Joint modeling of survival and longitudinal non-survival data: current methods and issues. Report of the DIA Bayesian joint modeling working group

Joint modelling of time-to-clinical malaria and parasite count in a cohort in an endemic area

Background

In malaria endemic areas such as sub-Saharan Africa, repeated exposure to malaria results in acquired immunity to clinical disease but not infection. In prospective studies, time-to-clinical malaria and longitudinal parasite count trajectory are often analysed separately which may result in inefficient estimates since these two processes can be associated. Including parasite count as a time-dependent covariate in a model of time-to-clinical malaria episode may also be inaccurate because while clinical malaria disease frequently leads to treatment which may instantly affect the level of parasite count, standard time-to-event models require that time-dependent covariates be external to the event process. We investigated whether jointly modelling time-to-clinical malaria disease and longitudinal parasite count improves precision in risk factor estimates and assessed the strength of association between the hazard of clinical malaria and parasite count.

Methods

Using a cohort data of participants enrolled with uncomplicated malaria in Malawi, a conventional Cox Proportional Hazards (PH) model of time-to-first clinical malaria episode with time-dependent parasite count was compared with three competing joint models. The joint models had different association structures linking a quasi-Poisson mixed-effects of parasite count and event-time Cox PH sub-models.

Results

There were 120 participants of whom 115 (95.8%) had >1 follow-up visit and 100 (87.5%) experienced the episode. Adults >15 years being reference, log hazard ratio for children <5 years was 0.74 (95% CI: 0.17, 1.26) in the joint model with best fit vs. 0.62 (95% CI: 0.04, 1.18) from the conventional Cox PH model. The log hazard ratio for the 5-15 years was 0.72 (95% CI: 0.22, 1.22) in the joint model vs.0.63 (95% CI: 0.11, 1.17) in the Cox PH model. The area under parasite count trajectory was strongly associated with the risk of clinical malaria, with a unit increase corresponding to-0.0012 (95% CI: -0.0021, -0.0004) decrease in log hazard ratio.

Conclusion

Jointly modelling longitudinal parasite count and time-to-clinical malaria disease improves precision in log hazard ratio estimates compared to conventional time-dependent Cox PH model. The improved precision of joint modelling may improve study efficiency and allow for design of clinical trials with relatively lower sample sizes with increased power.

Evaluating associations between the benefits and risks of drug therapy in type 2 diabetes: a joint modeling approach

OBJECTIVE

Precision medicine drug therapy seeks to maximize efficacy and minimize harm for individual patients. This will be difficult if drug response and side effects are positively associated, meaning that patients likely to respond best are at increased risk of side effects. We applied joint longitudinal-survival models to evaluate associations between drug response (longitudinal outcome) and the risk of side effects (survival outcome) for patients initiating type 2 diabetes therapy.

STUDY DESIGN AND SETTING

Participants were randomized to metformin (MFN), sulfonylurea (SU), or thiazolidinedione (TZD) therapy in the A Diabetes Outcome Progression Trial (ADOPT) drug efficacy trial (n=4,351). Joint models were parameterized for 1) current HbA1c response (change from baseline in HbA1c) and 2) cumulative HbA1c response (total HbA1c change).

RESULTS

With MFN, greater HbA1c response did not increase the risk of gastrointestinal events (HR per 1% absolute greater current response 0.82 [95% CI 0.67, 1.01]; HR per 1% higher cumulative response 0.90 [95% CI 0.81, 1.00]). With SU, greater current response was associated with an increased risk of hypoglycemia (HR 1.41 [95% CI 1.04, 1.91]). With TZD, greater response was associated with an increased risk of edema (current HR 1.45 [95% CI 1.05, 2.01]; cumulative 1.22 [95% CI 1.07, 1.38]) but not fracture.

CONCLUSION

Joint modeling provides a useful framework to evaluate the association between response to a drug and the risk of developing side effects. There may be great potential for widespread application of joint modeling to evaluate the risks and benefits of both new and established medications.

