Shared parameter models for joint analysis of longitudinal and survival data with left truncation due to delayed entry - Applications to cystic fibrosis

A joint analysis proposal of nonlinear longitudinal and time-to-event right-, interval-censored data for modeling pregnancy miscarriage

Pregnancy in-vitro fertilization (IVF) cases are associated with adverse first-trimester outcomes in comparison to spontaneously achieved pregnancies. Human chorionic gonadotrophin β subunit (β-HCG) is a well-known biomarker for the diagnosis and monitoring of pregnancy after IVF. Low levels of β-HCG during this period are related to miscarriage, ectopic pregnancy, and IVF procedure failures. Longitudinal profiles of β-HCG can be used to distinguish between normal and abnormal pregnancies and to assist and guide the clinician in better management and monitoring of post-IVF pregnancies. Therefore, assessing the association between longitudinally measured β-HCG serum concentration and time to early miscarriage is of crucial interest to clinicians. A common joint modeling approach is to use the longitudinal β-HCG trajectory to determine the risk of miscarriage. This work was motivated by a follow-up study with normal and abnormal pregnancies where β-HCG serum concentrations were measured in 173 young women during a gestational age of 9-86 days in Santiago, Chile. Some women experienced a miscarriage event, and their exact event times were unknown, so we have interval-censored data, with the event occurring between the last time of the observed measurement and ten days later. However, for those women belonging to the normal pregnancy group; that is, carrying a pregnancy to a full-term event, right censoring data are observed. Estimation procedures are based on the Stochastic Approximation of the Expectation-Maximization (SAEM) algorithm.

Lung Function Decline in Cystic Fibrosis: Impact of Data Availability and Modeling Strategies on Clinical Interpretations

Rationale: Studies estimating the rate of lung function decline in cystic fibrosis have been inconsistent regarding the methods used. How the methodology used impacts the validity of the results and comparability between studies is unknown. Objectives: The Cystic Fibrosis Foundation established a work group whose tasks were to examine the impact of differing approaches to estimating the rate of decline in lung function and to provide analysis guidelines. Methods: We used a natural history cohort of 35,252 individuals with cystic fibrosis aged ⩾6 years in the Cystic Fibrosis Foundation Patient Registry (CFFPR), 2003-2016. Modeling strategies using linear and nonlinear forms of marginal and mixed-effects models, which have previously quantified the rate of forced expiratory volume in 1 second (FEV1) decline (percent predicted per year), were evaluated under clinically relevant scenarios of available lung function data. Scenarios varied by sample size (overall CFFPR, medium-sized cohort of 3,000 subjects, and small-sized cohort of 150), data collection/reporting frequency (encounter, quarterly, and annual), inclusion of FEV1 during pulmonary exacerbation, and follow-up length (<2 yr, 2-5 yr, entire duration). Results: Rate of FEV1 decline estimates (percent predicted per year) differed between linear marginal and mixed-effects models; overall cohort estimates (95% confidence interval) were 1.26 (1.24-1.29) and 1.40 (1.38-1.42), respectively. Marginal models consistently estimated less rapid lung function decline than mixed-effects models across scenarios, except for short-term follow-up (both were ∼1.4). Rate of decline estimates from nonlinear models diverged by age 30. Among mixed-effects models, nonlinear and stochastic terms fit best, except for short-term follow-up (<2 yr). Overall CFFPR analysis from a joint longitudinal-survival model implied that an increase in rate of decline of 1% predicted per year in FEV1 was associated with a 1.52-fold (52%) increase in the hazard of death/lung transplant, but the results exhibited immortal cohort bias. Conclusions: Differences were as high as 0.5% predicted per year between rate of decline estimates, but we found estimates were robust to lung function data availability scenarios, except short-term follow-up and older age ranges. Inconsistencies among previous study results may be attributable to inherent differences in study design, inclusion criteria, or covariate adjustment. Results-based decision points reported herein will support researchers in selecting a strategy to model lung function decline most reflective of nuanced, study-specific goals.

