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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 modelling approach typically used in practice relies on strong modelling 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 ageing and we apply our approach to study the effect of becoming a widow on memory. We also compare our approach to several standard methods. [ABSTRACT FROM AUTHOR]

We develop and study an innovative method for jointly modeling longitudinal response and time-to-event data with a covariate subject to a limit of detection. The joint model assumes a latent process based on random effects to describe the association between longitudinal and time-to-event data. We study the role of the association parameter on the regression parameters estimators. We model the longitudinal and survival outcomes using linear mixed-effects and Weibull frailty models, respectively. Because of the limit of detection, missing covariate (explanatory variable, x) values may lead to the non-ignorable missing, resulting in biased parameter estimates with poor coverage probabilities of the confidence interval. We define and estimate the probability of missing due to the limit of detection. Then we develop a novel joint density and hence the likelihood function that incorporates the effect of left-censored covariate. Monte Carlo simulations show that the estimators of the proposed method are approximately unbiased and provide expected coverage probabilities for both longitudinal and survival submodels parameters. We also present an application of the proposed method using a large clinical dataset of pneumonia patients obtained from the Genetic and Inflammatory Markers of Sepsis study. [ABSTRACT FROM AUTHOR]

In this paper, a general regression model with responses missing not at random is considered. From a rank-based estimating equation, a rank-based estimator of the regression parameter is derived. Based on this estimator's asymptotic normality property, a consistent sandwich estimator of its corresponding asymptotic covariance matrix is obtained. In order to overcome the over-coverage issue of the normal approximation procedure, the empirical likelihood based on the rank-based gradient function is defined, and its asymptotic distribution is established. Extensive simulation experiments under different settings of error distributions with different response probabilities are considered, and the simulation results show that the proposed empirical likelihood approach has better performance in terms of coverage probability and average length of confidence intervals for the regression parameters compared with the normal approximation approach and its least-squares counterpart. A data example is provided to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

A longitudinal study commonly follows a set of variables, measured for each individual repeatedly over time, and usually suffers from incomplete data problem. A common approach for dealing with longitudinal categorical responses is to use the Generalized Linear Mixed Model (GLMM). This model induces the potential relation between response variables over time via a vector of random effects, assumed to be shared parameters in the non-ignorable missing mechanism. Most GLMMs assume that the random-effects parameters follow a normal or symmetric distribution and this leads to serious problems in real applications. In this paper, we propose GLMMs for the analysis of incomplete multivariate longitudinal categorical responses with a non-ignorable missing mechanism based on a shared parameter framework with the less restrictive assumption of skew-normality for the random effects. These models may contain incomplete data with monotone and non-monotone missing patterns. The performance of the model is evaluated using simulation studies and a well-known longitudinal data set extracted from a fluvoxamine trial is analyzed to determine the profile of fluvoxamine in ambulatory clinical psychiatric practice. [ABSTRACT FROM AUTHOR]

This paper considers several robust estimators for distribution functions and quantiles of a response variable when some responses may not be observed under the non-ignorable missing data mechanism. Based on a particular semiparametric regression model for non-ignorable missing response, we propose a nonparametric/semiparametric estimation method and an augmented inverse probability weighted imputation method to estimate the distribution function and quantiles of a response variable. Under some regularity conditions, we derive asymptotic properties of the proposed distribution function and quantile estimators. Two empirical log-likelihood functions are also defined to construct confidence intervals for distribution function of a response variable. Simulation studies show that our proposed methods are robust. In particular, the semiparametric estimator is more efficient than the nonparametric estimator, and the inverse probability weighted imputation estimator is bias-corrected. The Canadian Journal of Statistics 41: 575-595; 2013 © 2013 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

In longitudinal studies, missingness of data is often unavoidable. Valid estimators from the generalized linear mixed model usually rely on the correct specification of the missing data mechanism. An incorrectly specified missing mechanism may lead to a biased estimator. In this article, we propose a class of unbiased estimating equations using pairwise conditional technique to deal with the generalized linear mixed model under benign non-ignorable missingness where specification of the missing model is not needed. We show that the proposed estimator is consistent and asymptotically normal under certain conditions. Simulation results and an example using longitudinal course of neuropsychological data are also shown. [ABSTRACT FROM AUTHOR]

OSWALD (Object-oriented Software for the Analysis of Longitudinal Data) is flexible and powerful software written for S-PLUS for the analysis of longitudinal data with dropout for which there is little other software available in the public domain. The implementation of OSWALD is described through analysis of a psychiatric clinical trial that compares antidepressant effects in an elderly depressed sample and a simulation study. In the simulation study, three different dropout mechanisms: completely random dropout (CRD), random dropout (RD) and informative dropout (ID), are considered and the results from using OSWALD are compared across mechanisms. The parameter estimates for ID-simulated data show less bias with OSWALD under the ID missing data assumption than under the CRD or RD assumptions. Under an ID mechanism, OSWALD does not provide standard error estimates. We supplement OSWALD with a bootstrap procedure to derive the standard errors. This report illustrates the usage of OSWALD for analyzing longitudinal data with dropouts and how to draw appropriate conclusions based on the analytic results under different assumptions regarding the dropout mechanism. [Copyright &y& Elsevier]

Clinical trials comparing treatments that follow patients over a period of time often suffer from dropouts. In some cases, these dropouts are treatment related. It may be due to clinical improvement or deterioration. Such dropouts contribute partial information regarding the effectiveness of the treatment and should be included in the analysis appropriately. The methods proposed in the literature for such situations, such as the last observation carried forward method, the regression prediction method, etc., require assumptions that may be weak. When treatment related dropouts occur the distribution of the observations often resemble a truncated normal. Traditionally, dropouts would be treated as missing, and imputation methods would be applied for the missing data. Here, as an alternative, a method for analyzing the data under a truncated multivariate normal distribution is proposed. An Expectation-Maximization (EM) algorithm is applied to simplify the estimation of the truncated normal likelihood and to utilize standard software (such as SAS) for the analysis. A data set from a collaborative study conducted by the National Institute of Mental Health is used to illustrate the method. Some of the traditional methods are compared. [ABSTRACT FROM AUTHOR]