A Bayesian growth mixture model to examine maternal hypertension and birth outcomes

A sparse factor model for clustering high-dimensional longitudinal data

Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and uncover underlying disease mechanisms. However, analyzing such kind of data can be difficult due to its high dimensionality, heterogeneity and computational challenges. In this article, we propose a Bayesian nonparametric mixture model for clustering high-dimensional mixed-type (eg, continuous, discrete and categorical) longitudinal features. We employ a sparse factor model on the joint distribution of random effects and the key idea is to induce clustering at the latent factor level instead of the original data to escape the curse of dimensionality. The number of clusters is estimated through a Dirichlet process prior. An efficient Gibbs sampler is developed to estimate the posterior distribution of the model parameters. Analysis of real and simulated data is presented and discussed. Our study demonstrates that the proposed model serves as a useful analytical tool for clustering high-dimensional longitudinal data.

Joint clustering multiple longitudinal features: A comparison of methods and software packages with practical guidance

Clustering longitudinal features is a common goal in medical studies to identify distinct disease developmental trajectories. Compared to clustering a single longitudinal feature, integrating multiple longitudinal features allows additional information to be incorporated into the clustering process, which may reveal co-existing longitudinal patterns and generate deeper biological insight. Despite its increasing importance and popularity, there is limited practical guidance for implementing cluster analysis approaches for multiple longitudinal features and evaluating their comparative performance in medical datasets. In this paper, we provide an overview of several commonly used approaches to clustering multiple longitudinal features, with an emphasis on application and implementation through R software. These methods can be broadly categorized into two categories, namely model-based (including frequentist and Bayesian) approaches and algorithm-based approaches. To evaluate their performance, we compare these approaches using real-life and simulated datasets. These results provide practical guidance to applied researchers who are interested in applying these approaches for clustering multiple longitudinal features. Recommendations for applied researchers and suggestions for future research in this area are also discussed.

A Bayesian latent class model for predicting gestational age in health administrative data

Health administrative data are oftentimes of limited use in epidemiological study on drug safety in pregnancy, due to lacking information on gestational age at birth (GAB). Although several studies have proposed algorithms to estimate GAB using claims database, failing to incorporate the unique distributional shape of GAB, can introduce bias in estimates and subsequent modeling. Hence, we develop a Bayesian latent class model to predict GAB. The model employs a mixture of Gaussian distributions with linear covariates within each class. This approach allows modeling heterogeneity in the population by identifying latent subgroups and estimating class-specific regression coefficients. We fit this model in a Bayesian framework conducting posterior computation with Markov Chain Monte Carlo methods. The method is illustrated with a dataset of 10,043 Rhode Island Medicaid mother-child pairs. We found that the three-class and six-class mixture specifications maximized prediction accuracy. Based on our results, Medicaid women were partitioned into three classes, featured by extreme preterm or preterm birth, preterm or" early" term birth, and" late" term birth. Obstetrical complications appeared to pose a significant influence on class-membership. Altogether, compared to traditional linear models our approach shows an advantage in predictive accuracy, because of superior flexibility in modeling a skewed response and population heterogeneity.

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.

AAAPT: Assessment of the Acute Pain Trajectory

OBJECTIVE

Define and contrast acute pain trajectories vs. the aggregate pain measurements, summarize appropriate linear and nonlinear statistical analyses for pain trajectories at the patient level, and present methods to classify individual pain trajectories. Clinical applications of acute pain trajectories are also discussed.

SETTING

In 2016, an expert panel involving the Analgesic, Anesthetic, and Addiction Clinical Trial Translations, Innovations, Opportunities, and Networks (ACTTION), American Pain Society (APS), and American Academy of Pain Medicine (AAPM) established an initiative to create a pain taxonomy, named the ACTTION-APS-AAPM Pain Taxonomy (AAAPT), for the multidimensional classification of acute pain. The AAAPT panel commissioned the present report to provide further details on analysis of the individual acute pain trajectory as an important component of comprehensive pain assessment.

