Multiple imputation under Bayesianly smoothed pattern-mixture models for non-ignorable drop-out

Conventional pattern-mixture models can be highly sensitive to model misspecification. In many longitudinal studies, where the nature of the drop-out and the form of the population model are unknown, interval estimates from any single pattern-mixture model may suffer from undercoverage, because uncertainty about model misspecification is not taken into account. In this article, a new class of Bayesian random coefficient pattern-mixture models is developed to address potentially non-ignorable drop-out. Instead of imposing hard equality constraints to overcome inherent inestimability problems in pattern-mixture models, we propose to smooth the polynomial coefficient estimates across patterns using a hierarchical Bayesian model that allows random variation across groups. Using real and simulated data, we show that multiple imputation under a three-level linear mixed-effects model which accommodates a random level due to drop-out groups can be an effective method to deal with non-ignorable drop-out by allowing model uncertainty to be incorporated into the imputation process.     

Selection models and pattern-mixture models to analyse longitudinal quality of life data subject to drop-out

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 different set of parameters for the measurement and drop-out mechanisms. Since selection models and pattern-mixture models are based upon different factorizations of the joint distribution of measurement and drop-out mechanisms, comparing both models concerning, for example, treatment effect, is a useful form of a sensitivity analysis.     

Imputation-based strategies for clinical trial longitudinal data with nonignorable missing values

Biomedical research is plagued with problems of missing data, especially in clinical trials of medical and behavioral therapies adopting longitudinal design. After a literature review on modeling incomplete longitudinal data based on full-likelihood functions, this paper proposes a set of imputation-based strategies for implementing selection, pattern-mixture, and shared-parameter models for handling intermittent missing values and dropouts that are potentially nonignorable according to various criteria. Within the framework of multiple partial imputation, intermittent missing values are first imputed several times; then, each partially imputed data set is analyzed to deal with dropouts with or without further imputation. Depending on the choice of imputation model or measurement model, there exist various strategies that can be jointly applied to the same set of data to study the effect of treatment or intervention from multi-faceted perspectives. For illustration, the strategies were applied to a data set with continuous repeated measures from a smoking cessation clinical trial.     

The impact of missing data on estimation of health-related quality of life outcomes: an analysis of a randomized longitudinal clinical trial

Missing responses for health-related quality of life (HRQL) outcomes are common in clinical trials and may introduce bias as such data are often not missing at random. To evaluate the missingness (dropout) effect when comparing two treatment groups in a longitudinal randomized trial, we analyzed the Functional Assessment of Cancer Therapy Trial Outcome Index (TOI) change over 12 months for newly diagnosed patients with chronic myeloid leukemia. HRQL assessment was expected at baseline and months 1, 2, 3, 4, 5, 6, 9 and 12. We defined completers as those with baseline and month 12 TOI, and dropouts as all others as long as they had a baseline score. We defined censoring time as the time interval between baseline and the scheduled month 12 visit dates and approximate time-to-dropout as the time interval from baseline to the midpoint between date of the last reported TOI and the scheduled next visit date. A mixed-effects model was first built to assess treatment effect; a pattern-mixture model and a joint model were then built to account for non-ignorable dropout. Intermittent missing data were assumed to be missing at random. A square root transformation of TOI scores was taken to fulfill the normality and homogeneity assumption at each time point in all the models. The mixed-effects model revealed significant (P < 0.001) between-group differences at each visit except for baseline. The joint model generated similar parameter estimates as the separate longitudinal and survival sub-models with a significant association parameter (P = 0.039) indicating negative association between slope of TOI and hazard of dropout and thus non-ignorable dropout. The pattern-mixture model parameter estimates were fairly similar to those generated from the joint model. When non-ignorable missing data exist in longitudinal studies, a joint model is useful to quantify the relationship between dropout and outcome. In addition, it is important to examine underlying assumptions and utilize multiple missing data models including the pattern mixture model to assess sensitivity of model based inference to assumptions about missing mechanisms.     

A multiple imputation strategy for incomplete longitudinal data

Longitudinal studies are commonly used to study processes of change. Because data are collected over time, missing data are pervasive in longitudinal studies, and complete ascertainment of all variables is rare. In this paper a new imputation strategy for completing longitudinal data sets is proposed. The proposed methodology makes use of shrinkage estimators for pooling information across geographic entities, and of model averaging for pooling predictions across different statistical models. Bayes factors are used to compute weights (probabilities) for a set of models considered to be reasonable for at least some of the units for which imputations must be produced, imputations are produced by draws from the predictive distributions of the missing data, and multiple imputations are used to better reflect selected sources of uncertainty in the imputation process. The imputation strategy is developed within the context of an application to completing incomplete longitudinal variables in the so-called Area Resource File. The proposed procedure is compared with several other imputation procedures in terms of inferences derived with the imputations, and the proposed methodology is demonstrated to provide valid estimates of model parameters when the completed data are analysed. Extensions to other missing data problems in longitudinal studies are straightforward so long as the missing data mechanism can be assumed to be ignorable.     