Dynamic prediction of transition to psychosis using joint modelling

Considerable research has been conducted seeking risk factors and constructing prediction models for transition to psychosis in individuals at ultra-high risk (UHR). Nearly all such research has only employed baseline predictors, i.e. data collected at the baseline time point, even though longitudinal data on relevant measures such as psychopathology have often been collected at various time points. Dynamic prediction, which is the updating of prediction at a post-baseline assessment using baseline and longitudinal data accumulated up to that assessment, has not been utilized in the UHR context. This study explored the use of dynamic prediction and determined if it could enhance the prediction of frank psychosis onset in UHR individuals. An emerging statistical methodology called joint modelling was used to implement the dynamic prediction. Data from the NEURAPRO study (n = 304 UHR individuals), an intervention study with transition to psychosis study as the primary outcome, were used to investigate dynamic predictors. Compared with the conventional approach of using only baseline predictors, dynamic prediction using joint modelling showed significantly better sensitivity, specificity and likelihood ratios. As dynamic prediction can provide an up-to-date prediction for each individual at each new assessment post entry, it can be a useful tool to help clinicians adjust their prognostic judgements based on the unfolding clinical symptomatology of the patients. This study has shown that a dynamic approach to psychosis prediction using joint modelling has the potential to aid clinicians in making decisions about the provision of timely and personalized treatment to patients concerned.

Joint longitudinal and time-to-event models for multilevel hierarchical data

Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper, we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient may have more than one lesion, and each lesion is tracked over time, the data have a three-level hierarchical structure: repeated measurements taken at time points (level 1) clustered within lesions (level 2) within patients (level 3). We jointly model the lesion-specific longitudinal trajectories and patient-specific risk of death or disease progression by specifying novel association structures that combine information across lower level clusters (e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide user-friendly software for fitting the model under a Bayesian framework. Lastly, we discuss alternative situations in which additional clustering factor(s) occur at a level higher in the hierarchy than the patient-level, since this has implications for the model formulation.

Nonlinear association structures in flexible Bayesian additive joint models

Joint models of longitudinal and survival data have become an important tool for modeling associations between longitudinal biomarkers and event processes. The association between marker and log hazard is assumed to be linear in existing shared random effects models, with this assumption usually remaining unchecked. We present an extended framework of flexible additive joint models that allows the estimation of nonlinear covariate specific associations by making use of Bayesian P-splines. Our joint models are estimated in a Bayesian framework using structured additive predictors for all model components, allowing for great flexibility in the specification of smooth nonlinear, time-varying, and random effects terms for longitudinal submodel, survival submodel, and their association. The ability to capture truly linear and nonlinear associations is assessed in simulations and illustrated on the widely studied biomedical data on the rare fatal liver disease primary biliary cirrhosis. All methods are implemented in the R package bamlss to facilitate the application of this flexible joint model in practice.

A Likelihood Based Approach for Joint Modeling of Longitudinal Trajectories and Informative Censoring Process

We propose a joint modeling likelihood-based approach for studies with repeated measures and informative right censoring. Joint modeling of longitudinal and survival data are common approaches but could result in biased estimates if proportionality of hazards is violated. To overcome this issue, and given that the exact time of dropout is typically unknown, we modeled the censoring time as the number of follow-up visits and extended it to be dependent on selected covariates. Longitudinal trajectories for each subject were modeled to provide insight into disease progression and incorporated with the number follow-up visits in one likelihood function.

HIV Viral Suppression Trends Over Time Among HIV-Infected Patients Receiving Care in the United States, 1997 to 2015: A Cohort Study

BACKGROUND

Because HIV viral suppression is essential for optimal outcomes and prevention efforts, understanding trends and predictors is imperative to inform public health policy.

OBJECTIVE

To evaluate viral suppression trends in people living with HIV (PLWH), including the relationship of associated factors, such as demographic characteristics and integrase strand transfer inhibitor (ISTI) use.

DESIGN

Longitudinal observational cohort study.

SETTING

8 HIV clinics across the United States.

PARTICIPANTS

PLWH receiving clinical care.

