Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation

Inverse probability weighting (IPW) and multiple imputation are two widely adopted approaches dealing with missing data. The former models the selection probability, and the latter models data distribution. Consistent estimation requires correct specification of corresponding models. Although the augmented IPW method provides an extra layer of protection on consistency, it is usually not sufficient in practice as the true data‐generating process is unknown. This paper proposes a method combining the two approaches in the same spirit of calibration in sampling survey literature. Multiple models for both the selection probability and data distribution can be simultaneously accounted for, and the resulting estimator is consistent if any model is correctly specified. The proposed method is within the framework of estimating equations and is general enough to cover regression analysis with missing outcomes and/or missing covariates. Results on both theoretical and numerical investigation are provided.     

Evaluating a new test using a reference test with estimated sensitivity and specificity

Methodology is proposed for evaluating a new test using a reference test. Unlike previous methodology, sensitivity and the specificity of the reference test are not assumed to be known; instead they are estimated from data comparing the reference test with a gold standard.     

Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks

Abstract. An objective of randomized placebo‐controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain represented in the vaccine construct. Motivated by this objective, recently a mark‐specific proportional hazards (PH) model with a continuum of competing risks has been studied, where the genetic distance of the transmitting strain is the continuous ‘mark’ defined and observable only in failures. A high percentage of genetic marks of interest may be missing for a variety of reasons, predominantly because rapid evolution of HIV sequences after transmission before a blood sample is drawn from which HIV sequences are measured. This research investigates the stratified mark‐specific PH model with missing marks where the baseline functions may vary with strata. We develop two consistent estimation approaches, the first based on the inverse probability weighted complete‐case (IPW) technique, and the second based on augmenting the IPW estimator by incorporating auxiliary information predictive of the mark. We investigate the asymptotic properties and finite‐sample performance of the two estimators, and show that the augmented IPW estimator, which satisfies a double robustness property, is more efficient.