Pattern Mixture Models and Latent Class Models for the Analysis of Multivariate Longitudinal Data with Informative Dropouts

In longitudinal studies, missing data are ubiquitous. This article made a comparison of three model-based techniques for handling different types of missing data (i.e., missing at random (MAR)-based maximum likelihood (ML) approach, missing not at random (MNAR)-based Diggle–Kenward (DK) selection model and MNAR-based pattern mixture (PM) model) in longitudinal studies through a Monte Carlo simulation study. Two influential factors were considered: the dropout rates (5%, 10%, 20%, and 40%) and the sample sizes (100, 300, 500, and 1000) under MAR and MNAR missingness mechanisms respectively. The results indicated that the model selection was a crucial issue when researchers were dealing with missing data in longitudinal studies because under MNAR mechanism, DK method outperformed MAR-based ML approach, but PM method performed worse than MAR-based method did. The differences of the parameter estimation among three methods became more significant as the sample size and the dropout rate increased.

We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.

Purpose Our objectives were to (a) identify oral and pharyngeal physiologic swallowing impairment severity classes based on latent class analyses (LCAs) of the Modified Barium Swallow Impairment Profile (MBSImP) swallow task scores and (b) quantify the probability of severity class membership given composite MBSImP oral total (OT) and pharyngeal total (PT) scores. Method MBSImP scores were collected from a patient database of 319 consecutive modified barium swallow studies. Because of missing swallow task scores, LCA was performed using 25 multiply imputed data sets. Results LCA revealed a three-class structure for both oral and pharyngeal models. We identified OT and PT score intervals to assign subjects to oral and pharyngeal impairment latent severity classes, respectively, with high probability (probability of class membership ≥ 0.9 given OT or PT scores within specified ranges) and high confidence (95% credible interval [CI] widths ≤ 0.24 for all total scores within specified ranges). OT scores ranging from 0 to 10 and from 14 to 18 yielded assignments in Oral Latent Classes 1 and 2, respectively, while OT = 22 was assigned to Oral Latent Class 3. PT scores ranging from 0 to 13 and from 18 to 24 yielded assignments in Pharyngeal Latent Classes 1 and 2, respectively, while PT = 26 was assigned to Pharyngeal Latent Class 3. Conclusions LCA of MBSImP task-level data revealed significant underlying oral and pharyngeal ordinal class structures representing increasingly severe gradations of physiologic swallow impairment. Clinically meaningful OT and PT score ranges were derived facilitating latent class assignment. Supplemental Material https://doi.org/10.23641/asha.12315677.

BackgroundHealth-related quality of life (HRQoL) has become a major endpoint to assess the clinical benefit of new therapeutic strategies in oncology clinical trials. Typically, HRQoL outcomes are analyzed using linear mixed models (LMMs). However, longitudinal analysis of HRQoL in the presence of missing data remains complex and unstandardized. Our objective was to compare the modeling alternatives that account for informative dropout.MethodsWe investigated three alternative methods—the selection model (SM), pattern-mixture model (PMM), and shared-parameters model (SPM)—in relation to the LMM. We first compared them on the basis of methodological arguments highlighting their advantages and drawbacks. Then, we applied them to data from a randomized clinical trial that included 267 patients with advanced esophageal cancer for the analysis of four HRQoL dimensions evaluated using the European Organisation for Research and Treatment of Cancer (EORTC) QLQ-C30 questionnaire.ResultsWe highlighted differences in terms of outputs, interpretation, and underlying modeling assumptions; this methodological comparison could guide the choice of method according to the context. In the application, none of the four models detected a significant difference between the two treatment arms. The estimated effect of time on HRQoL varied according to the method: for all analyzed dimensions, the PMM estimated an effect that contrasted with those estimated by the SM and SPM; the LMM estimated effects were confirmed by the SM (on two of four HRQoL dimensions) and SPM (on three of four HRQoL dimensions).ConclusionsThe PMM, SM, or SPM should be used to confirm or invalidate the results of LMM analysis when informative dropout is suspected. Of these three alternative methods, the SPM appears to be the most interesting from both theoretical and practical viewpoints.Trial registrationThis study is registered with ClinicalTrials.gov, number NCT00861094.