Measuring Individual Benefits of Medical Treatments Using Longitudinal Hospital Data with Non-Ignorable Missing Responses Caused by Patient Discharge: Application to the Study of Benefits of Pain Management Post Spinal Fusion

Electronic health records (EHR) provide valuable resources for longitudinal studies and understanding risk factors associated with poor clinical outcomes. However, they may not contain complete follow-ups, and the missing data may not be at random since hospital discharge may depend in part on expected but unrecorded clinical outcomes that occur after patient discharge. These non-ignorable missing data requires appropriate analysis methods. Here, we are interested in measuring and analyzing individual treatment benefits of medical treatments in patients recorded in EHR databases. We present a method for predicting individual benefits that handles non-ignorable missingness due to hospital discharge. The longitudinal clinical outcome of interest is modeled simultaneously with the hospital length of stay using a joint mixed-effects model, and individual benefits are predicted through a frequentist approach: the empirical Bayesian approach. We illustrate our approach by assessing individual pain management benefits to patients who underwent spinal fusion surgery. By calculating sample percentiles of empirical Bayes predictors of individual benefits, we examine the evolution of individual benefits over time. We additionally compare these percentiles with percentiles calculated with a Monte Carlo approach. We showed that empirical Bayes predictors of individual benefits do not only allow examining benefits in specific patients but also reflect overall population trends reliably.

Traffic-related air pollution associated pulmonary pathophysiologic changes and cardiac injury in elderly patients with COPD

Traffic-related air pollution (TRAP) has shown enormous environmental toxicity, but its cardiorespiratory health impact on chronic obstructive pulmonary disease (COPD) has been less studied. We followed a panel of 45 COPD patients with 4 repeated clinical visits across 14 months in a traffic-predominated urban area of Beijing, China, with concurrent measurements of TRAP metrics (fine particulate matter, black carbon, oxides of nitrogen and carbon monoxide). Linear mixed-effect models were performed to evaluate the associations and potential pathways linking traffic pollution to indicators of spirometry, cardiac injury, inflammation and oxidative stress. We observed that interquartile range increases in moving averages of TRAP exposures at prior up to 7 days were associated with significant reductions in large and small airway functions, namely decreases in forced vital capacity of 3.1-9.3% and forced expiratory flow 25-75% of 5.9-16.4%. Higher TRAP levels were also associated with worsening of biomarkers relevant to lung injury (hepatocyte growth factor and surfactant protein D) and cardiac injury (high-sensitivity cardiac troponin I, B-type natriuretic peptide and soluble ST2), as well as enhanced airway/systemic inflammation and oxidative stress. Mediation analyses showed that TRAP exposures may prompt cardiac injury, possibly via worsening pulmonary pathophysiology. These findings highlight the importance of traffic pollution control priority in urban areas.

Modelling the association between biomarkers and clinical outcome: an introduction to nonlinear joint models

Nonlinear joint models are a powerful tool to precisely analyze the association between a nonlinear biomarker and a time-to-event process, such as death. Here, we review the main methodological techniques required to build these models and to make inferences and predictions. We describe the main clinical applications and discuss the future developments of such models.

Explaining the Sex Effect on Survival in Cystic Fibrosis: a Joint Modeling Study of UK Registry Data

BACKGROUND

Male sex is associated with better lung function and survival in people with cystic fibrosis but it is unclear whether the survival benefit is solely due to the sex-effect on lung function.

METHODS

This study analyzes data between 1996 and 2015 from the longitudinal registry study of the UK Cystic Fibrosis Registry. We jointly analyze repeated measurements and time-to-event outcomes to assess how much of the sex effect on lung function also explains survival. These novel methods allow examination of association between percent of forced expiratory volume in 1 second (%FEV1) and covariates such as sex and genotype, and survival, in the same modeling framework. We estimate the probability of surviving one more year with a probit model.

