Comment: Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data.
By Anastasios A. Tsiatis, Marie Davidian. 2008
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We congratulate Drs. Kang and Schafer (KS henceforth) for a careful and thought-provoking contribution to the literature regarding the so-called “double robustness” property, a topic that still engenders some confusion and disagreement. The authors’ approach of focusing on the simplest situation of estimation of the population mean μ of a response y when y is not observed on all subjects according to a missing at random (MAR) mechanism (equivalently, estimation of the mean of a potential outcome in a causal model under the assumption of no unmeasured confounders) is commendable, as the fundamental issues can be explored without the distractions of the messier notation and considerations required in more complicated settings. Indeed, as the article demonstrates, this simple setting is sufficient to highlight a number of key points. As noted eloquently by Molenberghs (2005), in regard to how such missing data/causal inference problems are best addressed, two “schools” may be identified: the “likelihood-oriented” school and the “weighting-based” school. As we have emphasized previously (Davidian, Tsiatis and Leon, 2005), we prefer to view inference from the vantage point of semi-parametric theory, focusing on the assumptions embedded in the statistical models leading to different “types” of estimators (i.e., “likelihood-oriented” or “weighting-based”) rather than on the forms of the estimators themselves. In this discussion, we hope to complement the presentation of the authors by elaborating on this point of view. Throughout, we use the same notation as in the paper.
Subfields: Statistics and Probability, Causal Inference & Discovery
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In Statistics and Probability
- Marie Davidian
- Anastasios A. Tsiatis
- Weihua Cao
- Eric B. Laber
- Nathan Kallus
- Michael R. Kosorok
- Peisong Han
- Masatoshi Uehara