A Bayesian model for longitudinal count data with non-ignorable dropout (original) (raw)
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A Bayesian Approach for Clustered Longitudinal Ordinal Outcome With Nonignorable Missing Data
Journal of the American Statistical Association, 2006
Asthma, a chronic inflammatory disease of the airways, affects an estimated 6.3 million children under age 18 in the United States. A key to successful asthma management, and hence improved quality of life (QOL), calls for an active partnership between asthma patients and their health care providers. To foster this partnership, an intervention program was designed and evaluated using a randomized longitudinal study. The study focused on several outcomes where typically missing data remained a pervasive problem. We suspected that the underlying missing-data mechanism may not be ignorable. Thus here we present a method for analyzing clustered longitudinal data with missing values resulting from a nonignorable missing-data mechanism. The transition Markov model with random effects was used to investigate changes in ordinal outcomes over time. A Bayesian pattern-mixture model with the flexibility to incorporate models for missing data in both outcome and time-varying covariates was used to model the nonignorable missing-data mechanism. The pattern-mixture model uses easy-to-understand parameters-namely, ratios of the cumulative odds across patterns with the complete-data pattern-as the reference pattern. Sensitivity analysis was performed using different prior distributions for the parameters. A fully Bayesian approach was derived by integrating over a class of prior distributions. The data from the Asthma Intervention Study were analyzed to explore the effect of the intervention program on improving QOL.
Behavior Research Methods, 2023
Valid inference can be drawn from a random-effects model for repeated measures that are incomplete if whether the data are missing or not, known as missingness, is independent of the missing data. Data that are missing completely at random or missing at random are two data types for which missingness is ignorable. Given ignorable missingness, statistical inference can proceed without addressing the source of the missing data in the model. If the missingness is not ignorable, however, recommendations are to fit multiple models that represent different plausible explanations of the missing data. A popular choice in methods for evaluating nonignorable missingness is a random-effects pattern-mixture model that extends a randomeffects model to include one or more between-subjects variables that represent fixed patterns of missing data. Generally straightforward to implement, a fixed pattern-mixture model is one among several options for assessing nonignorable missingness, and when it is used as the sole model to address nonignorable missingness, understanding the impact of missingness is greatly limited. This paper considers alternatives to a fixed pattern-mixture model for nonignorable missingness that are generally straightforward to fit and encourage researchers to give greater attention to the possible impact of nonignorable missingness in longitudinal data analysis. Patterns of both monotonic and non-monotonic (intermittently) missing data are addressed. Empirical longitudinal psychiatric data are used to illustrate the models. A small Monte Carlo data simulation study is presented to help illustrate the utility of such methods.
Bayesian sensitivity analysis of incomplete data: bridging pattern-mixture and selection models
Statistics in medicine, 2014
Pattern-mixture models (PMM) and selection models (SM) are alternative approaches for statistical analysis when faced with incomplete data and a nonignorable missing-data mechanism. Both models make empirically unverifiable assumptions and need additional constraints to identify the parameters. Here, we first introduce intuitive parameterizations to identify PMM for different types of outcome with distribution in the exponential family; then we translate these to their equivalent SM approach. This provides a unified framework for performing sensitivity analysis under either setting. These new parameterizations are transparent, easy-to-use, and provide dual interpretation from both the PMM and SM perspectives. A Bayesian approach is used to perform sensitivity analysis, deriving inferences using informative prior distributions on the sensitivity parameters. These models can be fitted using software that implements Gibbs sampling.
Bayesian Pattern Mixture Model for Longitudinal Binary Data with Nonignorable Missingness
Communications for Statistical Applications and Methods, 2015
In longitudinal studies missing data are common and require a complicated analysis. There are two popular modeling frameworks, pattern mixture model (PMM) and selection models (SM) to analyze the missing data. We focus on the PMM and we also propose Bayesian pattern mixture models using generalized linear mixed models (GLMMs) for longitudinal binary data. Sensitivity analysis is used under the missing not at random assumption.
