Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework

Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator for finite-population inference using a superpopulation model framework. We also clarify conditions for its robustness. For variance estimation, the conventional bootstrap inference is invalid for matching estimators with a fixed number of matches due to the nonsmoothness nature of the matching estimator. We propose a new replication variance estimator, which is asymptotically valid. The key strategy is to construct replicates directly based on the linear terms of the martingale representation for the matching estimator, instead of individual records of variables. Simulation studies confirm that the proposed method provides valid inference.

Improving External Validity of Epidemiologic Cohort Analyses: A Kernel Weighting Approach

For various reasons, cohort studies generally forgo probability sampling required to obtain population representative samples. However, such cohorts lack population-representativeness, which invalidates estimates of population prevalences for novel health factors only available in cohorts. To improve external validity of estimates from cohorts, we propose a kernel weighting (KW) approach that uses survey data as a reference to create pseudo-weights for cohorts. A jackknife variance is proposed for the KW estimates. In simulations, the KW method outperformed two existing propensity-score-based weighting methods in mean-squared error while maintaining confidence interval coverage. We applied all methods to estimating US population mortality and prevalences of various diseases from the non-representative US NIH-AARP cohort, using the sample from US-representative National Health Interview Survey (NHIS) as the reference. Assuming that the NHIS estimates are correct, the KW approach yielded generally less biased estimates compared to the existing propensity-score-based weighting methods.