Bayesian pattern-mixture models for dropout and intermittently missing data in longitudinal data analysis

Missing data and especially dropouts frequently arise in longitudinal data. Maximum likelihood estimates are consistent when data are missing at random (MAR) but, as this assumption is not checkable, pattern mixture models (PMM) have been developed to deal with informative dropout. More recently, latent class models (LCM) have been proposed as a way to relax PMM assumptions. The aim of this paper is to compare PMM and LCM in order to tackle informative dropout in a longitudinal study of cognitive ageing measured by several psychometric tests. Using a multivariate longitudinal model with a latent process, a sensitivity analysis was performed to compare estimates under the MAR assumption, from a PMM and from two LCM. In the PMM, dropout patterns are included as covariates in the multivariate longitudinal model. In the simple LCM, they are predictors of the class membership probabilities while, in the joint LCM, the dropout time is jointly modeled using a proportional hazard model depending on latent classes. We show that parameter interpretation is different in the two kinds of models and thus can lead to different estimated values. PMM parameters are adjusted on the dropout patterns while LCM parameters are adjusted on the latent classes. This difference is highlighted in our data set because the latent classes exhibit much more heterogeneity than dropout patterns. We suggest several complementary analyses to investigate the characteristics of latent classes in order to understand the meaning of the parameters when using LCM to deal with informative dropout.

The analysis of longitudinal data with non-ignorable missingness remains an active area in biostatistics research. This article discusses various random effects and latent process models which have been proposed for analyzing longitudinal binary data subject to both non-ignorable intermittent missing data and dropout. These models account for non-ignorable missingness by introducing random effects or a latent process which is shared between the response model and the model for the missing-data mechanism. We discuss various random effects and latent processes approaches and compare these approaches with analyses from an opiate clinical trial data set, which had high proportion of intermittent missingness and dropout. We also compare these random effect and latent process approaches with other methods for accounting for non-ignorable missingness using this data set.

Longitudinal designs for biomarker traits are very appealing for a number of reasons. First, the collection of repeated biomarker measurements over time allows investigators to characterize both the overall and individual trajectories in these measurements. This helps investigators to understand overall effects as well as how individuals vary around these average effects. Distinguishing individual heterogeneity from average trend is impossible without longitudinal data. This distinction is important for understanding individual between-subject in its own right, as well as in developing predictors of disease outcome from longitudinal marker data. There are many statistical issues that are unique to longitudinal data analysis ranging from correctly specifying realistic models which characterize average changes over time and individual variation, accounting for observations that are taken at unequally spaced observation times which may differ between individuals, to accounting for missing data due to occasionally missed measurements or loss to follow-up. When the reason for missing data is not related to the underlying observation process, most longitudinal data analysis methods can be routinely applied. However, complex modelling is necessary when the reason for missing an observation or dropout is directly related to the underlying outcome process [1–2]. Statistical techniques that appropriately analyze continuous and discrete longitudinal data have been discussed by many authors. Diggle, et al. [3] provides a good summary of these techniques for the practitioner, while Fitzmaurice et al. [4] discusses recent advances from a more technical perspective. The three papers in this section present innovative approaches for solving important methodological problems in biomarker studies. Most standard longitudinal data analysis techniques assume that the measurement process is independent of the outcome process. However, when the outcome is related to the underlying observation process, failure to properly account for the observation process can result in bias [5]. Schildcrout et al.[6] proposed an approach for regression modelling for longitudinal binary data where the outcome is measured with probabilities determined by an auxiliary variable that is related, but not identical to the binary outcome. Modelling multivariate longitudinal biomarker data is an increasingly common issue with the advent of an increasing number of important biomarker techniques (e.g., multiple cytokines in a multiplex assay or multiple reproductive hormones that describe complex biological phenomenon). Although various authors have proposed techniques for analyzing multivariate longitudinal data [7–8 and others], little work has focused on estimating multivariate linear mixed models under known constraints in the relationship between the multivariate outcomes. Roy et al [9] proposes such an approach for analyzing multivariate reproductive hormones over the menstrual cycle, where established relationships have solid biological justification. Finally, the collection of longitudinal biomarker data as disease predictors is becoming an increasingly important design in diagnostic medicine. Pfeiffer et al. [10] proposes flexible non-parametric methodology for combining biomarkers that exploits the longitudinal structure in formulating a score that is used for predicting a binary outcome.

A reanalysis of a longitudinal scleroderma clinical trial using non-ignorable missingness models

Analysis of binary longitudinal data with time-varying effects

Longitudinal semicontinuous data, characterized by repeated measures of a large portion of zeros and continuous positive values, are frequently encountered in many applications including biomedical, epidemiological, and social science studies. Two-part random effects models (TPREM) have been used to investigate the association between such longitudinal semicontinuous data and covariates accounting for the within-subject correlation. The existing TPREM is, however, limited to incorporate a functional covariate, which is often available in a longitudinal study. Moreover, the existing TPREM typically assumes the normality of subject-specific random effects, which can be easily violated when there exists a subgroup structure. In this article, we propose a nonparametric Bayesian functional TPREM to assess the relationship between the longitudinal semicontinuous outcome and various types of covariates including a functional covariate. The proposed model also relaxes the normality assumption for the random effects through a Dirichlet process mixture of normals, which allows for identifying an underlying subgroup structure. The methodology is illustrated through an application to social insurance expenditure data collected by the Korean Welfare Panel Study and a simulation study.