Using three waves of data from the European Community Household Panel, this paper estimates demand for physician services equations for 12 European countries. We focus on the selection of the most appropriate econometric specification for visits to general practitioners and to specialists among two-part and latent class models. The distinction between the demand of services from these two types of physicians allows us to distinguish cases in which two-part perform better than latent class models, evidence which is different from previous findings in the literature. The results suggest that latent class models are more appropriate than two-part models to estimate general practitioners utilisation while the opposite is found for visits to the specialists.

Missing data result in less precise and possibly biased effect estimates in single studies. Bias arising from studies with incomplete outcome data is naturally propagated in a meta‐analysis. Conventional analysis using only individuals with available data is adequate when the meta‐analyst can be confident that the data are missing at random (MAR) in every study—that is, that the probability of missing data does not depend on unobserved variables, conditional on observed variables. Usually, such confidence is unjustified as participants may drop out due to lack of improvement or adverse effects. The MAR assumption cannot be tested, and a sensitivity analysis to assess how robust results are to reasonable deviations from the MAR assumption is important. Two methods may be used based on plausible alternative assumptions about the missing data. Firstly, the distribution of reasons for missing data may be used to impute the missing values. Secondly, the analyst may specify the magnitude and uncertainty of possible departures from the missing at random assumption, and these may be used to correct bias and reweight the studies. This is achieved by employing a pattern mixture model and describing how the outcome in the missing participants is related to the outcome in the completers. Ideally, this relationship is informed using expert opinion. The methods are illustrated in two examples with binary and continuous outcomes. We provide recommendations on what trial investigators and systematic reviewers should do to minimize the problem of missing outcome data in meta‐analysis.

Often quantities of interest in psychology cannot be observed directly. These unobservable quantities, known as latent variables, tend to be complex, often multidimensional, constructs. In many cases these constructs are categorical, such that individuals belong to mutually exclusive and exhaustive unobservable subgroups. Latent class analysis (LCA) is a statistical approach to modeling a discrete latent variable using multiple, discrete observed variables as indicators. Examples of latent class variables that appear in the psychology literature include temperament type, substance use behavior, teaching style, stages of change in the transtheoretical model, and latent classes of risk. The first section of this chapter provides a conceptual introduction to the concept of a latent class followed by a technical introduction to the mathematical model, including multiple-groups LCA and LCA with covariates. This is followed by a discussion of parameter restrictions, model selection, and goodness-of-fit. The second section demonstrates LCA using the empirical example of depression subtypes in adolescence. Five latent classes were identified based on responses to eight questionnaire items assessing depression symptoms: Non-depressed (characterized by a low probability of reporting all eight depression symptoms), sad, disliked, sad + disliked, and depressed (characterized by a high probability of reporting all eight depression symptoms). The third section presents longitudinal extensions of the model, including repeated-measures LCA and latent transition analysis (LTA). The empirical example is extended to examine change in depression subtypes over time. The final sections describe recent extensions to the latent class model and areas that merit additional research in the future. Keywords: latent class analysis; latent transition analysis; latent variable model; categorical data

The authors illustrate how to perform maximum-likelihood estimation in latent class (LC) analysis when there are sampling weights. The methods are natural extensions of the approaches proposed by Clogg and Eliason (1987) and Magidson (1987) for dealing with sampling weights in the log-linear analysis of frequency tables. For the log-linear form of the LC model, the approach corresponds to a special case of Haberman's (1979) log-linear LC model with cell weights. This approach can also be applied to the probability formulation of the LC model with cell weights, which can accommodate many indicators. The authors propose an efficient estimation-maximization algorithm for estimating the parameters for this formulation. A small simulation study shows that the probability estimates obtained by this approach compare favorably to other weighting approaches. Several empirical examples are provided to illustrate various possible weighting methods in LC analysis.