脱落率加权调整在医学重复测量资料敏感性分析中的应用及其SAS程序实现

目的:探讨脱落率加权调整在医学重复测量资料敏感性分析中的应用和SAS实现过程。方法:运用SAS 9.4软件编写SAS程序,采用重复测量混合效应模型对多变量重复测量资料进行协方差分析;同时,分别引入试验总体脱落率和各组脱落率,构建基于脱落率加权调整的模式混合模型进行敏感性分析。结果:重复测量资料安慰剂组、低剂量组和高剂量...     

Bayesian consensus clustering for multivariate longitudinal data

In clinical and epidemiological studies, there is a growing interest in studying the heterogeneity among patients based on longitudinal characteristics to identify subtypes of the study population. Compared to clustering a single longitudinal marker, simultaneously clustering multiple longitudinal markers allow additional information to be incorporated into the clustering process, which reveals co-existing longitudinal patterns and generates deeper biological insight. In the current study, we propose a Bayesian consensus clustering (BCC) model for multivariate longitudinal data. Instead of arriving at a single overall clustering, the proposed model allows each marker to follow marker-specific local clustering and these local clusterings are aggregated to find a global (consensus) clustering. To estimate the posterior distribution of model parameters, a Gibbs sampling algorithm is proposed. We apply our proposed model to the primary biliary cirrhosis study to identify patient subtypes that may be associated with their prognosis. We also perform simulation studies to compare the clustering performance between the proposed model and existing models under several scenarios. The results demonstrate that the proposed BCC model serves as a useful tool for clustering multivariate longitudinal data.     

On the performance of random-coefficient pattern-mixture models for non-ignorable drop-out

Random-coefficient pattern-mixture models (RCPMMs) have been proposed for longitudinal data when drop-out is thought to be non-ignorable. An RCPMM is a random-effects model with summaries of drop-out time included among the regressors. The basis of every RCPMM is extrapolation. We review RCPMMs, describe various extrapolation strategies, and show how analyses may be simplified through multiple imputation. Using simulated and real data, we show that alternative RCPMMs that fit equally well may lead to very different estimates for parameters of interest. We also show that minor model misspecification can introduce biases that are quite large relative to standard errors, even in fairly small samples. For many scientific applications, where the form of the population model and nature of the drop-out are unknown, interval estimates from any single RCPMM may suffer from undercoverage because uncertainty about model specification is not taken into account.     

Linear discriminant models for unbalanced longitudinal data

This paper discusses statistical methods for the classification of observations into one of two or more groups based on longitudinal observations. Measurements on subjects in longitudinal medical studies are often collected at different times and on a different number of occasions. Classical multivariate methods for linear discriminant analysis are difficult to apply to repeated measurements due to the highly unbalanced structure observed in these data. Linear models for the analysis of longitudinal data proposed by Laird and Ware and non-linear models proposed by Lindstrom and Bates can be used to estimate population parameters for a discriminant model that classifies individuals into distinct predefined groups or populations. An example is presented using data from a study in 150 pregnant women in Santiago, Chile, in order to predict normal versus abnormal pregnancy outcomes.     

Influence analysis for skew‐normal semiparametric joint models of multivariate longitudinal and multivariate survival data

The normality assumption of measurement error is a widely used distribution in joint models of longitudinal and survival data, but it may lead to unreasonable or even misleading results when longitudinal data reveal skewness feature. This paper proposes a new joint model for multivariate longitudinal and multivariate survival data by incorporating a nonparametric function into the trajectory function and hazard function and assuming that measurement errors in longitudinal measurement models follow a skew‐normal distribution. A Monte Carlo Expectation‐Maximization (EM) algorithm together with the penalized‐splines technique and the Metropolis–Hastings algorithm within the Gibbs sampler is developed to estimate parameters and nonparametric functions in the considered joint models. Case deletion diagnostic measures are proposed to identify the potential influential observations, and an extended local influence method is presented to assess local influence of minor perturbations. Simulation studies and a real example from a clinical trial are presented to illustrate the proposed methodologies. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust estimation of partially linear models for longitudinal data with dropouts and measurement error

Outliers, measurement error, and missing data are commonly seen in longitudinal data because of its data collection process. However, no method can address all three of these issues simultaneously. This paper focuses on the robust estimation of partially linear models for longitudinal data with dropouts and measurement error. A new robust estimating equation, simultaneously tackling outliers, measurement error, and missingness, is proposed. The asymptotic properties of the proposed estimator are established under some regularity conditions. The proposed method is easy to implement in practice by utilizing the existing standard generalized estimating equations algorithms. The comprehensive simulation studies show the strength of the proposed method in dealing with longitudinal data with all three features. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition study and confirms the effectiveness of the intervention in producing weight loss at month 9. Copyright © 2016 John Wiley & Sons, Ltd.     

