Regularized Latent Class Model for Joint Analysis of High-Dimensional Longitudinal Biomarkers and a Time-to-Event Outcome

Describing complex disease progression using joint latent class models for multivariate longitudinal markers and clinical endpoints

Neurodegenerative diseases are characterized by numerous markers of progression and clinical endpoints. For instance, multiple system atrophy (MSA), a rare neurodegenerative synucleinopathy, is characterized by various combinations of progressive autonomic failure and motor dysfunction, and a very poor prognosis. Describing the progression of such complex and multi-dimensional diseases is particularly difficult. One has to simultaneously account for the assessment of multivariate markers over time, the occurrence of clinical endpoints, and a highly suspected heterogeneity between patients. Yet, such description is crucial for understanding the natural history of the disease, staging patients diagnosed with the disease, unravelling subphenotypes, and predicting the prognosis. Through the example of MSA progression, we show how a latent class approach modeling multiple repeated markers and clinical endpoints can help describe complex disease progression and identify subphenotypes for exploring new pathological hypotheses. The proposed joint latent class model includes class-specific multivariate mixed models to handle multivariate repeated biomarkers possibly summarized into latent dimensions and class-and-cause-specific proportional hazard models to handle time-to-event data. Maximum likelihood estimation procedure, validated through simulations is available in the lcmm R package. In the French MSA cohort comprising data of 598 patients during up to 13 years, five subphenotypes of MSA were identified that differ by the sequence and shape of biomarkers degradation, and the associated risk of death. In posterior analyses, the five subphenotypes were used to explore the association between clinical progression and external imaging and fluid biomarkers, while properly accounting for the uncertainty in the subphenotypes membership.

Great diversity in the utilization and reporting of latent growth modeling approaches in type 2 diabetes: A literature review

Introduction

The progression of complications of type 2 diabetes (T2D) is unique to each patient and can be depicted through individual temporal trajectories. Latent growth modeling approaches (latent growth mixture models [LGMM] or latent class growth analysis [LCGA]) can be used to classify similar individual trajectories in a priori non-observed groups (latent groups), sharing common characteristics. Although increasingly used in the field of T2D, many questions remain regarding the utilization of these methods.

Objective

To review the literature of longitudinal studies using latent growth modeling approaches to study T2D.

Methods

MEDLINE (Ovid), EMBASE, CINAHL and Wb of Science were searched through August 25th, 2021. Data was collected on the type of latent growth modeling approaches (LGMM or LCGA), characteristics of studies and quality of reporting using the GRoLTS-Checklist and presented as frequencies.

Results

From the 4,694 citations screened, a total of 38 studies were included. The studies were published beetween 2011 and 2021 and the length of follow-up ranged from 8 weeks to 14 years. Six studies used LGMM, while 32 studies used LCGA. The fields of research varied from clinical research, psychological science, healthcare utilization research and drug usage/pharmaco-epidemiology. Data sources included primary data (clinical trials, prospective/retrospective cohorts, surveys), or secondary data (health records/registries, medico-administrative). Fifty percent of studies evaluated trajectory groups as exposures for a subsequent clinical outcome, while 24% used predictive models of group membership and 5% used both. Regarding the quality of reporting, trajectory groups were adequately presented, however many studies failed to report important decisions made for the trajectory group identification.

Conclusion

Although LCGA were preferred, the contexts of utilization were diverse and unrelated to the type of methods. We recommend future authors to clearly report the decisions made regarding trajectory groups identification.

Backward joint model and dynamic prediction of survival with multivariate longitudinal data

An important approach to dynamic prediction of time-to-event outcomes using longitudinal data is based on modeling the joint distribution of longitudinal and time-to-event data. The widely used joint model for this purpose is the shared random effect model. Presumably, adding more longitudinal predictors improves the predictive accuracy. However, the shared random effect model can be computationally difficult or prohibitive when a large number of longitudinal variables are used. In this paper, we study an alternative way of modeling the joint distribution of longitudinal and time-to-event data. Under this formulation, the log-likelihood involves no more than one-dimensional integration, regardless of the number of longitudinal variables in the model. Therefore, this model is particularly suitable in dynamic prediction problems with large number of longitudinal predictors. The model fitting can be implemented with tractable and stable computation by using a combination of pseudo maximum likelihood estimation, Expectation-Maximization algorithm, and convex optimization. We evaluate the proposed methodology and its predictive accuracy with varying number of longitudinal variables using simulations and data from a primary biliary cirrhosis study.

