Non-parametric Conditional Mean Cumulative Function for Random-interval Count Data with Application in Medical Follow-up Study

A non-parametric test procedure is proposed to address the random-interval observation with imbalanced count data in a medical follow study. Proposed test statistics are constructed based on the integrated weighted differences between the mean cumulative function of the recurrences event with conditions on different treatment groups. The proposed non-parametric test procedure can detect the departure from the null hypothesis based on the weighted difference between conditional mean cumulative functions. The proposed test procedure is concerned with non-parametric comparisons with time-independent covariates and non-informative censoring processes. The mixed Poisson process is constructed, and a multivariate non-homogeneous Poisson process serves as a benchmark for the multivariate mixed Poisson process. The performance of the proposed non-parametric test procedure is investigated through a simulation study with an illustration of a numerical example in a medical follow-up study obtained from the skin cancer chemoprevention trial conducted by the University of Wisconsin Comprehensive Cancer Center.