RESULTS

The dataset includes 81,129 lung function measurements of %FEV1 on 9,741 patients seen between 1996 and 2015 and captures 1,543 deaths. Males compared with females experienced a more gradual decline in %FEV1 (difference 0.11 per year 95% confidence interval [CI] = 0.08, 0.14). After adjusting for confounders, both overall level of %FEV1 and %FEV1 rate of change are associated with the concurrent hazard for death. There was evidence of a male survival advantage (probit coefficient 0.15; 95% CI = 0.10, 0.19) which changed little after adjustment for %FEV1 using conventional approaches but was attenuated by 37% on adjustment for %FEV1 level and slope in the joint model (0.09; 95% CI = 0.06, 0.12).

CONCLUSIONS

We estimate that about 37% of the association of sex on survival in cystic fibrosis is mediated through lung function.

Flexible link functions in a joint hierarchical Gaussian process model

Many longitudinal studies often require jointly modeling a biomarker and an event outcome, in order to provide more accurate inference and dynamic prediction of disease progression. Cystic fibrosis (CF) studies have illustrated the benefits of these models, primarily examining the joint evolution of lung-function decline and survival. We propose a novel joint model within the shared-parameter framework that accommodates nonlinear lung-function trajectories, in order to provide more accurate inference on lung-function decline over time and to examine the association between evolution of lung function and risk of a pulmonary exacerbation (PE) event recurrence. Specifically, a two-level Gaussian process (GP) is used to estimate the nonlinear longitudinal trajectories and a flexible link function is introduced for a more accurate depiction of the binary process on the event outcome. Bayesian model assessment is used to evaluate each component of the joint model in simulation studies and an application to longitudinal data on patients receiving care from a CF center. A nonlinear structure is suggested by both longitudinal continuous and binary evaluations. Including a flexible link function improves model fit to these data. The proposed hierarchical GP model with a flexible power link function where Laplace distribution is the baseline (spep) has the best fit of all joint models considered, characterizing how accelerated lung-function decline corresponds to increased odds of experiencing another PE.

Modelling of viral load dynamics and CD4 cell count progression in an antiretroviral naive cohort: using a joint linear mixed and multistate Markov model

Background

Patients infected with HIV may experience a succession of clinical stages before the disease diagnosis and their health status may be followed-up by tracking disease biomarkers. In this study, we present a joint multistate model for predicting the clinical progression of HIV infection which takes into account the viral load and CD4 count biomarkers.

Methods

The data is from an ongoing prospective cohort study conducted among antiretroviral treatment (ART) naïve HIV-infected women in the province of KwaZulu-Natal, South Africa. We presented a joint model that consists of two related submodels: a Markov multistate model for CD4 cell count transitions and a linear mixed effect model for longitudinal viral load dynamics.

Results

Viral load dynamics significantly affect the transition intensities of HIV/AIDS disease progression. The analysis also showed that patients with relatively high educational levels (β = − 0.004; 95% confidence interval [CI]:-0.207, − 0.064), high RBC indices scores (β = − 0.01; 95%CI:-0.017, − 0.002) and high physical health scores (β = − 0.001; 95%CI:-0.026, − 0.003) were significantly were associated with a lower rate of viral load increase over time. Patients with TB co-infection (β = 0.002; 95%CI:0.001, 0.004), having many sex partners (β = 0.007; 95%CI:0.003, 0.011), being younger age (β = 0.008; 95%CI:0.003, 0.012) and high liver abnormality scores (β = 0.004; 95%CI:0.001, 0.01) were associated with a higher rate of viral load increase over time. Moreover, patients with many sex partners (β = − 0.61; 95%CI:-0.94, − 0.28) and with a high liver abnormality score (β = − 0.17; 95%CI:-0.30, − 0.05) showed significantly reduced intensities of immunological recovery transitions. Furthermore, a high weight, high education levels, high QoL scores, high RBC parameters and being of middle age significantly increased the intensities of immunological recovery transitions.

Conclusion

Overall, from a clinical perspective, QoL measurement items, being of a younger age, clinical attributes, marital status, and educational status are associated with the current state of the patient, and are an important contributing factor to extend survival of the patients and guide clinical interventions. From a methodological perspective, it can be concluded that a joint multistate model approach provides wide-ranging information about the progression and assists to provide specific dynamic predictions and increasingly precise knowledge of diseases.