Joint modelling of longitudinal and time-to-event data: an illustration using CD4 count and mortality in a cohort of patients initiated on antiretroviral therapy

Investigating the Determinants of Mortality before CD4 Count Recovery in a Cohort of Patients Initiated on Antiretroviral Therapy in South Africa Using a Fine and Gray Competing Risks Model

CD4 count recovery is the main goal for an HIV patient who initiated ART. Early ART initiation in HIV patients can help restore immune function more effectively, even when they have reached an advanced stage. Some patients may respond positively to ART and attain CD4 count recovery. Meanwhile, other patients failing to recover their CD4 count due to non-adherence, treatment resistance and virological failure might lead to HIV-related complications and death. The purpose of this study was to find the determinants of death in patients who failed to recover their CD4 count after initiating antiretroviral therapy. The data used in this study was obtained from KwaZulu-Natal, South Africa, where 2528 HIV-infected patients with a baseline CD4 count of <200 cells/mm3 were initiated on ART. We used a Fine-Gray sub-distribution hazard and cumulative incidence function to estimate potential confounding factors of death, where CD4 count recovery was a competing event for failure due to death. Patients who had no tuberculosis were 1.33 times at risk of dying before attaining CD4 count recovery [aSHR 1.33; 95% CI (0.96-1.85)] compared to those who had tuberculosis. Rural patients had a higher risk of not recovering and leading to death [aSHR 1.97; 95% CI (1.57-2.47)] than those from urban areas. The patient's tuberculosis status, viral load, regimen, baseline CD4 count, and location were significant contributors to death before CD4 count recovery. Intervention programs targeting HIV testing in rural areas for early ART initiation and promoting treatment adherence are recommended.

Joint modeling of longitudinal CD4 count data and time to first occurrence of composite outcome

In this study, we jointly modeled longitudinal CD4 count data and survival outcome (time-to-first occurrence of composite outcome of death, cardiac tamponade or constriction) in other to investigate the effects of Mycobacterium indicus pranii immunotherapy and the CD4 count measurements on the hazard of the composite outcome among patients with HIV and tuberculous (TB) pericarditis. In this joint modeling framework, the models for longitudinal and the survival data are linked by an association structure. The association structure represents the hazard of the event for 1-unit increase in the longitudinal measurement. Models fitting and parameter estimation were carried out using R version 4.2.3. The association structure that represents the strength of the association between the hazard for an event at time point j and the area under the longitudinal trajectory up to the same time j provides the best fit. We found that 1-unit increase in CD4 count results in 2 % significant reduction in the hazard of the composite outcome. Among HIV and TB pericarditis individuals, the hazard of the composite outcome does not differ between of M.indicus pranii versus placebo. Application of joint models to investigate the effect of M.indicus pranii on the hazard of the composite outcome is limited. Hence, this study provides information on the effect of M.indicus pranii on the hazard of the composite outcome among HIV and TB pericarditis patients.

Choice of baseline hazards in joint modeling of longitudinal and time-to-event cancer survival data

Longitudinal time-to-event analysis is a statistical method to analyze data where covariates are measured repeatedly. In survival studies, the risk for an event is estimated using Cox-proportional hazard model or extended Cox-model for exogenous time-dependent covariates. However, these models are inappropriate for endogenous time-dependent covariates like longitudinally measured biomarkers, Carcinoembryonic Antigen (CEA). Joint models that can simultaneously model the longitudinal covariates and time-to-event data have been proposed as an alternative. The present study highlights the importance of choosing the baseline hazards to get more accurate risk estimation. The study used colon cancer patient data to illustrate and compare four different joint models which differs based on the choice of baseline hazards [piecewise-constant Gauss-Hermite (GH), piecewise-constant pseudo-adaptive GH, Weibull Accelerated Failure time model with GH & B-spline GH]. We conducted simulation study to assess the model consistency with varying sample size (N = 100, 250, 500) and censoring (20 %, 50 %, 70 %) proportions. In colon cancer patient data, based on Akaike information criteria (AIC) and Bayesian information criteria (BIC), piecewise-constant pseudo-adaptive GH was found to be the best fitted model. Despite differences in model fit, the hazards obtained from the four models were similar. The study identified composite stage as a prognostic factor for time-to-event and the longitudinal outcome, CEA as a dynamic predictor for overall survival in colon cancer patients. Based on the simulation study Piecewise-PH-aGH was found to be the best model with least AIC and BIC values, and highest coverage probability(CP). While the Bias, and RMSE for all the models showed a competitive performance. However, Piecewise-PH-aGH has shown least bias and RMSE in most of the combinations and has taken the shortest computation time, which shows its computational efficiency. This study is the first of its kind to discuss on the choice of baseline hazards.