Latent trait shared-parameter mixed models for missing ecological momentary assessment data

Latent trait shared-parameter mixed models for ecological momentary assessment (EMA) data containing missing values are developed in which data are collected in an intermittent manner. In such studies, data are often missing due to unanswered prompts. Using item response theory models, a latent trait is used to represent the missing prompts and modeled jointly with a mixed model for bivariate longitudinal outcomes. Both one- and two-parameter latent trait shared-parameter mixed models are presented. These new models offer a unique way to analyze missing EMA data with many response patterns. Here, the proposed models represent missingness via a latent trait that corresponds to the students' “ability” to respond to the prompting device. Data containing more than 10 300 observations from an EMA study involving high school students' positive and negative affects are presented. The latent trait representing missingness was a significant predictor of both positive affect and negative affect outcomes. The models are compared to a missing at random mixed model. A simulation study indicates that the proposed models can provide lower bias and increased efficiency compared to the standard missing at random approach commonly used with intermittent missing longitudinal data.     

Non-linear models for the analysis of longitudinal data.

Given the importance of longitudinal studies in biomedical research, it is not surprising that considerable attention has been given to linear and generalized linear models for the analysis of longitudinal data. A great deal of attention has also been given to non-linear models for repeated measurements, particularly in the field of pharmacokinetics. In this article, a brief overview of non-linear models for the analysis of repeated measures is given. Particular emphasis is placed on mixed-effects non-linear models and on various estimation procedures proposed for such models. Several of these estimation procedures are compared via a simulation study. In addition, simulation is used to investigate the effects of model misspecification, particularly with respect to one's choice of random-effects. A relatively straightforward measure useful in selecting an appropriate set of random effects is investigated and found to perform reasonably well.     

Multiple outputation for the analysis of longitudinal data subject to irregular observation

Observational cohort studies often feature longitudinal data subject to irregular observation. Moreover, the timings of observations may be associated with the underlying disease process and must thus be accounted for when analysing the data. This paper suggests that multiple outputation, which consists of repeatedly discarding excess observations, may be a helpful way of approaching the problem. Multiple outputation was designed for clustered data where observations within a cluster are exchangeable; an adaptation for longitudinal data subject to irregular observation is proposed. We show how multiple outputation can be used to expand the range of models that can be fitted to irregular longitudinal data. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian analysis of nonlinear mixed‐effects mixture models for longitudinal data with heterogeneity and skewness

It is a common practice to analyze complex longitudinal data using nonlinear mixed‐effects (NLME) models with normality assumption. The NLME models with normal distributions provide the most popular framework for modeling continuous longitudinal outcomes, assuming individuals are from a homogeneous population and relying on random‐effects to accommodate inter‐individual variation. However, the following two issues may standout: (i) normality assumption for model errors may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates, particularly, if the data exhibit skewness and (ii) a homogeneous population assumption may be unrealistically obscuring important features of between‐subject and within‐subject variations, which may result in unreliable modeling results. There has been relatively few studies concerning longitudinal data with both heterogeneity and skewness features. In the last two decades, the skew distributions have shown beneficial in dealing with asymmetric data in various applications. In this article, our objective is to address the simultaneous impact of both features arisen from longitudinal data by developing a flexible finite mixture of NLME models with skew distributions under Bayesian framework that allows estimates of both model parameters and class membership probabilities for longitudinal data. Simulation studies are conducted to assess the performance of the proposed models and methods, and a real example from an AIDS clinical trial illustrates the methodology by modeling the viral dynamics to compare potential models with different distribution specifications; the analysis results are reported. Copyright © 2014 John Wiley & Sons, Ltd.     

A quasi F-test for functional linear models with functional covariates and its application to longitudinal data

Functional linear models are useful in analyzing data from designed experiments and observational studies with functional responses, as well as longitudinal data with a large number of repeated measures on each subject. We propose a quasi F-test for functional linear models with functional covariates and outcomes. We develop a numerical procedure and an efficient approximation for computing p-values, and present a simple way to test individual predictors. For illustration, we apply the proposed procedure to a longitudinal depression data set with repeatedly measured methamphetamine use as a predictor. We conduct a simulation study to assess the size and the power of the test.     

