Doubly robust estimates for binary longitudinal data analysis with missing response and missing covariates

Causal inference for longitudinal data based on historical controls

Use of historical data has become a hot topic recently, considered to provide a way to reduce patient burden, lower drug development cost, and make innovative therapies available to patients earlier. In a single-arm study designed to examine the benefit of an experimental treatment, there is often a desire to compare the outcomes of patients receiving the new intervention with those receiving a control treatment, which can be extracted from sources such as historical trials or electronic medical records. Since the treatment is not randomly assigned, there is a need to adjust for the potential imbalance in key patient characteristics between the current study and historical controls. If the outcome of interest is measured longitudinally and subject to random missing, the required adjustment becomes more complicated. In this paper, we propose a doubly robust adjustment procedure specifically designed for longitudinal data analysis with missing data. The proposed method yields valid analysis results, if either the propensity score model or the mixed effects model for repeated measures (MMRM) regression model is correctly specified. An extensive numerical study is conducted to examine the performance of the proposed method. Data from a real clinical trial comparing with historical data are analyzed as an example applying the proposed procedure.

Weighted generalized estimating equations and unified estimation for longitudinal data with nonmonotone missing data patterns

Missing data are a major complication in longitudinal data analysis. Weighted generalized estimating equations (WGEEs, Robins et al, J Am Stat Assoc 1995;90:106-121) were developed to deal with missing response data. They have been extended for data with both missing responses and missing covariates (Chen et al, J Am Stat Assoc 2010;105:336-353). However, it may introduce more variability in dealing with the correlation structure of the responses. We propose new WGEEs for missing at random data where both response and (time-dependent) covariates may have values missing in nonmonotone missing data patterns. We also explain how to improve the estimation efficiency of WGEEs using a unified approach (Zhao and Liu, AStA Adv Stat Anal 2021;105(1):87-101). The proposed unified estimator is consistent and more efficient than the regular WGEE estimator. It is computationally simple and can be directly implemented in standard software. Simulation studies for both continuous response and binary response data are provided to examine the performance of the proposed estimators. A clinical trial example investigating the quality of life of women with early-stage breast cancer and the associated factors is analyzed.

Bayesian semi-parametric G-computation for causal inference in a cohort study with MNAR dropout and death

Causal inference with observational longitudinal data and time-varying exposures is often complicated by time-dependent confounding and attrition. The G-computation formula is one approach for estimating a causal effect in this setting. The parametric modeling approach typically used in practice relies on strong modeling assumptions for valid inference, and moreover depends on an assumption of missing at random, which is not appropriate when the missingness is missing not at random (MNAR) or due to death. In this work we develop a flexible Bayesian semi-parametric G-computation approach for assessing the causal effect on the subpopulation that would survive irrespective of exposure, in a setting with MNAR dropout. The approach is to specify models for the observed data using Bayesian additive regression trees, and then use assumptions with embedded sensitivity parameters to identify and estimate the causal effect. The proposed approach is motivated by a longitudinal cohort study on cognition, health, and aging, and we apply our approach to study the effect of becoming a widow on memory. We also compare our approach to several standard methods.

A multiple robust propensity score method for longitudinal analysis with intermittent missing data

Longitudinal data are very popular in practice, but they are often missing in either outcomes or time-dependent risk factors, making them highly unbalanced and complex. Missing data may contain various missing patterns or mechanisms, and how to properly handle it for unbiased and valid inference still presents a significant challenge. Here, we propose a novel semiparametric framework for analyzing longitudinal data with both missing responses and covariates that are missing at random and intermittent, a general and widely encountered situation in observational studies. Within this framework, we consider multiple robust estimation procedures based on innovative calibrated propensity scores, which offers additional relaxation of the misspecification of missing data mechanisms and shows more satisfactory numerical performance. Also, the corresponding robust information criterion on consistent variable selection for our proposed model is developed based on empirical likelihood-based methods. These advocated methods are evaluated in both theory and extensive simulation studies in a variety of situations, showing competing properties and advantages compared to the existing approaches. We illustrate the utility of our approach by analyzing the data from the HIV Epidemiology Research Study.

An R package for model fitting, model selection and the simulation for longitudinal data with dropout missingness

Missing data arise frequently in clinical and epidemiological fields, in particular in longitudinal studies. This paper describes the core features of an R package wgeesel, which implements marginal model fitting (i.e., weighted generalized estimating equations, WGEE; doubly robust GEE) for longitudinal data with dropouts under the assumption of missing at random. More importantly, this package comprehensively provide existing information criteria for WGEE model selection on marginal mean or correlation structures. Also, it can serve as a valuable tool for simulating longitudinal data with missing outcomes. Lastly, a real data example and simulations are presented to illustrate and validate our package.

