Discussion of “Identifiability and Estimation of Causal Effects in Randomized Trials with Noncompliance and Completely Nonignorable Missing Data”

We congratulate Chen, Geng, and Zhou (CGZ) on an important contribution to the analysis of randomized trials with noncompliance and missing data, two common complications in randomized trials. Most previous methods for analyzing trials in which noncompliance and missing data occur together have either assumed (i) the outcomes are missing at random or (ii) latent ignorability. Missing at random or latent ignorability assume that missingness is not related to the outcome within certain strata of random assignment, compliance, and treatment received. For situations in which missingness is related to outcomes within these strata, CGZ develop novel methods of identifying causal effects. To emphasize the importance of CGZ's methods and illustrate several points, we consider a trial in which missingness might be related to outcome. We use the same notation as CGZ throughout. Ferro et al. (1996) conducted a trial of methods for teaching breast self-examination (BSE) for breast cancer screening in which women were randomly assigned to either a standard treatment of receiving mailed information about BSE (Z = 0) or an enhanced treatment of attendance in a self-exam course in addition to receiving the mailed information (Z = 1). A woman was considered to have received the treatment (D = 1) if she attended the self-exam course. Of the women assigned to attend the self-exam course, only 55% of the women actually attended the course. The primary outcome for the study was whether or not a woman practiced BSE 1 year after the beginning of the study, where the outcome was obtained from a mailed self-administered questionnaire. Only 65% of the women returned the questionnaire (R = 1). The data, taken from Mealli et al.'s (2004) Table 1, are shown in our Table 1. There are structural zeros for Z = 0, D = 1 because women assigned to the standard treatment could not attend the self-exam course. Missingness might depend on the outcome because women who are practicing BSE might feel more commitment to returning a questionnaire for a study on BSE. Missingness might also depend on compliance class and random assignment. For example, if lack of cooperativeness in returning the questionnaire is associated with lack of cooperativeness in following assigned protocol, we would expect never-takers to have more missingness than compliers.