MEASUREMENTS

To understand trends in viral suppression (≤400 copies/mL), annual viral suppression rates from 1997 to 2015 were determined. Analyses were repeated with tests limited to 1 random test per person per year and using inverse probability of censoring weights to address loss to follow-up. Joint longitudinal and survival models and linear mixed models of PLWH receiving antiretroviral therapy (ART) were used to examine associations between viral suppression or continuous viral load (VL) levels and demographic factors, substance use, adherence, and ISTI use.

RESULTS

Viral suppression increased from 32% in 1997 to 86% in 2015 on the basis of all tests among 31 930 PLWH. In adjusted analyses, being older (odds ratio [OR], 0.76 per decade [95% CI, 0.74 to 0.78]) and using an ISTI-based regimen (OR, 0.54 [CI, 0.51 to 0.57]) were associated with lower odds of having a detectable VL, and black race was associated with higher odds (OR, 1.68 [CI, 1.57 to 1.80]) (P < 0.001 for each). Similar patterns were seen with continuous VL levels; when analyses were limited to 2010 to 2015; and with adjustment for adherence, substance use, or depression.

LIMITATION

Results are limited to PLWH receiving clinical care.

CONCLUSION

HIV viral suppression rates have improved dramatically across the United States, which is likely partially attributable to improved ART, including ISTI-based regimens. However, disparities among younger and black PLWH merit attention.

PRIMARY FUNDING SOURCE

National Institutes of Health.

Investigation of one-stage meta-analysis methods for joint longitudinal and time-to-event data through simulation and real data application

Background: Joint modeling of longitudinal and time‐to‐event data is often advantageous over separate longitudinal or time‐to‐event analyses as it can account for study dropout, error in longitudinally measured covariates, and correlation between longitudinal and time‐to‐event outcomes. The current literature on joint modeling focuses mainly on the analysis of single studies with a lack of methods available for the meta‐analysis of joint data from multiple studies.

Methods: We investigate a variety of one‐stage methods for the meta‐analysis of joint longitudinal and time‐to‐event outcome data. These methods are applied to the INDANA dataset to investigate longitudinally measured systolic blood pressure, with each of time to death, time to myocardial infarction, and time to stroke. Results are compared to separate longitudinal or time‐to‐event meta‐analyses. A simulation study is conducted to contrast separate versus joint analyses over a range of scenarios.

Results: The performance of the examined one‐stage joint meta‐analytic models varied. Models that accounted for between study heterogeneity performed better than models that ignored it. Of the examined methods to account for between study heterogeneity, under the examined association structure, fixed effect approaches appeared preferable, whereas methods involving a baseline hazard stratified by study were least time intensive.

Conclusions: One‐stage joint meta‐analytic models that accounted for between study heterogeneity using a mix of fixed effects or a stratified baseline hazard were reliable; however, models examined that included study level random effects in the association structure were less reliable.

Longitudinal body weight and sputum conversion in patients with tuberculosis, Southwest Ethiopia: a retrospective follow-up study

OBJECTIVES

To describe the association between change in body weight and sputum smear conversion and to identify factors linked with body weight and sputum smear conversion in Jimma University Specialized Hospital, Southwest Ethiopia.

DESIGN

A retrospective follow-up study.

SETTING

Teaching hospital in Southwest Ethiopia.

PARTICIPANTS

A total of 450 patients with tuberculosis (TB) were included in the follow-up between 2011 and 2013.

MAIN OUTCOME MEASURES

The association between body weight and sputum conversion was measured using joint modelling.

RESULTS

The association between change in body weight and change in sputum conversion was -0.698 (p<0.001). A strong inverse association between change in body weight and change in sputum conversion was observed. The study variables sex, age, type of TB, HIV status, dose of anti-TB drug and length of enrolment to TB treatment were significantly associated with change in body weight of patients with TB. The study variables age, type of TB, dose of anti-TB drug and length of enrolment were significantly associated with change in sputum status of patients with TB.

CONCLUSIONS

Among patients with TB who were on anti-TB treatment, increase in body weight and positive sputum status were inversely related over time. TB prevention and control strategies should give emphasis on factors such as female sex, older age, non-pulmonary positive type of TB, HIV-positive, lower dose of anti-TB drug and length of enrolment to TB treatment during monitoring of trends in body weight and sputum status.

