the performance of the test statistics LLR and LWLR¿, showing that the empirical size is close to the nominal significance level and that the power of the test depends on the association between the covariates and the survival time. A data set together with a toy example are used to illustrate the LLR test. The data set explores the study Epidemiology of Diabetes Interventions and Complications (Sparling and others, 2006) which includes interval-censored data. A software implementation of our method is available on github (https://github.com/RamonOller/LWLRtest).Peer ReviewedPostprint (author's final draft