Design In various types of biomedical studies, subjects drop out for reasons related to failure. For example, less healthy patients may seek treatment elsewhere or healthier subjects may be discharged from hospital prior to the end of the study. Typically, inference requires strong assumptions about the dropout mechanism (Baker, Wax, and Patterson, 1993) (BWP). The primary motivation of double sampling is to provide information to relax the distributional assumptions. There are two basic designs. Dropout double sampling. At the time of dropout, a subject is randomly assigned to follow-up or no follow-up. This is the design in FRangakis and Rubin (FR), where dropout was loss to follow-up, failure time was time from surgery to failure of prosthesis, and administrative censoring varied, depending on time of entry. Initial double sampling. At the start of the study, such as time of surgery or randomization to treatment assignment, subjects are randomly assigned to either a partial follow-up (PF) or full follow-up (FF) group. If a subject in the FF group drops out of the study, he is followed until failure or administrative censoring. If a subject in the partial followup group drops out, he is not followed after dropout. This is the design in BWP, where dropout was discharge from the hospital, failure time was time of infection following surgery, and administrative censoring was fixed at 30 days. Initial double sampling is a special case of dropout double sampling. Imagine that, as a result of initial double sampling, each subject is randomly assigned a label, either PF or FF, and when dropout occurs, subjects are randomly assigned to follow-up or not based on the PF and FF labels. The only difference with dropout double sampling is the additional random assignment to PF and FF among subjects who did not drop out. This extra information is not used in either the FR or BWP analysis.