Gender-specific trends in cigarette smoking and lung cancer incidence: A two-stage age-stratified Bayesian joinpoint model

BACKGROUND

Previous studies have explored population-level smoking trends and the incidence of lung cancer, but none has jointly modeled them. This study modeled the relationship between smoking rate and incidence of lung cancer, by gender, in the U.S. adult population and estimated the lag time between changes in smoking trend and changes in incidence trends.

METHODS

The annual total numbers of smokers, by gender, were obtained from the database of the National Health Interview Survey (NHIS) program of the Centers for Disease Control and Prevention (CDC) for the years 1976 through 2018. The population-level incidence data for lung and bronchus cancers, by gender and five-year age group, were obtained for the same years from the Surveillance, Epidemiology, and End Results (SEER) program database of the National Cancer Institute. A Bayesian joinpoint statistical model, assuming Poisson errors, was developed to explore the relationship between smoking and lung cancer incidence in the time trend.

RESULTS

The model estimates and predicts the rate of change of incidence in the time trend, adjusting for expected smoking rate in the population, age, and gender. It shows that smoking trend is a strong predictor of incidence trend and predicts that rates will be roughly equal for males and females in the year 2023, then the incidence rate for females will exceed that of males. In addition, the model estimates the lag time between smoking and incidence to be 8.079 years.

CONCLUSIONS

Because there is a three-year delay in reporting smoking related data and a four-year delay for incidence data, this model provides valuable predictions of smoking rate and associated lung cancer incidence before the data are available. By recognizing differing trends by gender, the model will inform gender specific aspects of public health policy related to tobacco use and its impact on lung cancer incidence.

Dynamic predictions from longitudinal CD4 count measures and time to death of HIV/AIDS patients using a Bayesian joint model

A Bayesian joint modeling approach to dynamic prediction of HIV progression and mortality allows individualized predictions to be made for HIV patients, based on monitoring of their CD4 counts. This study aims to provide predictions of patient-specific trajectories of HIV disease progression and survival. Longitudinal data on 254 HIV/AIDS patients who received ART between 2009 and 2014, and who had at least one CD4 count observed, were employed in a Bayesian joint model of disease progression. Different forms of association structure that relate the longitudinal CD4 biomarker and time to death were assessed; and predictions were averaged over the different models using Bayesian model averaging. The individual follow-up times ranged from 1 to 120 months, with a median of 22 months and IQR 7-39 months. The estimates of the association structure parameters from two of the three models considered indicated that the HIV mortality hazard at any time point is associated with the rate of change in the underlying value of the CD4 count. Model averaging the dynamic predictions resulted in only one of the hypothesized association structures having non-zero weight in almost all time points for each individual, with the exception of twelve patients, for whom other association structures were preferred at a few time points. The predictions were found to be different when we averaged them over models than when we derived them from the highest posterior weight model alone. The model with highest posterior weight for almost all time points for each individual gave an estimate of the association parameter of -0.02 implying that for a unit increase in the CD4 count, the hazard of HIV mortality decreases by a factor (hazard ratio) of 0.98. Functional status and alcohol intake are important contributing factors that affect the mean square root of CD4 measurements.

Using joint models to study the association between CD4 count and the risk of death in TB/HIV data

Background

The association structure linking the longitudinal and survival sub-models is of fundamental importance in the joint modeling framework and the choice of this structure should be made based on the clinical background of the study. However, this information may not always be accessible and rationale for selecting this association structure has received relatively little attention in the literature. To this end, we aim to explore four alternative functional forms of the association structure between the CD4 count and the risk of death and provide rationale for selecting the optimal association structure for our data. We also aim to compare the results obtained from the joint model to those obtained from the time-varying Cox model.

Methods

We used data from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) AIDS Treatment programme, the Starting Antiretroviral Therapy at Three Points in Tuberculosis (SAPiT) study, an open-label, three armed randomised, controlled trial between June 2005 and July 2010 (N=642). In our analysis, we combined the early and late integrated arms and compared results to the sequential arm. We utilized the Deviance Information Criterion (DIC) to select the final model with the best structure, with smaller values indicating better model adjustments to the data.

Results

Patient characteristics were similar across the study arms. Combined integrated therapy arms had a reduction of 55% in mortality (HR:0.45, 95% CI:0.28-0.72) compared to the sequential therapy arm. The joint model with a cumulative effects functional form was chosen as the best association structure. In particular, our joint model found that the area under the longitudinal profile of CD4 count was strongly associated with a 21% reduction in mortality (HR:0.79, 95% CI:0.72-0.86). Where as results from the time-varying Cox model showed a 19% reduction in mortality (HR:0.81, 95% CI:0.77-0.84).