A general GEE framework for the analysis of longitudinal ordinal missing data and related issues

Generalized estimating equations (GEEs) are a well-known method for the analysis of categorical longitudinal data. This method presents computational simplicity and provides consistent parameter estimates that have a population-averaged interpretation. However, with missing data, the resulting parameter estimates are consistent only under the strong assumption of missing completely at random (MCAR). Some corrections can be done when the missing data mechanism is missing at random (MAR): inverse probability weighting GEE (WGEE) and multiple imputation GEE (MIGEE). A recent method combining ideas of these two approaches has a doubly robust property in the sense that one only needs to correctly specify the weight or the imputation model in order to obtain consistent estimates for the parameters. In this work, a proportional odds model is assumed and a doubly robust estimator is proposed for the analysis of ordinal longitudinal data with intermittently missing responses and covariates under the MAR mechanism. In addition, the association structure is modelled by means of either the correlation coefficient or local odds ratio. The performance of the proposed method is compared to both WGEE and MIGEE through a simulation study. The method is applied to a dataset related to rheumatic mitral stenosis.

Estimation of response from longitudinal binary data with nonignorable missing values in migraine trials

In migraine trials pain relief responses from a headache at specific time points and sustained pain relief response over a period of time are important efficacy measures. When there are missing records of individual time point pain scores and/or headache recurrences during a migraine trial, the common approach used in practice to estimate the sustained response is statistically inconsistent even if the data are missing completely at random. Methods dealing with nonignorable longitudinal missing data usually assume certain models for the missing mechanism which can not be checked as they involve unobserved data. Taking advantage of the specific definition of the 'sustained pain relief' response, we propose two estimating methods based on intuitive imputation, which do not require model assumptions on the missing probability or specification of the correlation structure among the longitudinal observations. The consistency of the proposed methods is discussed in theory and their empirical performances are assessed through intensive simulation studies. The simulation results show that the proposed methods perform well in terms of reducing bias and mean square error except in several extreme cases which are unlikely to happen in real trials. The application of the proposed methods is illustrated in a real data analysis.

Dealing with missing covariates in epidemiologic studies: a comparison between multiple imputation and a full Bayesian approach

Incomplete data are generally a challenge to the analysis of most large studies. The current gold standard to account for missing data is multiple imputation, and more specifically multiple imputation with chained equations (MICE). Numerous studies have been conducted to illustrate the performance of MICE for missing covariate data. The results show that the method works well in various situations. However, less is known about its performance in more complex models, specifically when the outcome is multivariate as in longitudinal studies. In current practice, the multivariate nature of the longitudinal outcome is often neglected in the imputation procedure, or only the baseline outcome is used to impute missing covariates. In this work, we evaluate the performance of MICE using different strategies to include a longitudinal outcome into the imputation models and compare it with a fully Bayesian approach that jointly imputes missing values and estimates the parameters of the longitudinal model. Results from simulation and a real data example show that MICE requires the analyst to correctly specify which components of the longitudinal process need to be included in the imputation models in order to obtain unbiased results. The full Bayesian approach, on the other hand, does not require the analyst to explicitly specify how the longitudinal outcome enters the imputation models. It performed well under different scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

Test the reliability of doubly robust estimation with missing response data

In statistical inference, one has to make sure that the underlying regression model is correctly specified otherwise the resulting estimation may be biased. Model checking is an important method to detect any departure of the regression model from the true one. Missing data are a ubiquitous problem in social and medical studies. If the underlying regression model is correctly specified, recent researches show great popularity of the doubly robust (DR) estimates method for handling missing data because of its robustness to the misspecification of either the missing data model or the conditional mean model, that is, the model for the conditional expectation of true regression model conditioning on the observed quantities. However, little work has been devoted to the goodness of fit test for DR estimates method. In this article, we propose a testing method to assess the reliability of the estimator derived from the DR estimating equation with possibly missing response and always observed auxiliary variables. Numerical studies demonstrate that the proposed test can control type I errors well. Furthermore the proposed method can detect departures from model assumptions in the marginal mean model of interest powerfully. A real dementia data set is used to illustrate the method for the diagnosis of model misspecification in the problem of missing response with an always observed auxiliary variable for cross-sectional data.

Marginal methods for clustered longitudinal binary data with incomplete covariates

Many analyses for incomplete longitudinal data are directed to examining the impact of covariates on the marginal mean responses. We consider the setting in which longitudinal responses are collected from individuals nested within clusters. We discuss methods for assessing covariate effects on the mean and association parameters when covariates are incompletely observed. Weighted first and second order estimating equations are constructed to obtain consistent estimates of mean and association parameters when covariates are missing at random. Empirical studies demonstrate that estimators from the proposed method have negligible finite sample biases in moderate samples. An application to the National Alzheimer's Coordinating Center (NACC) Uniform Data Set (UDS) demonstrates the utility of the proposed method.

A latent-variable marginal method for multi-level incomplete binary data

Incomplete multi-level data arise commonly in many clinical trials and observational studies. Because of multi-level variations in this type of data, appropriate data analysis should take these variations into account. A random effects model can allow for the multi-level variations by assuming random effects at each level, but the computation is intensive because high-dimensional integrations are often involved in fitting models. Marginal methods such as the inverse probability weighted generalized estimating equations can involve simple estimation computation, but it is hard to specify the working correlation matrix for multi-level data. In this paper, we introduce a latent variable method to deal with incomplete multi-level data when the missing mechanism is missing at random, which fills the gap between the random effects model and marginal models. Latent variable models are built for both the response and missing data processes to incorporate the variations that arise at each level. Simulation studies demonstrate that this method performs well in various situations. We apply the proposed method to an Alzheimer's disease study.