Novel statistical procedures based on likelihood structures: Frequentist, Bayesian and hybrid concept, with application to health related studies
The parametric likelihood (PL) concept is commonly used in biomedical studies and clinical experiments to develop efficient estimators or/and powerful tests strategies. We introduce novel PL procedures to analyze problematic data, e.g., data subject to additive measurement error (ME) and limit of detection (LOD). It is well-known that PL methods are not robust when the parametric assumptions regarding data distributions are violated. For example, PL ratio type tests control the Type I error poorly when corresponding assumptions are not met. We propose and examine various nonparametric likelihood methods based on data subject to ME or/and LOD. In order to provide robust and accurate estimations, we develop novel nonparametric posterior expectations using the empirical likelihood (EL) methodology in Bayesian concept. We also employ EL to construct tests for evaluating two-sample means and quantiles. In order to use possible prior information regarding data, we further modify the proposed EL based tests by involving Bayesian mechanisms.