Investigation of one-stage meta-analysis methods for joint longitudinal and time-to-event data through simulation and real data application

Background: Joint modeling of longitudinal and time-to-event data is often advantageous over separate longitudinal or time-to-event analyses as it can account for study dropout, error in longitudinally measured covariates, and correlation between longitudinal and time-to-event outcomes. The current literature on joint modeling focuses mainly on the analysis of single studies with a lack of methods available for the meta-analysis of joint data from multiple studies. Methods: We investigate a variety of one-stage methods for the meta-analysis of joint longitudinal and time-to-event outcome data. These methods are applied to the INDANA dataset to investigate longitudinally measured systolic blood pressure, with each of time to death, time to myocardial infarction, and time to stroke. Results are compared to separate longitudinal or time-to-event meta-analyses. A simulation study is conducted to contrast separate versus joint analyses over a range of scenarios. Results: The performance of the examined one-stage joint meta-analytic models varied. Models that accounted for between study heterogeneity performed better than models that ignored it. Of the examined methods to account for between study heterogeneity, under the examined association structure, fixed effect approaches appeared preferable, whereas methods involving a baseline hazard stratified by study were least time intensive. Conclusions: One-stage joint meta-analytic models that accounted for between study heterogeneity using a mix of fixed effects or a stratified baseline hazard were reliable; however, models examined that included study level random effects in the association structure were less reliable.     

Marginalized models for longitudinal ordinal data with application to quality of life studies

Random effects are often used in generalized linear models to explain the serial dependence for longitudinal categorical data. Marginalized random effects models (MREMs) for the analysis of longitudinal binary data have been proposed to permit likelihood-based estimation of marginal regression parameters. In this paper, we propose a model to extend the MREM to accommodate longitudinal ordinal data. Maximum marginal likelihood estimation is proposed utilizing quasi-Newton algorithms with Monte Carlo integration of the random effects. Our approach is applied to analyze the quality of life data from a recent colorectal cancer clinical trial. Dropout occurs at a high rate and is often due to tumor progression or death. To deal with events due to progression/death, we used a mixture model for the joint distribution of longitudinal measures and progression/death times and use principal stratification to draw causal inferences about survivors.     

Principal interactions analysis for repeated measures data: application to gene-gene and gene-environment interactions

Many existing cohorts with longitudinal data on environmental exposures, occupational history, lifestyle/ behavioral characteristics, and health outcomes have collected genetic data in recent years. In this paper, we consider the problem of modeling gene-gene and gene-environment interactions with repeated measures data on a quantitative trait. We review possibilities of using classical models proposed by Tukey (1949) and Mandel (1961) using the cell means of a two-way classification array for such data. Although these models are effective for detecting interactions in the presence of main effects, they fail miserably if the interaction structure is misspecified. We explore a more robust class of interaction models that are based on a singular value decomposition of the cell-means residual matrix after fitting the additive main effect terms. This class of additive main effects and multiplicative interaction models (Gollob, 1968) provide useful summaries for subject-specific and time-varying effects as represented in terms of their contribution to the leading eigenvalues of the interaction matrix. It also makes the interaction structure more amenable to geometric representation. We call this analysis 'principal interactions analysis'. While the paper primarily focuses on a cell-mean-based analysis of repeated measures outcome, we also introduce resampling-based methods that appropriately recognize the unbalanced and longitudinal nature of the data instead of reducing the response to cell means. We illustrate the proposed methods by using data from the Normative Aging Study, a longitudinal cohort study of Boston area veterans since 1963. We carry out simulation studies under an array of classical interaction models and common epistasis models to illustrate the properties of the principal interactions analysis procedure in comparison with the classical alternatives. Copyright ? 2012 John Wiley & Sons, Ltd.     

Residuals analysis of the generalized linear models for longitudinal data

The generalized estimation equation (GEE) method, one of the generalized linear models for longitudinal data, has been used widely in medical research. However, the related sensitivity analysis problem has not been explored intensively. One of the possible reasons for this was due to the correlated structure within the same subject. We showed that the conventional residuals plots for model diagnosis in longitudinal data could mislead a researcher into trusting the fitted model. A non-parametric method, named the Wald-Wolfowitz run test, was proposed to check the residuals plots both quantitatively and graphically. The rationale proposedin this paper is well illustrated with two real clinical studies in Taiwan.