On varieties of doubly robust estimators under missingness not at random with a shadow variable.
Suppose we are interested in the mean of an outcome variable missing not at random. Suppose however that one has available a fully observed shadow variable, which is associated with the outcome but independent of the missingness process conditional on covariates and the possibly unobserved outcome. Such a variable may be a proxy or a mismeasured version of the outcome and is available for all individuals. We have previously established necessary and sufficient conditions for identification of the full data law in such a setting, and have described semiparametric estimators including a doubly robust estimator of the outcome mean. Here, we propose two alternative estimators, which may be viewed as extensions of analogous methods under missingness at random, but enjoy different properties. We assess the correctness of the required working models via straightforward goodness-of-fit tests.
Beijing International Center for Mathematical Research, Peking University, 5 Summer Palace Road, Haidian District, Beijing 100871, P.R.C.
Wang
W
Miao
Department of Biostatistics, Harvard University, 677 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. , etchetge@hsph.harvard.edu.
Eric J
EJ
Tchetgen Tchetgen
Doubly robust estimation; Missingness not at random; Shadow variable