Multiple imputation for propensity score analysis with covariates missing at random: some clarity on within and across methods

In epidemiology and social sciences, propensity score methods are popular for estimating treatment effects using observational data, and multiple imputation is popular for handling covariate missingness. However, how to appropriately use multiple imputation for propensity score analysis is not completely clear. This paper aims to bring clarity on the consistency (or lack thereof) of methods that have been proposed, focusing on the within approach (where the effect is estimated separately in each imputed dataset and then the multiple estimates are combined) and the across approach (where typically propensity scores are averaged across imputed datasets before being used for effect estimation). We show that the within method is valid and can be used with any causal effect estimator that is consistent in the full-data setting. Existing across methods are inconsistent, but a different across method that averages the inverse probability weights across imputed datasets is consistent for propensity score weighting. We also comment on methods that rely on imputing a function of the missing covariate rather than the covariate itself, including imputation of the propensity score and of the probability weight. Based on consistency results and practical flexibility, we recommend generally using the standard within method. Throughout, we provide intuition to make the results meaningful to the broad audience of applied researchers

Predicting Differences in Model Parameters with Individual Parameter Contribution Regression Using the R Package ipcr

Unmodeled differences between individuals or groups can bias parameter estimates and may lead to false-positive or false-negative findings. Such instances of heterogeneity can often be detected and predicted with additional covariates. However, predicting differences with covariates can be challenging or even infeasible, depending on the modeling framework and type of parameter. Here, we demonstrate how the individual parameter contribution (IPC) regression framework, as implemented in the R package ipcr, can be leveraged to predict differences in any parameter across a wide range of parametric models. First and foremost, IPC regression is an exploratory analysis technique to determine if and how the parameters of a fitted model vary as a linear function of covariates. After introducing the theoretical foundation of IPC regression, we use an empirical data set to demonstrate how parameter differences in a structural equation model can be predicted with the ipcr package. Then, we analyze the performance of IPC regression in comparison to alternative methods for modeling parameter heterogeneity in a Monte Carlo simulation.Peer Reviewe

Triply robust estimation under missing at random

Missing data is frequently encountered in many areas of statistics. Imputation and propensity score weighting are two popular methods for handling missing data. These methods employ some model assumptions, either the outcome regression or the response propensity model. However, correct specification of the statistical model can be challenging in the presence of missing data. Doubly robust estimation is attractive as the consistency of the estimator is guaranteed when either the outcome regression model or the propensity score model is correctly specified. In this paper, we first employ information projection to develop an efficient and doubly robust estimator under indirect model calibration constraints. The resulting propensity score estimator can be equivalently expressed as a doubly robust regression imputation estimator by imposing the internal bias calibration condition in estimating the regression parameters. In addition, we generalize the information projection to allow for outlier-robust estimation. Thus, we achieve triply robust estimation by adding the outlier robustness condition to the double robustness condition. Some asymptotic properties are presented. The simulation study confirms that the proposed method allows robust inference against not only the violation of various model assumptions, but also outliers

Nonparametric methods for the estimation of the conditional distribution of an interval-censored lifetime given continuous covariates

Cette thèse contribue au développement de l'estimation non paramétrique de la fonction de survie conditionnelle étant donné une covariable continue avec données censurées. Elle est basée sur trois articles écrits avec mon directeur de thèse, le professeur Thierry Duchesne. Le premier article, intitulé "Une généralisation de l'estimateur de Turnbull pour l'estimation non paramétrique de la fonction de survie conditionnelle avec données censurées par intervalle, " a été publié en 2011 dans Lifetime Data Analysis, vol. 17, pp. 234 - 255. Le deuxième article, intitulé "Sur la performance de certains estimateurs nonparamétriques de la fonction de survie conditionnelle avec données censurées par intervalle, " est parru en 2011 dans la revue Computational Statistics & Data Analysis, vol. 55, pp. 3355-3364. Le troisième article, intitulé "Estimation de la fonction de survie conditionnelle d'un temps de défaillance étant donné une covariable variant dans le temps avec observations censurées par intervalles", sera bientôt soumis à la revue Statistica Sinica