Nonparametric analysis of factorial designs with random missingness: Bivariate data

We propose a nonparametric approach to the analysis of factorial designs where each subject is observed at two time points and both observations are subject to missingness. The procedures are fully nonparametric in that they do not require continuity, and do not impose models to describe the relation of the response distribution in different factor-level combinations. The approach for estimating and testing treatment and time effects is based on a method, which we introduce, for estimating a distribution function. The method requires a pattern-mixture-type assumption on the missingness mechanism, which is weaker than the missing-completely-at-random assumption but neither weaker nor stronger than the missing-at-random assumption. This missingness assumption is the minimal requirement for nonparametric analysis. Comparisons with normal-based likelihood ratio tests indicate that the proposed tests fare well when the data are normal and homoscedastic, and outperform them in many other cases. Simulations also confirm that the proposed method has higher power than common nonparametric complete-pairs tests for observations missing completely at random. Finally, a dataset on the delinquent values of boys released from correctional institutions is analyzed and discussed.