Conclusions

In this paper we have shown that the “current value” association structure is not always the best structure that expresses the correct relationship between the outcomes in all settings, which is why it is crucial to explore alternative clinically meaningful association structures that links the longitudinal and survival processes.

A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics

Clinical trials investigate treatment endpoints that usually include measurements of pharmacodynamic and efficacy biomarkers in early‐phase studies and patient‐reported outcomes as well as event risks or rates in late‐phase studies. In recent years, a systematic trend in clinical trial data analytics and modeling has been observed, where retrospective data are integrated into a quantitative framework to prospectively support analyses of interim data and design of ongoing and future studies of novel therapeutics. Joint modeling is an advanced statistical methodology that allows for the investigation of clinical trial outcomes by quantifying the association between baseline and/or longitudinal biomarkers and event risk. Using an exemplar data set from non‐small cell lung cancer studies, we propose and test a workflow for joint modeling. It allows a modeling scientist to comprehensively explore the data, build survival models, investigate goodness‐of‐fit, and subsequently perform outcome predictions using interim biomarker data from an ongoing study. The workflow illustrates a full process, from data exploration to predictive simulations, for selected multivariate linear and nonlinear mixed‐effects models and software tools in an integrative and exhaustive manner.

Serum Albumin Trends in Relation With Prognosis of Individuals Receiving Hemodialysis Therapy

Introduction

Hypoalbuminemia is recognized as an indication of protein-energy depletion in several disease states. According to many studies, hemodialysis (HD) patients who have decreased baseline serum albumin levels exhibit a poor prognosis. However, serum albumin does not stay at a constant level with the progress of the disease, considering that only a baseline value may not precisely reflect prognostic value. The study objective was to ascertain whether there is a link between serum albumin trajectories and all-cause mortality in incident HD patients. 

Methods

Retrospective cohort analysis was conducted in the HD unit at the University of Health Sciences, Kayseri Training and Research Hospital, Nephrology Clinic between June 19, 2010, and December 29, 2017. A total of 408 individuals aged 18 years or older, who had at least one measurement of serum albumin at baseline, were enrolled. The outcome was all-cause death. Time-dependent Cox regression and joint model were used to investigate the associations between serum albumin trend in time and the risk of all-cause mortality.

Results

Mean (SD) age was 62.17 (12.33) years, and 50.7% were male. At baseline, the mean (SD) albumin level was 3.59 (0.27). A faster decrease (per 1-SD increase in negative slope) in serum albumin levels was associated with increased risk of all-cause mortality (HR, 1.63; 95% CI, 1.08-2.84; p=0.023) in a fully adjusted joint model with slope parameterization. Also, an annual 1-SD increase in albumin level declined the hazard of all-cause mortality by 22% (HR, 0.78; 95% CI, 0.66-0.92; p=0.008) in a fully adjusted joint model with value parameterization. Similar results were obtained from time-dependent Cox models.

Conclusion

These findings suggest that longitudinal albumin evaluation, including the rate of change as a slope parameter, may be valuable for risk stratification of patients receiving HD.

Nonlinear mixed-effects modeling of longitudinal count data: Bayesian inference about median counts based on the marginal zero-inflated discrete Weibull distribution

This article proposes a Bayesian regression model for nonlinear zero-inflated longitudinal count data that models the median count as an alternative to the mean count. The nonlinear model generalizes a recently introduced linear mixed-effects model based on the zero-inflated discrete Weibull (ZIDW) distribution. The ZIDW distribution is more robust to severe skewness in the data than conventional zero-inflated count distributions such as the zero-inflated negative binomial (ZINB) distribution. Moreover, the ZIDW distribution is attractive because of its convenience to model the median counts given its closed-form quantile function. The median is a more robust measure of central tendency than the mean when the data, for instance, zero-inflated counts, are right-skewed. In an application of the model we consider a biphasic mixed-effects model consisting of an intercept term and two slope terms. Conventionally, the ZIDW model separately specifies the predictors for the zero-inflation probability and the counting process's median count. In our application, the two latent class interpretations are not clinically plausible. Therefore, we propose a marginal ZIDW model that directly models the biphasic median counts marginally. We also consider the marginal ZINB model to make inferences about the nonlinear mean counts over time. Our simulation study shows that the models have good properties in terms of accuracy and confidence interval coverage.