Regularized Latent Class Analysis for Polytomous Item Responses: An Application to SPM-LS Data

The last series of Raven's standard progressive matrices (SPM-LS) test was studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCMs). For dichotomous item response data, an alternative estimation approach based on fused regularization for RLCMs is proposed. For polytomous item responses, different alternative fused regularization penalties are presented. The usefulness of the proposed methods is demonstrated in a simulated data illustration and for the SPM-LS dataset. For the SPM-LS dataset, it turned out the regularized latent class model resulted in five partially ordered latent classes. In total, three out of five latent classes are ordered for all items. For the remaining two classes, violations for two and three items were found, respectively, which can be interpreted as a kind of latent differential item functioning.

Association of Glycemic Control Trajectory with Short-Term Mortality in Diabetes Patients with High Cardiovascular Risk: a Joint Latent Class Modeling Study

BACKGROUND

The relationship between risk factor or biomarker trajectories and contemporaneous short-term clinical outcomes is poorly understood. In diabetes patients, it is unknown whether hemoglobin A1c (HbA1c) trajectories are associated with clinical outcomes and can inform care in scenarios in which a single HbA1c is uninformative, for example, after a diagnosis of coronary artery disease (CAD).

OBJECTIVE

To compare associations of HbA1c trajectories and single HbA1c values with short-term mortality in diabetes patients evaluated for CAD DESIGN: Retrospective observational cohort study PARTICIPANTS: Diabetes patients (n = 7780) with and without angiographically defined CAD MAIN MEASURES: We used joint latent class mixed models to simultaneously fit HbA1c trajectories and estimate association with 2-year mortality after cardiac catheterization, adjusting for clinical and demographic covariates.

KEY RESULTS

Three HBA1c trajectory classes were identified: individuals with stable glycemia (class A; n = 6934 [89%]; mean baseline HbA1c 6.9%), with declining HbA1c (class B; n = 364 [4.7%]; mean baseline HbA1c 11.6%), and with increasing HbA1c (class C; n = 482 [6.2%]; mean baseline HbA1c 8.5%). HbA1c trajectory class was associated with adjusted 2-year mortality (3.0% [95% CI 2.8, 3.2] for class A, 3.1% [2.1, 4.2] for class B, and 4.2% [3.4, 4.9] for class C; global P = 0.047, P = 0.03 comparing classes A and C, P > 0.05 for other pairwise comparisons). Baseline HbA1c was not associated with 2-year mortality (P = 0.85; hazard ratios 1.01 [0.96, 1.06] and 1.02 [0.95, 1.10] for HbA1c 7-9% and ≥ 9%, respectively, relative to HbA1c < 7%). The association between HbA1c trajectories and mortality did not differ between those with and without CAD (interaction P = 0.1).

CONCLUSIONS

In clinical settings where single HbA1c measurements provide limited information, HbA1c trajectories may help stratify risk of complications in diabetes patients. Joint latent class modeling provides a generalizable approach to examining relationships between biomarker trajectories and clinical outcomes in the era of near-universal adoption of electronic health records.

A latent unknown clustering integrating multi-omics data (LUCID) with phenotypic traits

MOTIVATION

Epidemiologic, clinical and translational studies are increasingly generating multiplatform omics data. Methods that can integrate across multiple high-dimensional data types while accounting for differential patterns are critical for uncovering novel associations and underlying relevant subgroups.

RESULTS

We propose an integrative model to estimate latent unknown clusters (LUCID) aiming to both distinguish unique genomic, exposure and informative biomarkers/omic effects while jointly estimating subgroups relevant to the outcome of interest. Simulation studies indicate that we can obtain consistent estimates reflective of the true simulated values, accurately estimate subgroups and recapitulate subgroup-specific effects. We also demonstrate the use of the integrated model for future prediction of risk subgroups and phenotypes. We apply this approach to two real data applications to highlight the integration of genomic, exposure and metabolomic data.

AVAILABILITY AND IMPLEMENTATION

The LUCID method is implemented through the LUCIDus R package available on CRAN (https://CRAN.R-project.org/package=LUCIDus).

SUPPLEMENTARY INFORMATION

Supplementary materials are available at Bioinformatics online.