An imputation based empirical likelihood approach to pretest-posttest studies.

Pretest-posttest studies are an important and popular method for assessing treatment effects or the effectiveness of an intervention in many areas of scientific research. There are two distinct features for this type of study: availability of baseline information for all subjects in the study and missingness by design of measures of the responses. Important recent research advances on this topic include Leon et al. (2003) on efficient estimation of the treatment effect, and Huang et al. (2008) on a semi-parametric estimation procedure based on empirical likelihood (EL) where the mean responses for the treatment group and the control group are handled separately. EL ratio confidence intervals or tests for the treatment effect, however, cannot be constructed under the approach used by Huang et al. (2008). In this paper, we use an alternative EL formulation, which directly involves the parameter of interest, i.e., the treatment effect, and incorporates baseline information through an imputation approach. Our focus is to derive the EL ratio confidence intervals and tests for the treatment effect under the proposed imputation-based framework. Theoretical results are developed, and finite sample performances of the proposed methods with comparison to existing approaches are investigated through simulation studies. An application to a real data set is also presented. The Canadian Journal of Statistics 43: 378-402; 2015 © 2015 Statistical Society of Canada [ABSTRACT FROM AUTHOR]