Comment: Incomplete Data in Clinical Studies: Analysis, Sensitivity, and Sensitivity Analysis
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Joseph G. Ibrohim Department of Biostatistics. School ofhblic Health, University of North Carolina at Chapel Hill
Key Words Identifiability; Missing data: Nonignorable missing data; Software Correspondence Address Joseph G.Ibrahim, Department of Biostatistics. School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420 (email: [email protected]).
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Comment: Incomplete Data in Clinical Studies: Analysis, Sensitivity, and Sensitivity Analysis
I would like to congratulate Dr. Molenberghs for writing an excellent article that gives a comprehensive overview of so many important issues in missing data, especially nonignorable missing data in longitudinal studies. The article nicely examines the three basic approaches to nonignorable missing data modeling, these being selection models (SeMs), pattern mixture models (PMMs),and shared parameter models. Similarities, motivations, contrasts, and connections between these three modeling methods are very nicely made throughout the article. A comprehensive review of modeling and inference issues is given for these classes of models. One of the most important issues discussed in the article is the notion that for every missing not at random (MNAR) model is a missing at random (MAR) counterpart. This is an interesting and important finding. The MAR counterpart given in Eq. l3 for the PMM corresponds to a mixture distribution resulting from summing the last component of Eq. 12 with respect to the distribution of the missing data indicators r;. One issue here is that working with Eq. l3 may be quite computationally challenging, and in order to feasibly compute it, one must place restrictions on the distribution in the last factor (Eq. 12) in order to make the model identifiable. One issue that I have never liked about PMMs is that to make them identifiable, one generally
needs a massive set of restrictions on the parameters of the sampling model conditional on the missing data indicators. One question I had was whether the MNAR and MAR counterpart idea also holds for (a) SeMs, (b) missing covariate data, (c) missing covariate and response data, and (d) semiparametric models, such as survival models with right censored data. It was not clear from the development if this connection is available in these settings. An often misunderstood issue with nonignorable missing data models is the issue of model identifiability and model assessment. Model selection and comparison is a tricky and elusive issue in the presence of nonignorable missing data. In the SeM as well as other frameworks, although there is not enough information in the data to pin down the specific form of the nonignorable missing data mechanism, such nonignorable missing data models are often identifiable in the sense that the parameters of the sampling model and missing data mechanism can be estimated and are finite. In this sense, fitting these types of nonigorable models makes sense, and it also makes sense to compare the fits of a class of identifiable nonignorable m
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