METHODS

Linear mixed models and nonlinear models (e.g., regression splines and polynomial models) can be applied to analyze the acute pain trajectory. Alternatively, methods for classifying individual pain trajectories (e.g., using the 50% confidence interval of the random slope approach or using latent class analyses) can be applied in the clinical context to identify different trajectories of resolving pain (e.g., rapid reduction or slow reduction) or persisting pain. Each approach has advantages and disadvantages that may guide selection. Assessment of the acute pain trajectory may guide treatment and tailoring to anticipated symptom recovery. The acute pain trajectory can also serve as a treatment outcome measure, informing further management.

CONCLUSIONS

Application of trajectory approaches to acute pain assessments enables more comprehensive measurement of acute pain, which forms the cornerstone of accurate classification and treatment of pain.

Bayesian nonparametric latent class model for longitudinal data

Latent class models have been widely used in longitudinal studies to uncover unobserved heterogeneity in a population and find the characteristics of the latent classes simultaneously using the class allocation probabilities dependent on predictors. However, previous latent class models for longitudinal data suffer from uncertainty in the choice of the number of latent classes. In this study, we propose a Bayesian nonparametric latent class model for longitudinal data, which allows the number of latent classes to be inferred from the data. The proposed model is an infinite mixture model with predictor-dependent class allocation probabilities; an individual longitudinal trajectory is described by the class-specific linear mixed effects model. The model parameters are estimated using Markov chain Monte Carlo methods. The proposed model is validated using a simulated example and a real-data example for characterizing latent classes of estradiol trajectories over the menopausal transition using data from the Study of Women's Health Across the Nation.

A Latent Class Approach to Modeling Trajectories of Health Care Cost in Pediatric Cystic Fibrosis

Introduction. Estimating costs of medical care attributable to treatments over time is difficult due to costs that cannot be explained solely by observed risk factors. Unobserved risk factors cannot be accounted for using standard econometric techniques, potentially leading to imprecise prediction. The goal of this work is to describe methodology to account for latent variables in the prediction of longitudinal costs. Methods. Latent class growth mixture models (LCGMMs) predict class membership using observed risk factors and class-specific distributions of costs over time. Our motivating example models cost of care for children with cystic fibrosis from birth to age 17. We compare a generalized linear mixed model (GLMM) with LCGMMs. Both models use the same covariates and distribution to predict average costs by combinations of observed risk factors. We adopt a Bayesian estimation approach to both models and compare results using the deviance information criterion (DIC). Results. The 3-class LCGMM model has a lower DIC than the GLMM. The LCGMM latent classes include a low-cost group where costs increase slowly over time, a medium-cost group with initial higher costs than the low-cost group and with more rapidly increasing costs at older ages, and a high-cost group with a U-shaped trajectory. The risk profile-specific mixtures of classes are used to predict costs over time. The LCGMM model shows more delineation of costs by age by risk profile and with less uncertainty than the GLMM model. Conclusions. The LCGMM approach creates flexible prediction models when using longitudinal cost data. The Bayesian estimation approach to LCGMM presented fits well into cost-effectiveness modeling where the estimated trajectories and class membership can be used for prediction.

Ambulatory Blood Pressure Trajectory and Perceived Stress in Relation to Birth Outcomes in Healthy Pregnant Adolescents

OBJECTIVE

An early decline in resting blood pressure (BP), followed by an upward climb, is well documented and indicative of a healthy pregnancy course. Although BP is considered both an effector of stress and a clinically meaningful measurement in pregnancy, little is known about its trajectory in association with birth outcomes compared with other stress effectors. The current prospective longitudinal study examined BP trajectory and perceived stress in association with birth outcomes (gestational age (GA) at birth and birth weight (BW) percentile corrected for GA) in pregnant adolescents, a group at risk for stress-associated poor birth outcomes.

METHODS

Healthy pregnant nulliparous adolescents (n = 139) were followed from early pregnancy through birth. At three time points (13-16, 24-27, and 34-37 gestational weeks ±1 week), the Perceived Stress Scale was collected along with 24-hour ambulatory BP (systolic and diastolic) and electronic diary reporting of posture. GA at birth and BW were abstracted from medical records.

