Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism

A Nuisance-Free Inference Procedure Accounting for the Unknown Missingness with Application to Electronic Health Records

We study how to conduct statistical inference in a regression model where the outcome variable is prone to missing values and the missingness mechanism is unknown. The model we consider might be a traditional setting or a modern high-dimensional setting where the sparsity assumption is usually imposed and the regularization technique is popularly used. Motivated by the fact that the missingness mechanism, albeit usually treated as a nuisance, is difficult to specify correctly, we adopt the conditional likelihood approach so that the nuisance can be completely ignored throughout our procedure. We establish the asymptotic theory of the proposed estimator and develop an easy-to-implement algorithm via some data manipulation strategy. In particular, under the high-dimensional setting where regularization is needed, we propose a data perturbation method for the post-selection inference. The proposed methodology is especially appealing when the true missingness mechanism tends to be missing not at random, e.g., patient reported outcomes or real world data such as electronic health records. The performance of the proposed method is evaluated by comprehensive simulation experiments as well as a study of the albumin level in the MIMIC-III database.

Stability Enhanced Variable Selection for a Semiparametric Model with Flexible Missingness Mechanism and Its Application to the ChAMP Study

This paper is motivated by the analytical challenges we encounter when analyzing the ChAMP (Chondral Lesions And Meniscus Procedures) study, a randomized controlled trial to compare debridement to observation of chondral lesions in arthroscopic knee surgery. The main outcome, WOMAC (Western Ontario and McMaster Universities Osteoarthritis Index) pain score, is derived from the patient's responses to the questionnaire collected in the study. The major goal is to identify potentially important variables that contribute to this outcome. In this paper, the model of interest is a semiparametric model for the pain score. To address the missing data issue, we adopt a flexible missingness mechanism which is much more versatile in practice than a single parametric model. Then we propose a pairwise conditional likelihood approach to estimate the unknown parameter in the semiparametric model without the need of modeling its nonparametric counterpart nor the missingness mechanism. For variable selection we apply a regularization approach with a variety of stability enhanced tuning parameter selection methods. We conduct comprehensive simulation studies to evaluate the performance of the proposed method. We also apply the proposed method to the ChAMP study to demonstrate its usefulness.

Estimators based on Unconventional Likelihoods with Nonignorable Missing Data and its Application to a Children's Mental Health Study

Nonignorable missing-data is common in studies where the outcome is relevant to the subject's behavior. Ibrahim et al. (2001) fitted a logistic regression for a binary outcome subject to nonignorable missing data, and they proposed to replace the outcome in the mechanism model with an auxiliary variable that is completely observed. They had to correctly specify a model for the auxiliary variable; unfortunately the outcome variable subject to nonignorable missingness is still involved. The correct specification of this model is mysterious. Instead, we propose two unconventional likelihood based estimation procedures where the nonignorable missingness mechanism model could be completely bypassed. We apply our proposed methods to the children's mental health study and compare their performance with existing methods. The large sample properties of the proposed estimators are rigorously justified, and their finite sample behaviors are examined via comprehensive simulation studies.

A Comparison of High Dimensional Variable Selection Methods with Missing Covariates in a Prostate Cancer Study

Prostate cancer is the most common cancer in American men. Dozens of specific genes have been shown to be correlated to prostate cancer, to benign and non-benign cancer cases, from a biology perspective. In this paper, we apply a penalized logistic regression model with different penalty functions to select genes that contribute to benign and non-benign cases, based on the data from a prostate cancer study. The tuning parameter is determined by cross validation. In order to take into account some specific genes that have been classified as prostate cancer genes through biology research but with missing values, multiple imputation is adopted to create complete data sets. We analyze the prostate cancer data by comparing the selection results with completely observed data only, and the results with imputed data. We also conduct a simulation study to validate our proposed method.