Analysis of ordinal longitudinal data under nonignorable missingness and misreporting: An application to Alzheimer’s disease study

The context of this thesis explores efficiency measures in higher education (HE) in England. Measures of efficiency serve as a crucial link between the economic sustainability of the HE sector and the policymaking establishment. Given that the idea of efficient allocation of resources, in a period of tighter budget constraints, curtailed government funding and increasing competition for a greater share for research funding and number of students has such a powerful influence, the concept of efficiency becomes meaningful serving as a basis for decisions to improve resource allocation. Understanding the nature of efficiency aims to put in place a simpler and more efficient HE and research system in England that encourages competition and choice, enhances quality, and ensures greater accountability and value for money. The thesis unfolds two main disciplines of technical and cost efficiency in HE in England. Therefore the research objectives discussed are driven upon that conceptualization of efficiency and provide further insights into first, the effects of merger activity on efficiency, and second on whether permanent or transient (in) efficiency dominates the English HE sector. Those topics are key aspects and critically important for both policy change and ongoing institutional and structural reform and as thus are explored in the lines of this thesis. Regarding the first research objective on the potential effect of mergers on Higher Education Institutions’ (HEIs) efficiency, in a first stage analysis efficiency scores of English universities are derived for a 17-year period using the frontier estimation method data envelopment analysis (DEA). A second stage analysis explores the effect of merger and other factors on efficiency. We find that mean efficiency for the sector has varied around 60 percent to 70 percent, but that the efficiency levels of the vast majority of individual HEIs are not significantly different from each other. Merged HEIs have efficiency which is 5 percentage points higher post-merger than non-merging HEIs holding all else constant; moreover the efficiency impact of merger comes within 2 years of the merger taking place. Of the other factors included in the second stage analysis, pre-1992 universities have lower efficiency than other types of institution. In addition, having a higher proportion of income from government sources is an incentive to greater efficiency. Finally, a sensitivity analysis was conducted which exposed the post-merger efficiency results to a different method assessment as a validation test of the proposed policy implications. The sensitivity analysis resulted in confirming the main findings of efficiency improvements in the units received the treatment of merger. Turning to the second research objective, a common weakness in most of the models dealing with efficiency is their deficiency to account for unobserved heterogeneity that finally lead to biased efficiency estimates. Most of the cost efficiency frontier models, focused either on the transient or on the persistent part of cost inefficiency, confounding firm effects (that are not part of inefficiency) with persistent inefficiency or blending persistent inefficiency with latent heterogeneity. However a decomposition of the two parts, persistent (long –term) and transient/residual (short-term) inefficiencies, provides an in-depth analysis of whether short term practises or more long term structural changes within colleges and universities affect the degree of cost efficiency in the English HE sector. This distinction seems to be further appealing to the policy makers as a regulatory asset that aims at improving the efficiency of the sector through incentive reforms. Hence, more recent developments in panel data allow a further appealing distinction in the cost efficiency of HEIs in which unobserved firm effects (firm heterogeneity) can be disentangled from time invariant and time varying inefficiency. Hence the purpose of this thesis is partly to assess the level of persistent and transient inefficiency in the English HE sector from 2008/09 to 2013/14 by using a four-way error component model (persistent and transient inefficiency, random firm effects and noise) and so as to retain the apparatus of statistical inference stemming from a generalised true random effects (GTRE) model based on maximum simulated likelihood (MSL) techniques. In order to provide evidence that the aforementioned method ameliorates the predicted power of the model we offer a comparative study through the fundamental models applied in the literature so far. Consequently, statistical inference will be attempted by countering the efficiency estimates of a GRTE model with a random effects (RE) model proposed by Pitt and Lee (1981), informative on the persistent part, and a true random effects model (TRE) proposed by Greene (2005a, 2005b), enlightening the transient part. Finally, omitted variables bias will be controlled by implementing a MGTRE model, minimizing the resulting heterogeneity bias. The comparison reinforces the validity of the GTRE model since it captures every single component of inefficacy while heterogeneity is controlled. For the English HE inefficiency is considered as persistent since short-run efficiency estimates are proven to be higher than the long-run. This gives further rise for more comprehensive and structural changes rather than simple mechanisms for short-term cost savings.

