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

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Survival Analysis

Background:

• Biomedical studies often link longitudinal measurements with time-to-event outcomes.
• Longitudinal-survival joint models are complex and difficult to interpret.
• A simpler preliminary test is needed to assess associations between these processes.

Purpose of the Study:

• To propose the Longitudinal-Longitudinal-Survival (LLR) test as a longitudinal extension of the log-rank test.
• To provide a method for assessing the association between time-to-event outcomes and time-dependent covariates.
• To introduce the weighted log-rank test statistics (LWLR) for emphasizing covariate effects over time.

Main Methods:

• The LLR test statistic is proposed as a longitudinal extension of the log-rank test.
• The asymptotic distribution of LLR is derived using a permutation approach.
• Simulation studies evaluate the performance of LLR and LWLR statistics.
• A toy example and the Epidemiology of Diabetes Interventions and Complications dataset illustrate the LLR test.

Main Results:

• The LLR test provides evidence of plausible associations between time-to-event outcomes and time-dependent covariates.
• The empirical size of the LLR and LWLR tests is close to the nominal significance level.
• The power of the tests is influenced by the association between covariates and survival time.

Conclusions:

• The LLR test serves as a valuable preliminary tool for evaluating associations in longitudinal-survival data.
• LWLR statistics offer flexibility in emphasizing covariate effects across the time axis.
• Software implementation is available for practical application of the LLR test.