Integrated exclusive hypothesis test for response missing at random

This study presents a novel method with its computational scheme for testing the exclusive hypothesis in regression models with missing responses under the missing at random (MAR) mechanism. The proposed integrated exclusive hypothesis test addresses the challenge of testing whether a response variable is associated with at most one or multiple factors among a set of predictors, based on the inverse probability weighted (IPW) estimation and the -2-loss-difference test statistics, which are combined to form an integrated decision criterion. The asymptotic properties are established, showing high theoretical and computational efficiency. Numerical experiments demonstrate the validation and robustness of the proposed methodology. As an application, the proposed test is used on an AIDS clinical dataset collected from AIDS Clinical Trials Group Protocol 175.