The last-observation-carried-forward imputation method is commonly used for imputing data missing due to dropouts in longitudinal clinical trials. The method assumes that outcome remains constant at the last observed value after dropout which is unlikely in many clinical trials. Recently, random-effects regression models have become popular for analysis of longitudinal clinical trial data with dropouts. However, inference obtained from random-effects regression models is valid when the missing-at-random dropout process is present. The random-effects pattern-mixture model, on the other hand provides an approach that is valid under more general missingness mechanisms. In this article we describe the use of random-effects pattern-mixture models under different patterns for dropouts. First, subjects are divided into groups depending on their missing-data patterns and then model parameters are estimated for each pattern. Finally, overall estimates are obtained by averaging over the missing-data patterns and corresponding standard errors are obtained using the delta method. A typical longitudinal clinical trial data set is used to illustrate and compare the above methods of data analyses in the presence of missing data due to dropouts.

PurposeThe purpose of this paper is to examine the relationship between corporate social responsibility (CSR) and corporate financial performance (CFP) of Malaysian public listed companies (PLCs) as an emerging market setting.Design/methodology/approachA longitudinal data analysis with a large‐sample testing was carried out from 200 Malaysian PLCs by using panel data analysis during a seven‐years period. The statistical power with fixed effect and random effect model was utilized.FindingsResults of earlier estimations indicate that there are positive and significant related of the CSR on CFP. Two of the CSR dimensions, namely employee relations and community involvement, were found to be positively related to financial performance. This proves that CSR practices can be considered as effort to enhance the financial performance of PLCs in Malaysia. The results also reveal that there is limited evidence of the relationship between CSR and CFP in the longterm.Practical implicationsThese findings suggest that Malaysian PLCs should be involved consistently in their CSR practices because CSR has a significant impact on improving financial performance in Malaysian PLCs.Originality/valueThe majority of studies on CSR in Malaysia pertain to the analysis of such reporting and motivations of managers toward CSR practices. This study conducts a comprehensive empirical research on the relationship between CSR and CFP in Malaysian PLCs.

In longitudinal studies data are collected on the same set of units for more than one occasion. In medical studies it is very common to have mixed Poisson and continuous longitudinal data. In such studies, for different reasons, some intended measurements might not be available resulting in a missing data setting. When the probability of missingness is related to the missing values, the missingness mechanism is termed nonrandom. The stochastic expectation-maximization (SEM) algorithm and the parametric fractional imputation (PFI) method are developed to handle nonrandom missingness in mixed discrete and continuous longitudinal data assuming different covariance structures for the continuous outcome. The proposed techniques are evaluated using simulation studies. Also, the proposed techniques are applied to the interstitial cystitis data base (ICDB) data.

A survey on machine and statistical learning for longitudinal analysis of neuroimaging data in Alzheimer’s disease

In analysis of longitudinal data, it is not uncommon that observation times of repeated measurements are subject-specific and correlated with underlying longitudinal outcomes. Taking account of the dependence between observation times and longitudinal outcomes is critical under these situations to assure the validity of statistical inference. In this article, we propose a flexible joint model for longitudinal data analysis in the presence of informative observation times. In particular, the new procedure considers the shared random-effect model and assumes a time-varying coefficient for the latent variable, allowing a flexible way of modeling longitudinal outcomes while adjusting their association with observation times. Estimating equations are developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, with variance-covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. One additional advantage of the procedure is that it provides a unified framework to test whether the effect of the latent variable is zero, constant, or time-varying. Simulation studies show that the proposed approach is appropriate for practical use. An application to a bladder cancer data is also given to illustrate the methodology.

Longitudinal data analysis is an increasingly popular approach because evaluating change is of central interest in many areas of research. Using advanced statistical techniques such as multilevel modeling (MLM) and structural equation modeling (SEM), longitudinal data analysis allows for the simultaneous evaluation of intra-individual change and interindividual differences in intra-individual change. This chapter presents an overview of both MLM and SEM approaches to evaluating change with different functional forms for continuous panel data, including linear, curvilinear, nonlinear, and spline curve models. This chapter also covers a variety of longitudinal models that take advantage of the flexibility of SEM over MLM, including autoregressive cross-lagged, latent difference, fully latent, parallel process, and second-order curve models. The chapter closes with a discussion of the advantages and disadvantages of MLM and SEM in modeling change, along with a brief review of advances in longitudinal data analysis.

Asthma is an important chronic disease of childhood. An intervention programme for managing asthma was designed on principles of self-regulation and was evaluated by a randomized longitudinal study.The study focused on several outcomes, and, typically, missing data remained a pervasive problem. We develop a pattern-mixture model to evaluate the outcome of intervention on the number of hospitalizations with non-ignorable dropouts. Pattern-mixture models are not generally identifiable as no data may be available to estimate a number of model parameters. Sensitivity analyses are performed by imposing structures on the unidentified parameters.We propose a parameterization which permits sensitivity analyses on clustered longitudinal count data that have missing values due to non-ignorable missing data mechanisms. This parameterization is expressed as ratios between event rates across missing data patterns and the observed data pattern and thus measures departures from an ignorable missing data mechanism. Sensitivity analyses are performed within a Bayesian framework by averaging over different prior distributions on the event ratios. This model has the advantage of providing an intuitive and flexible framework for incorporating the uncertainty of the missing data mechanism in the final analysis.