Semiparametric mixture methods for the analysis of correlated counting and survival processes with applications to study design

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This proposal develops efficient methods for the design of clinical studies that monitor recurrent events, for example, skin or other cancer recurrences or epileptic seizures. Sometimes continuous monitoring of individuals experiencing recurrent events is not possible or imperative. There may be situations where, ethically, patients need not be subjected to such monitoring based on the need for care, and at the same time, funds spent in continuous or overly-frequent monitoring could be better allocated; alternatively, events may occur too frequently for their exact times of occurrence to be recorded. Statistical challenges to the design of studies that monitor recurrent events lie in determining optimal times for followup and the number of followup times required, accounting for the numerous distinctions that characterize studies of human subjects, for example, substantial heterogeneity in responses to treatments amongst individuals and missingness of data. The methods employed by the proposed research afford minimal assumptions on the underlying process that generates recurrences, making them highly generalizable.