Effect of In-Bed Leg Cycling and Electrical Stimulation of the Quadriceps on Global Muscle Strength in Critically Ill Adults: A Randomized Clinical Trial

IMPORTANCE

Early in-bed cycling and electrical muscle stimulation may improve the benefits of rehabilitation in patients in the intensive care unit (ICU).

OBJECTIVE

To investigate whether early in-bed leg cycling plus electrical stimulation of the quadriceps muscles added to standardized early rehabilitation would result in greater muscle strength at discharge from the ICU.

DESIGN, SETTING, AND PARTICIPANTS

Single-center, randomized clinical trial enrolling critically ill adult patients at 1 ICU within an 1100-bed hospital in France. Enrollment lasted from July 2014 to June 2016 and there was a 6-month follow-up, which ended on November 24, 2016.

INTERVENTIONS

Patients were randomized to early in-bed leg cycling plus electrical stimulation of the quadriceps muscles added to standardized early rehabilitation (n = 159) or standardized early rehabilitation alone (usual care) (n = 155).

MAIN OUTCOMES AND MEASURES

The primary outcome was muscle strength at discharge from the ICU assessed by physiotherapists blinded to treatment group using the Medical Research Council grading system (score range, 0-60 points; a higher score reflects better muscle strength; minimal clinically important difference of 4 points). Secondary outcomes at ICU discharge included the number of ventilator-free days and ICU Mobility Scale score (range, 0-10; a higher score reflects better walking capability). Functional autonomy and health-related quality of life were assessed at 6 months.

RESULTS

Among 314 randomized patients, 312 (mean age, 66 years; women, 36%; receiving mechanical ventilation at study inclusion, 78%) completed the study and were included in the analysis. The median global Medical Research Council score at ICU discharge was 48 (interquartile range [IQR], 29 to 58) in the intervention group and 51 (IQR, 37 to 58) in the usual care group (median difference, -3.0 [95% CI, -7.0 to 2.8]; P = .28). The ICU Mobility Scale score at ICU discharge was 6 (IQR, 3 to 9) in both groups (median difference, 0 [95% CI, -1 to 2]; P = .52). The median number of ventilator-free days at day 28 was 21 (IQR, 6 to 25) in the intervention group and 22 (IQR, 10 to 25) in the usual care group (median difference, 1 [95% CI, -2 to 3]; P = .24). Clinically significant events occurred during mobilization sessions in 7 patients (4.4%) in the intervention group and in 9 patients (5.8%) in the usual care group. There were no significant between-group differences in the outcomes assessed at 6 months.

CONCLUSIONS AND RELEVANCE

In this single-center randomized clinical trial involving patients admitted to the ICU, adding early in-bed leg cycling exercises and electrical stimulation of the quadriceps muscles to a standardized early rehabilitation program did not improve global muscle strength at discharge from the ICU.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT02185989.

Understanding Dynamic Status Change of Hospital Stay and Cost Accumulation via Combining Continuous and Finitely Jumped Processes

The Coxian phase-type models and the joint models of longitudinal and event time have been extensively used in the studies of medical outcome data. Coxian phase-type models have the finite-jump property while the joint models usually assume a continuous variation. The gap between continuity and discreteness makes the two models rarely used together. In this paper, a partition-based approach is proposed to jointly model the charge accumulation process and the time to discharge. The key construction of our new approach is a set of partition cells with their boundaries determined by a family of differential equations. Using the cells, our new approach makes it possible to incorporate finite jumps induced by a Coxian phase-type model into the charge accumulation process, therefore taking advantage of both the Coxian phase-type models and joint models. As a benefit, a couple of measures of the "cost" of staying in each medical stage (identified with phases of a Coxian phase-type model) are derived, which cannot be approached without considering the joint models and the Coxian phase-type models together. A two-step procedure is provided to generate consistent estimation of model parameters, which is applied to a subsample drawn from a well-known medical cost database.

joineRML: a joint model and software package for time-to-event and multivariate longitudinal outcomes

BACKGROUND

Joint modelling of longitudinal and time-to-event outcomes has received considerable attention over recent years. Commensurate with this has been a rise in statistical software options for fitting these models. However, these tools have generally been limited to a single longitudinal outcome. Here, we describe the classical joint model to the case of multiple longitudinal outcomes, propose a practical algorithm for fitting the models, and demonstrate how to fit the models using a new package for the statistical software platform R, joineRML.