RESULTS

After adjustment for posture and pre-pregnancy body mass index, hierarchical mixed-model linear regression showed the expected early decline (B = -0.18, p = .023) and then increase (B = 0.01, p < .001) of diastolic BP approximating a U-shape; however, systolic BP displayed only an increase (B = 0.01, p = .010). In addition, the models indicated a stronger systolic and diastolic BP U-shape for early GA at birth and lower BW percentile and an inverted U-shape for late GA at birth and higher BW percentile. No effects of perceived stress were observed.

CONCLUSIONS

These results replicate the pregnancy BP trajectory from previous studies of adults and indicate that the degree to which the trajectory emerges in adolescence may be associated with variation in birth outcomes, with a moderate U-shape indicating the healthiest outcomes.

Shape invariant mixture model for clustering non-linear longitudinal growth trajectories

In longitudinal studies, it is often of great interest to cluster individual trajectories based on repeated measurements taken over time. Non-linear growth trajectories are often seen in practice, and the individual data can also be measured sparsely, and at irregular time points, which may complicate the modeling process. Motivated by a study of pregnant women hormone profiles, we proposed a shape invariant growth mixture model for clustering non-linear growth trajectories. Bayesian inference via Monte Carlo Markov Chain was employed to estimate the parameters of interest. We compared our model to the commonly used growth mixture model and functional clustering approach by simulation studies. Results from analyzing the real data and simulated data were presented and discussed.

Bayesian Latent Class Analysis Tutorial

This article is a how-to guide on Bayesian computation using Gibbs sampling, demonstrated in the context of Latent Class Analysis (LCA). It is written for students in quantitative psychology or related fields who have a working knowledge of Bayes Theorem and conditional probability and have experience in writing computer programs in the statistical language R . The overall goals are to provide an accessible and self-contained tutorial, along with a practical computation tool. We begin with how Bayesian computation is typically described in academic articles. Technical difficulties are addressed by a hypothetical, worked-out example. We show how Bayesian computation can be broken down into a series of simpler calculations, which can then be assembled together to complete a computationally more complex model. The details are described much more explicitly than what is typically available in elementary introductions to Bayesian modeling so that readers are not overwhelmed by the mathematics. Moreover, the provided computer program shows how Bayesian LCA can be implemented with relative ease. The computer program is then applied in a large, real-world data set and explained line-by-line. We outline the general steps in how to extend these considerations to other methodological applications. We conclude with suggestions for further readings.

Methods for analyzing observational longitudinal prognosis studies for rheumatic diseases: a review & worked example using a clinic-based cohort of juvenile dermatomyositis patients

Most outcome studies of rheumatic diseases report outcomes ascertained on a single occasion. While single assessments are sufficient for terminal or irreversible outcomes, they may not be sufficiently informative if outcomes change or fluctuate over time. Consequently, longitudinal studies that measure non-terminal outcomes repeatedly afford a better understanding of disease evolution.Longitudinal studies require special analytic methods. Newer longitudinal analytic methods have evolved tremendously to deal with common challenges in longitudinal observational studies. In recent years, an increasing number of studies have used longitudinal design. This review aims to help readers understand and apply the findings from longitudinal studies. Using a cohort of children with juvenile dermatomyositis (JDM), we illustrate how to study evolution of disease activity in JDM using longitudinal methods.

Developmental Trajectories of Suicidal Thoughts and Behaviors From Adolescence Through Adulthood

OBJECTIVE

Little is known about the patterns among individuals in the long-term course of suicidal thoughts and behaviors (STBs). The objective of this study was to identify developmental trajectories of STBs from adolescence through young adulthood, as well as risk and protective covariates, and nonsuicidal outcomes associated with these trajectories.

