Nonparametric MLE incorporation of heterogeneity and model testing into premarked cohort studies

We utilize mixture models and nonparametric maximum likelihood estimation to both develop a likelihood ratio test (lrt) for a common simplifying assumption and to allow heterogeneity within premarked cohort studies. Our methods allow estimation of the entire probability model and thus one can not only estimate many parameters of interest but one can also bootstrap from the estimated model to predict many things, including the standard deviations of estimators. Simulations suggest that our lrt has the appropriate protection for Type I error and often has good power. In practice, our lrt is important for determining the appropriateness of estimators and in examining if a simple design with only one capture period could be utilized for a future similar study.