RESULTS

A multivariate linear mixed sub-model is specified for the longitudinal outcomes, and a Cox proportional hazards regression model with time-varying covariates is specified for the event time sub-model. The association between models is captured through a zero-mean multivariate latent Gaussian process. The models are fitted using a Monte Carlo Expectation-Maximisation algorithm, and inferences are based on approximate standard errors from the empirical profile information matrix, which are contrasted to an alternative bootstrap estimation approach. We illustrate the model and software on a real data example for patients with primary biliary cirrhosis with three repeatedly measured biomarkers.

CONCLUSIONS

An open-source software package capable of fitting multivariate joint models is available. The underlying algorithm and source code makes use of several methods to increase computational speed.

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

Many longitudinal studies observe time to occurrence of a clinical event such as death, while also collecting serial measurements of one or more biomarkers that are predictive of the event, or are surrogate outcomes of interest. Joint modeling can be used to examine the relationship between the biomarker and the event, and also as a way of adjusting analyses of the biomarker for non-ignorable dropout. In settings such as registry studies, an additional complexity is caused when follow-up of subjects is delayed, referred to as left-truncation of follow-up in the survival analysis setting. If not adjusted for, this can cause bias in estimation of parameters of the survival distribution for the clinical event and in parameters of the longitudinal outcome such as the profile or rate of change over time because subjects may die or have the clinical event before follow-up starts. This paper illustrates how a broad class of shared parameter models can be used to jointly model a time to event outcome along with a longitudinal marker using available nonlinear mixed modeling software, when follow-up times are left truncated. Methods are applied to jointly model survival and decline in lung function in cystic fibrosis patients.

A new method for analysing transition to psychosis: Joint modelling of time-to-event outcome with time-dependent predictors

An active area in psychosis research is the identification of predictors of transition to a psychotic state among those who are assessed as being at high risk of psychosis. Many of the potential predictors are time dependent in the sense that they may change over time and are measured at a number of assessment time points. Examples are various psychopathological measures such as negative symptoms, positive symptoms, depression, and anxiety. Most research in transition to psychosis has not made use of the dynamic nature of these measures, probably because suitable statistical methods and software have not been easily available. However, a relatively new statistical methodology is well suited to include such time-dependent predictors in transition to psychosis analysis. This methodology is called joint modelling and has recently been incorporated in mainstream statistical software. This paper describes this methodology and demonstrates its usefulness using data from one of the pioneering studies on transition to psychosis.

Joint Models of Longitudinal and Time-to-Event Data with More Than One Event Time Outcome: A Review

Methodological development and clinical application of joint models of longitudinal and time-to-event outcomes have grown substantially over the past two decades. However, much of this research has concentrated on a single longitudinal outcome and a single event time outcome. In clinical and public health research, patients who are followed up over time may often experience multiple, recurrent, or a succession of clinical events. Models that utilise such multivariate event time outcomes are quite valuable in clinical decision-making. We comprehensively review the literature for implementation of joint models involving more than a single event time per subject. We consider the distributional and modelling assumptions, including the association structure, estimation approaches, software implementations, and clinical applications. Research into this area is proving highly promising, but to-date remains in its infancy.

The Effect of MSM and CD4+ Count on the Development of Cancer AIDS (AIDS-defining Cancer) and Non-cancer AIDS in the HAART Era

BACKGROUND

The HIV epidemic is increasing among Men who have Sex with Men (MSM) and the risk for AIDS defining cancer (ADC) is higher among them.

OBJECTIVE

To examine the effect of MSM and CD4+ count on time to cancer AIDS (ADC) and noncancer AIDS in competing risks setting in the HAART era.