Accommodating taste heterogeneity in railway passenger choice models based on internet booking data

A choice to use a seat belt is largely dependent on the psychology of the vehicles’ occupants, and thus those decisions are expected to be characterized by preference heterogeneity. Despite the importance of seat belt use on the safety of the roadways, the majority of existing studies ignored the heterogeneity in the data and used a very standard statistical or descriptive method to identify the factors of using a seatbelt. Application of the right statistical method is of crucial importance to unlock the underlying factors of the choice being made by vehicles’ occupants. Thus, this study was conducted to identify the contributory factors to the front-seat passengers’ choice of seat belt usage, while accounting for the choice preference heterogeneity. The latent class model has been offered to replace the mixed logit model by replacing a continuous distribution with a discrete one. However, one of the shortcomings of the latent class model is that the homogeneity is assumed across a same class. A further extension is to relax the assumption of homogeneity by allowing some parameters to vary across the same group. The model could still be extended to overlay some attributes by considering attributes non-attendance (ANA), and aggregation of common-metric attributes (ACMA). Thus, this study was conducted to make a comparison across goodness of fit of the discussed models. Beside a comparison based on goodness of fit, the share of individuals in each class was used to see how it changes based on various model specifications. In summary, the results indicated that adding another layer to account for the heterogeneity within the same class of the latent class (LC) model, and accounting for ANA and ACMA would improve the model fit. It has been discussed in the content of the manuscript that accounting for ANA, ACMA and an extra layer of heterogeneity does not just improve the model goodness of fit, but largely impacts the share of class allocation of the models.

The Latent Class Structure of Exercise and Eating Behavior

Joint models (JMs) for longitudinal and time-to-event data are an important class of biostatistical models in health and medical research. When the study population consists of heterogeneous subgroups, standard JMs may be inadequate, leading to misleading results or loss of information. Joint latent class models (JLCMs) and their variants have been proposed to incorporate latent class structures into JMs. JLCMs are useful for identifying latent subgroups, uncovering deeper insights into relationships between the outcomes, and improving prediction performance. We consider the problem of Bayesian inference for the generic form of JLCMs, which poses significant computational challenges due to the complex nature of the posterior distribution. We propose a new Bayesian inference framework to tackle these challenges. Our approach leverages state-of-the-art Markov chain Monte Carlo techniques and parallel computing for parameter estimation and model selection regarding the number of latent classes. Through a simulation study, we demonstrate the feasibility and superiority of our proposed method over the existing approach. Additionally, we provide practical guidance on model and prior specification, which has received little attention, to facilitate the implementation of such complex models. We illustrate our method using data from the PAQUID prospective cohort study, where the outcomes of interest include a longitudinal measurement of cognitive performance and time to dementia diagnosis. Our analysis provides deeper insights into the latent class characteristics underlying the study population.

Background: Over the last two decades, latent class analysis (LCA) has been extensively used to statistically identify phenotypes of childhood wheeze; however, less has been discussed on the external factors affecting the outcomes of LCA models in phenotype identification research. Objective: To understand the potential cause of variability in the number/types of wheeze phenotypes identified by means of LCA and to assess the performance of these models under different conditions. Methods: Here, we examined the effects of several data characteristics (sample size, data collection age and intervals), and model dimensionality (number of latent classes) on the classification of wheeze phenotypes by means of latent class and transition analysis. We also identified critical and redundant data collection points in discriminating phenotypes of wheeze using two different variable selection methods, stepwise-backward elimination, and genetic algorithm. Results: Small sample sizes suggested fewer wheeze sub-groups as they were underpowered to detect less frequently observed wheeze phenotypes. There was a strong interplay between sample size, number of data collection points and the optimal number of wheeze phenotypes extracted. A variable selection algorithm applied to LCA resulted in the exclusion of 6 redundant/non-informative time points (Month 6, Month 30, Month 69, Month 91, Month 140 and Month 198) as they contained very little discriminative and/or extra information about the wheeze classes. Conclusions: Input data characteristics and model complexity were found to be very influential on the classification of wheeze phenotypes and prevalence of each class in the population.

