Nonparametric Finite Mixture: Applications in Overcoming Misclassification Bias

Investigating the differential effect of treatments in groups defined by patient characteristics is of paramount importance in personalized medicine research. In some studies, participants are first classified as having or not of the characteristic of interest by diagnostic tools, but such classifiers may not be perfectly accurate. The impact of diagnostic misclassification in statistical inference has been recently investigated in parametric model contexts and shown to introduce severe bias in estimating treatment effects and give grossly inaccurate inferences. The article aims to address these problems in a fully nonparametric setting. Methods for consistently estimating and testing meaningful yet nonparametric treatment effects are developed. Along the way, we also construct estimators for misclassification error rates and investigate their asymptotic properties. The proposed methods are applicable for outcomes measured in ordinal, discrete, or continuous scales. They do not require any assumptions, such as the existence of moments. Simulation results show significant advantages of the proposed methods in bias reduction, coverage probability, and power. The applications of the proposed methods are illustrated with gene expression profiling of bronchial airway brushing in asthmatic and healthy control subjects. Supplementary materials for this article are available online.