METHOD

Using Ontario HIV Treatment Network Cohort Study data, HIV-positive adults diagnosed between January 1997 and October 2012 having baseline CD4+ counts ≤ 500 cells/mm3 were evaluated. Two survival outcomes, cancer AIDS and non-cancer AIDS, were treated as competing risks. Kaplan-Meier analysis, Cox cause-specific hazards (CSH) model and joint modeling of longitudinal and survival outcomes were used.

RESULTS

Among the 822 participants, 657 (79.9%) were males; 686 (83.5%) received anti-retroviral (ARV) ever. Regarding risk category, the majority (58.5%) were men who have Sex with men (MSM). Mean age was 37.4 years (SD = 10.3). In the multivariate Cox CSH models, MSM were not associated with cancer AIDS but with non-cancer AIDS [HR = 2.92; P = 0.055, HR = 0.54; P = 0.0009, respectively]. However, in joint models of longitudinal and survival outcomes, MSM were associated with cancer AIDS but not with non-cancer AIDS [HR = 3.86; P = 0.013, HR = 0.73; P = 0.10]. CD4+ count, age, ARV ever were associated with both events in the joint models.

CONCLUSION

This study demonstrates the importance of considering competing risks, and timedependent biomarker in the survival model. MSM have higher hazard for cancer AIDS. CD4+ count is associated with both survival outcomes.

Investigation of 2-stage meta-analysis methods for joint longitudinal and time-to-event data through simulation and real data application

Background

Joint modelling of longitudinal and time‐to‐event data is often preferred over separate longitudinal or time‐to‐event analyses as it can account for study dropout, error in longitudinally measured covariates, and correlation between longitudinal and time‐to‐event outcomes. The joint modelling literature focuses mainly on the analysis of single studies with no methods currently available for the meta‐analysis of joint model estimates from multiple studies.

Methods

We propose a 2‐stage method for meta‐analysis of joint model estimates. These methods are applied to the INDANA dataset to combine joint model estimates of systolic blood pressure with time to death, time to myocardial infarction, and time to stroke. Results are compared to meta‐analyses of separate longitudinal or time‐to‐event models. A simulation study is conducted to contrast separate versus joint analyses over a range of scenarios.

Results

Using the real dataset, similar results were obtained by using the separate and joint analyses. However, the simulation study indicated a benefit of use of joint rather than separate methods in a meta‐analytic setting where association exists between the longitudinal and time‐to‐event outcomes.

Conclusions

Where evidence of association between longitudinal and time‐to‐event outcomes exists, results from joint models over standalone analyses should be pooled in 2‐stage meta‐analyses.

Mammographic Density Reduction as a Prognostic Marker for Postmenopausal Breast Cancer: Results Using a Joint Longitudinal-Survival Modeling Approach

Previous studies have linked reductions in mammographic density after a breast cancer diagnosis to an improved prognosis. These studies focused on short-term change, using a 2-stage process, treating estimated change as a fixed covariate in a survival model. We propose the use of a joint longitudinal-survival model. This enables us to model long-term trends in density while accounting for dropout as well as for measurement error. We studied the change in mammographic density after a breast cancer diagnosis and its association with prognosis (measured by cause-specific mortality), overall and with respect to hormone replacement therapy and tamoxifen treatment. We included 1,740 women aged 50–74 years, diagnosed with breast cancer in Sweden during 1993–1995, with follow-up until 2008. They had a total of 6,317 mammographic density measures available from the first 5 years of follow-up, including baseline measures. We found that the impact of the withdrawal of hormone replacement therapy on density reduction was larger than that of tamoxifen treatment. Unlike previous studies, we found that there was an association between density reduction and survival, both for tamoxifen-treated women and women who were not treated with tamoxifen.

