Covariate hypothesis tests for the cure rate in mixture cure models based on martingale difference correlation

Cure models are a class of survival models used to analyze time-to-event data that allow the possibility that the event never occurs for a certain percentage $1-p$, of the population. These methods allow for direct modelling of the cure rate and the influence of covariates on this rate. A common goal is to test whether the cure rate depends on a specific covariate or a set of covariates. The availability of methods to test the effect of covariates on the cure rate is limited in the literature. This paper proposes nonparametric hypothesis tests for the effect of covariates on the cure probability based on the martingale difference correlation. Two methods are used to approximate the null distribution of the test statistic: A permutation test and a chi-square test. The methodology is further extended to the case of two covariates using the partial martingale difference correlation. The performance of the proposed tests is evaluated through a simulation study under various scenarios, and the method is applied to a dataset on rheumatoid arthritis patients.