A Further Study of Propensity Score Calibration in Missing Data Analysis

Wang

et al. 2021

Statistics in Medicine

Self Cite

The inverse probability weighted Cox model is frequently used to estimate the marginal hazard ratio. Its validity requires a crucial condition that the propensity score model be correctly specified. To provide protection against misspecification of the propensity score model, we propose a weighted estimation method rooted in the empirical likelihood theory. The proposed estimator is multiply robust in that it is guaranteed to be consistent when a set of postulated propensity score models contains a correctly specified model. Our simulation studies demonstrate satisfactory finite sample performance of the proposed method in terms of consistency and efficiency. We apply the proposed method to compare the risk of postoperative hospitalization between sleeve gastrectomy and Roux‐en‐Y gastric bypass using data from a large medical claims and billing database. We further extend the development to multisite studies to enable each site to postulate multiple site‐specific propensity score models.

Section: Discussionmentioning

confidence: 99%

Estimating the marginal hazard ratio by simultaneously using a set of propensity score models: A multiply robust approach

Shu

Wang

et al. 2021

Statistics in Medicine

Self Cite

“…Han (2014b)), the dependence is rather complex, which makes a general comparison of efficiency between estimators using different working models very difficult. But the derivations provide some guidance on how the empirical process theory is applied, and the results give formulations of the asymptotic variance, both of which are important for investigations of efficiency under some specific situations such as those which were considered in Han (2018) for mean regression.…”

Section: Scenarios (B) and (C)mentioning

confidence: 99%

A General Framework for Quantile Estimation with Incomplete Data

Journal of the Royal Statistical Society Series B: Statistical Methodology

Kong

Zhao

et al. 2019

Self Cite

Summary Quantile estimation has attracted significant research interest in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. We propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The method proposed is capable of dealing with many different missingness settings. We mainly study three of them: estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates; estimating the conditional quantile of a fully observed response while the covariates are partially available; estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables. The method proposed allows multiple models for both the missingness probability and the data distribution. The resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified. The asymptotic distributions are established by using empirical process theory.

“…In the recent literature, Han 33 discussed that modifying the propensity scores as inverse weights essentially agrees with Deville and Särndal 1 in survey literature and showed that directly optimizing an objective function under calibration constraints leads to improving efficiency and robustness 34,35 . Likewise, a number of AIPW estimators have been proposed to calibrate the propensity scores by paring estimating equations and augmentation terms so that they achieve certain efficiency as well as dealing with double robustness 13,36‐38 .…”

Section: Discussionmentioning

confidence: 89%

Combining multiple imputation with raking of weights: An efficient and robust approach in the setting of nearly true models

Shaw

Lumley

2021

Statistics in Medicine

Multiple imputation (MI) provides us with efficient estimators in model‐based methods for handling missing data under the true model. It is also well‐understood that design‐based estimators are robust methods that do not require accurately modeling the missing data; however, they can be inefficient. In any applied setting, it is difficult to know whether a missing data model may be good enough to win the bias‐efficiency trade‐off. Raking of weights is one approach that relies on constructing an auxiliary variable from data observed on the full cohort, which is then used to adjust the weights for the usual Horvitz‐Thompson estimator. Computing the optimally efficient raking estimator requires evaluating the expectation of the efficient score given the full cohort data, which is generally infeasible. We demonstrate MI as a practical method to compute a raking estimator that will be optimal. We compare this estimator to common parametric and semi‐parametric estimators, including standard MI. We show that while estimators, such as the semi‐parametric maximum likelihood and MI estimator, obtain optimal performance under the true model, the proposed raking estimator utilizing MI maintains a better robustness‐efficiency trade‐off even under mild model misspecification. We also show that the standard raking estimator, without MI, is often competitive with the optimal raking estimator. We demonstrate these properties through several numerical examples and provide a theoretical discussion of conditions for asymptotically superior relative efficiency of the proposed raking estimator.