Nonparametric conditional mean cumulative functions for comparison of random-interval counting processes with applications to panel count data analysis in medical study

In medical study, patients are treated with different treatments may have different follow-up schedule. Patients will visit clinic periodically, the actual time-to-event occurrence of disease is unknown, and only the number of occurrence between two consecutive visits is recorded. This is also referred as panel count data. Whenever the event have multiple occurrence, the event process is referred as recurrence process and is treated as a random point process over the follow-up time. A broad range of test procedures have been proposed for continuous observation processes in time-to-event data analysis, but only a few test procedures are applicable for discrete time observations when only panel count data are available. In practice, the number of clinical visits and clinical visit times are different for each patient. i.e, the observation processes are not identical. The number of patients assigned in each treatment group could also be imbalanced. However, most of the existing nonparametric test procedures proposed for treatment effectiveness comparison assume that each treatment has identical observation processes and are conducted for balanced sample size. When the observation processes between treatments are different, the existing test procedures are less significance in detecting the departure from the null hypothesis and provide misleading results. To address this, the study is focused on the development of a nonparametric test procedure which is constructed based on the integrated weighted differences between the mean cumulative function of the recurrences event with condition on treatment group. The test procedure is also extended to take into account multivariate recurrence processes, when the recurrent process has multi-type events. The empirical power of the proposed test statistics in detecting the departure from the null hypothesis are evaluated via Monte Carlo simulation study. The findings show that the proposed method works well under the tested situations. For efficiency comparison, the proposed test is evaluated through real data analysis and the results are in line with earlier research.

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