This paper investigates freight market segmentation to seek the potential market of modal shift from road to rail-based intermodal (only pre- and end- haulage are transported by road), using discrete choice analysis. The Defficient design approach was used to generate SP scenarios. The data, including 2160 SP observations of 135 companies, was collected in China's Yangtze River Delta region. The multinomial logit (MNL) model, the mixed logit (ML) model, and the latent class (LC) model were constructed successively. Freight mode attributes (cost, time and reliability), shipment characteristics (distance, time threshold), cargo characteristics (value and density) were considered. In addition, the logistics elements such as the stages of production process and psychological characteristics such as choice inertia were also introduced in this paper. The results show that the LC model with segment variables performs better than the counterpart without segment variables, the MNL model and the ML model. Using the LC model, shippers are classified into four market segments. There are significant differences in shippers' preference among different classes. Based on the class membership function, the characteristic of each class can be identified by a combination of different attributes. The difficulty of achieving the modal shift from road to rail-based intermodal is ranked according to the values of attributes, further determining the priority of the potential market. This study helps to understand the shippers' freight mode choice better. Rail service suppliers can design transportation products that match the shippers' demand characteristics for different classes to improve the market share.

Estimation of prevalence and diagnostic test accuracy in tuberculosis (TB) prevalence surveys suffer from reference standard and verification biases. The former is attributed to the imperfect reference test used to bacteriologically confirm TB disease. The latter occurs when only the participants screening positive for any TB-compatible symptom or chest X-ray abnormality are selected for bacteriological testing (verification). Bayesian latent class analysis (LCA) alleviates the reference standard bias but suffers verification bias in TB prevalence surveys. This work aims to identify best-practice approaches to simultaneously alleviate the reference standard and verification biases in the estimates of pulmonary TB prevalence and diagnostic test performance in TB prevalence surveys. We performed a secondary analysis of 9869 participants aged ≥15 years from a community-based multimorbidity screening study in a rural district of KwaZulu-Natal, South Africa (Vukuzazi study). Participants were eligible for bacteriological testing using Xpert Ultra and culture if they reported any cardinal TB symptom or had an abnormal chest X-ray finding. We conducted Bayesian LCA in five ways to handle the unverified individuals: (i) complete-case analysis, (ii) analysis assuming the unverified individuals would be negative if bacteriologically tested, (iii) analysis of multiply-imputed datasets with imputation of the missing bacteriological test results for the unverified individuals using multivariate imputation via chained equations (MICE), and simultaneous imputation of the missing bacteriological test results in the analysis model assuming the missing bacteriological test results were (iv) missing at random (MAR), and (v) missing not at random (MNAR). We compared the results of (i)-(iii) to the analysis based on a composite reference standard (CRS) of Xpert Ultra and culture. Through simulation with an overall true prevalence of 2.0%, we evaluated the ability of the models to alleviate both biases simultaneously. Based on simulation, Bayesian LCA with simultaneous imputation of the missing bacteriological test results under the assumption that the missing data are MAR and MNAR alleviate the reference standard and verification biases. CRS-based analysis and Bayesian LCA assuming the unverified are negative for TB alleviate the biases only when the true overall prevalence is <3.0%. Complete-case analysis produced biased estimates. In the Vukuzazi study, Bayesian LCA with simultaneous imputation of the missing bacteriological test results under the MAR and MNAR assumptions produced overall PTB prevalence of 0.9% (95% Credible Interval (CrI): 0.6-1.9) and 0.7% (95% CrI: 0.5-1.1) respectively alongside realistic estimates of overall diagnostic test sensitivity and specificity with substantially overlapping 95% CrI. The CRS-based analysis and Bayesian LCA assuming the unverified were negative for TB produced 0.7% (95% CrI: 0.5-0.9) and 0.7% (95% CrI: 0.5-1.2) overall PTB prevalence respectively with realistic estimates of overall diagnostic test sensitivity and specificity. Unlike CRS-based analysis, Bayesian LCA of multiply-imputed data using MICE mitigates both biases. The findings demonstrate the efficacy of these advanced techniques in alleviating the reference standard and verification biases, enhancing the robustness of community-based screening programs. Imputing missing values as negative for bacteriological tests is plausible under realistic assumptions.