METHOD

A total of 180 adolescents (ages 12-18 years at recruitment) were repeatedly assessed over an average of 13.6 years (2,273 assessments) since their psychiatric hospitalization. Trajectories were based on ratings of STBs at each assessment. Covariates included psychiatric risk factors (proportion of time in episodes of psychiatric disorders, hopelessness, trait anxiety, impulsivity, and aggression in adulthood, sexual and physical abuse, parental history of suicidal behavior), protective factors (survival and coping beliefs, social support in adulthood, parenthood), and nonsuicidal outcomes (social adjustment and functional impairment in adulthood, school drop-out, incarcerations).

RESULTS

Using a Bayesian group-based trajectory model, 4 trajectories of STBs were identified: an increasing risk class (11%); a highest overall risk class (12%); a decreasing risk class (33%); and a low risk class (44%). The 4 classes were associated with distinct patterns of correlates in risk and protective factors and nonsuicidal outcomes.

CONCLUSION

Adolescents and young adults have heterogeneous developmental trajectories of STBs. These trajectories and their covariates may inform strategies for predicting STBs and targeting interventions for individuals at risk for suicidal behavior.

Early diagnosis of gestational trophoblastic neoplasia based on trajectory classification with compartment modeling

BACKGROUND

In randomized clinical trials or observational studies, it is common to collect biomarker values longitudinally on a cohort of individuals. The investigators may be interested in grouping individuals that share similar changes of biomarker values and use these groups for diagnosis or therapeutic purposes. However, most classical model-based classification methods rely mainly on empirical models such as splines or polynomials and do not reflect the physiological processes.

METHODS

A model-based classification method was developed for longitudinal biomarker measurements through a pharmacokinetic model that describes biomarker changes over time. The method is illustrated using data on human Chorionic Gonadotrophic Hormone measurements after curettage of hydatidiform moles.

RESULTS

The resulting classification was linked to the evolution toward gestational trophoblastic neoplasia and may be used as a tool for early diagnosis. The diagnostic accuracy of the pharmacokinetic model was more reproducible than the one of a purely mathematical model that did not take into account the biological processes.

CONCLUSION

The use of pharmacokinetic models in model-based classification approaches can lead to clinically useful classifications.

An application of Bayesian growth mixture modelling to estimate infection incidences from repeated serological tests

Diagnoses of infectious diseases are often performed using antibody detection through enzyme-linked immunosorbent assay techniques. These data are usually dichotomized into positive and negative samples using a fixed cut-off and prevalences of infection are subsequently estimated assuming perfect correspondence between the dichotomized test results and infection status. In contrast to this approach, in this case study, we estimate the effect of distributing insecticide impregnated bednets to prevent Leishmania infection through mixture modelling of the original continuous data. We analyze the data from a cluster randomized intervention trial using a generalized latent variable model consisting of a longitudinal mixture model for the observed outcome and a Hidden Markov model for the underlying unobserved disease status to estimate the effect of an intervention. The response and structural models are jointly estimated in a Bayesian framework. This model has the advantage that it avoids the need to choose an arbitrary cut-off and allows for uncertainty in the infection status. In this paper, we describe the development of the model and selection of priors, the application to the motivating data, model checking and simulation results.

Health span approximates life span among many supercentenarians: compression of morbidity at the approximate limit of life span

We analyze the relationship between age of survival, morbidity, and disability among centenarians (age 100-104 years), semisupercentenarians (age 105-109 years), and supercentenarians (age 110-119 years). One hundred and four supercentenarians, 430 semisupercentenarians, 884 centenarians, 343 nonagenarians, and 436 controls were prospectively followed for an average of 3 years (range 0-13 years). The older the age group, generally, the later the onset of diseases, such as cancer, cardiovascular disease, dementia, and stroke, as well as of cognitive and functional decline. The hazard ratios for these individual diseases became progressively less with older and older age, and the relative period of time spent with disease was lower with increasing age group. We observed a progressive delay in the age of onset of physical and cognitive function impairment, age-related diseases, and overall morbidity with increasing age. As the limit of human life span was effectively approached with supercentenarians, compression of morbidity was generally observed.