Biostatistics, 2005
In this work, we fit pattern-mixture models to data sets with responses that are potentially missing not at random (MNAR, Little and Rubin, 1987). In estimating the regression parameters that are identifiable, we use the pseudo maximum likelihood method based on exponential families. This procedure provides consistent estimators when the mean structure is correctly specified for each pattern, with further information on the variance structure giving an efficient estimator. The proposed method can be used to handle a variety of continuous and discrete outcomes. A test built on this approach is also developed for model simplification in order to improve efficiency. Simulations are carried out to compare the proposed estimation procedure with other methods. In combination with sensitivity analysis, our approach can be used to fit parsimonious semi-parametric pattern-mixture models to outcomes that are potentially MNAR. We apply the proposed method to an epidemiologic cohort study to examine cognition decline among elderly.
A Bayesian approach to analyse overdispersed longitudinal count data
Journal of Applied Statistics, 2015
In this paper, we consider a model for repeated count data, with within-subject correlation and/or overdispersion. It extends both the generalized linear mixed model and the negative-binomial model. This model, proposed in a likelihood context [17,18] is placed in a Bayesian inferential framework. An important contribution takes the form of Bayesian model assessment based on pivotal quantities, rather than the often less adequate DIC. By means of a real biological data set, we also discuss some Bayesian model selection aspects, using a pivotal quantity proposed by Johnson [12].
Statistics in Medicine, 2002
Longitudinally observed quality of life data with large amounts of drop-out are analysed. First we used the selection modelling framework, frequently used with incomplete studies. An alternative method consists of using pattern-mixture models. These are also straightforward to implement, but result in a di erent set of parameters for the measurement and drop-out mechanisms. Since selection models and pattern-mixture models are based upon di erent factorizations of the joint distribution of measurement and drop-out mechanisms, comparing both models concerning, for example, treatment e ect, is a useful form of a sensitivity analysis. 1024 B. MICHIELS ET AL.
A Bayesian model for time-to-event data with informative censoring
Biostatistics, 2012
Randomized trials with dropouts or censored data and discrete time-to-event type outcomes are frequently analyzed using the Kaplan-Meier or product limit (PL) estimation method. However, the PL method assumes that the censoring mechanism is noninformative and when this assumption is violated, the inferences may not be valid. We propose an expanded PL method using a Bayesian framework to incorporate informative censoring mechanism and perform sensitivity analysis on estimates of the cumulative incidence curves. The expanded method uses a model, which can be viewed as a pattern mixture model, where odds for having an event during the follow-up interval (t k−1 , t k ], conditional on being at risk at t k−1 , differ across the patterns of missing data. The sensitivity parameters relate the odds of an event, between subjects from a missing-data pattern with the observed subjects for each interval. The large number of the sensitivity parameters is reduced by considering them as random and assumed to follow a log-normal distribution with prespecified mean and variance. Then we vary the mean and variance to explore sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the expanded model, thus allowing exploration of the sensitivity to inferences as departures from the inferences under the MAR assumption. The proposed approach is applied to data from the TRial Of Preventing HYpertension.
Application of random-effects pattern-mixture models for missing data in longitudinal studies
Psychological Methods, 1997
Random-effects regression models have become increasingly popular for analysis of longitudinal data. A key advantage of the random-effects approach is that it can be applied when subjects are not measured at the same number of timepoints. In this article we describe use of random-effects pattern-mixture models to further handle and describe the influence of missing data in longitudinal studies. For this approach, subjects are first divided into groups depending on their missing-data pattern and then variables based on these groups are used as model covariates. Tn this way, researchers are able to examine the effect of missing-data patterns on the outcome (or outcomes) of interest. Furthermore, overall estimates can be obtained by averaging over the missing-data patterns. A psychiatric clinical trials data set is used to illustrate the random-effects pattern-mixture approach to longitudinal data analysis with missing data.
A Bayesian nonparametric model for count functional data
2012
Count functional data arise in a variety of applications, including longitudinal, spatial and imaging studies measuring functional count responses for each subject under study. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applications, and hierarchical Poisson models make restrictive assumptions about over-dispersion in marginal distributions. This article discuss a class of nonparametric Bayes count functional data models introduced in Canale and Dunson , which are constructed through rounding real-valued underlying processes. Computational algorithms are developed using Markov chain Monte Carlo and the methods are illustrated through application to asthma inhaler usage.