Deductive semiparametric estimation in Double-Sampling Designs with application to PEPFAR
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Robust estimators in missing data problems often use semiparametric estimation. Such estimation usually requires the analytic form of the efficient influence function (EIF), the derivation of which can be ad hoc and difficult. Recent work has shown how the derivation of EIF in such problems can be made deductive using the functional derivative representation of the EIF in nonparametric models. This approach, however, requires deriving a mixture of a continuous distribution and a point mass, which can itself be challenging for complicated problems. We propose to address this challenge using a "discrete support" structure, therefore making the deductive semiparametric estimation feasible to more complicated designs and estimands. The discrete support is a space constructed from the observed data, which enables (i) approximation of the observed data distribution, and (ii) numerical computation of the deductive semiparametric estimators. The method is expected to produce semiparametric locally efficient estimators within finite steps without knowledge of the EIF. We apply the new method to estimating the mortality rate in a double-sampling design of the President's Emergency Plan for AIDS Relief program. We also analyze the sensitivity of the estimated mortality rate to the inclusion criteria of double-samples.
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