Non-parametric conditional mean cumulative function for random-interval observations in panel count data analysis

In medical follow-up study, patients are treated with different treatments may have different follow-up schedule and the number of patients assigned in each treatment group may not be balanced. To address this, a non-parametric test procedure is proposed. The proposed test statistics is constructed based on the integrated weighted differences between the mean cumulative function of the recurrences event with condition on treatment group. The analysis also includes the multi- type of panel count data that involves covariate, and the clinical follow-up pattern is different between treatment groups, which produce random interval observations. In medical follow-up study, one of the main interests is to analyse treatment effect given covariates. It becomes more challenging when the clinical follow-up times are different among patients and there exist multi-type event with multiple occurrences between sub-sequences follow-ups. The proposed non-parametric test procedure able to detect the departure from the null hypothesis based on weighted difference between conditional mean cumulative functions. The performance of the proposed non-parametric test procedure is evaluated through simulation study. The test procedure gives a good empirical power based on the tested situations for random-interval observation processes. In addition, the efficiency of the proposed method is examined through the real data analysis obtained from the skin cancer chemoprevention trial conducted by the University of Wisconsin Comprehensive Cancer Center. The multivariate analysis shows that the overall DFMO treatment effect on reducing the recurrent of non-melanoma skin cancers are not statistically significant related to gender and number of prior skin cancers which are in line with existing study. The proposed test procedure is concerned on non-parametric comparisons with time independent covariates and non- informative censoring processes. Further work such as assessing the time dependent covariates and consider informative censoring processes could give more insight on panel count data analysis.