Joint modeling of longitudinal and survival data with a covariate subject to a limit of detection

We develop and study an innovative method for jointly modeling longitudinal response and time-to-event data with a covariate subject to a limit of detection. The joint model assumes a latent process based on random effects to describe the association between longitudinal and time-to-event data. We study the role of the association parameter on the regression parameters estimators. We model the longitudinal and survival outcomes using linear mixed-effects and Weibull frailty models, respectively. Because of the limit of detection, missing covariate (explanatory variable, x) values may lead to the non-ignorable missing, resulting in biased parameter estimates with poor coverage probabilities of the confidence interval. We define and estimate the probability of missing due to the limit of detection. Then we develop a novel joint density and hence the likelihood function that incorporates the effect of left-censored covariate. Monte Carlo simulations show that the estimators of the proposed method are approximately unbiased and provide expected coverage probabilities for both longitudinal and survival submodels parameters. We also present an application of the proposed method using a large clinical dataset of pneumonia patients obtained from the Genetic and Inflammatory Markers of Sepsis study.

Flexible Bayesian additive joint models with an application to type 1 diabetes research

The joint modeling of longitudinal and time-to-event data is an important tool of growing popularity to gain insights into the association between a biomarker and an event process. We develop a general framework of flexible additive joint models that allows the specification of a variety of effects, such as smooth nonlinear, time-varying and random effects, in the longitudinal and survival parts of the models. Our extensions are motivated by the investigation of the relationship between fluctuating disease-specific markers, in this case autoantibodies, and the progression to the autoimmune disease type 1 diabetes. Using Bayesian P-splines, we are in particular able to capture highly nonlinear subject-specific marker trajectories as well as a time-varying association between the marker and event process allowing new insights into disease progression. The model is estimated within a Bayesian framework and implemented in the R-package bamlss.

Dynamic predictions using flexible joint models of longitudinal and time-to-event data

Joint models for longitudinal and time-to-event data are particularly relevant to many clinical studies where longitudinal biomarkers could be highly associated with a time-to-event outcome. A cutting-edge research direction in this area is dynamic predictions of patient prognosis (e.g., survival probabilities) given all available biomarker information, recently boosted by the stratified/personalized medicine initiative. As these dynamic predictions are individualized, flexible models are desirable in order to appropriately characterize each individual longitudinal trajectory. In this paper, we propose a new joint model using individual-level penalized splines (P-splines) to flexibly characterize the coevolution of the longitudinal and time-to-event processes. An important feature of our approach is that dynamic predictions of the survival probabilities are straightforward as the posterior distribution of the random P-spline coefficients given the observed data is a multivariate skew-normal distribution. The proposed methods are illustrated with data from the HIV Epidemiology Research Study. Our simulation results demonstrate that our model has better dynamic prediction performance than other existing approaches. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

stpm: an R package for stochastic process model

Background

The Stochastic Process Model (SPM) represents a general framework for modeling the joint evolution of repeatedly measured variables and time-to-event outcomes observed in longitudinal studies, i.e., SPM relates the stochastic dynamics of variables (e.g., physiological or biological measures) with the probabilities of end points (e.g., death or system failure). SPM is applicable for analyses of longitudinal data in many research areas; however, there are no publicly available software tools that implement this methodology.

Results

We developed an R package stpm for the SPM-methodology. The package estimates several versions of SPM currently available in the literature including discrete- and continuous-time multidimensional models and a one-dimensional model with time-dependent parameters. Also, the package provides tools for simulation and projection of individual trajectories and hazard functions.

Conclusion

In this paper, we present the first software implementation of the SPM-methodology by providing an R package stpm, which was verified through extensive simulation and validation studies. Future work includes further improvements of the model. Clinical and academic researchers will benefit from using the presented model and software. The R package stpm is available as open source software from the following links: https://cran.r-project.org/package=stpm(stable version) or https://github.com/izhbannikov/spm(developer version).

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1538-7) contains supplementary material, which is available to authorized users.

Using nationwide ‘big data’ from linked electronic health records to help improve outcomes in cardiovascular diseases: 33 studies using methods from epidemiology, informatics, economics and social science in the ClinicAl disease research using LInked Bespoke studies and Electronic health Records (CALIBER) programme

Background

Electronic health records (EHRs), when linked across primary and secondary care and curated for research use, have the potential to improve our understanding of care quality and outcomes.

Objective

To evaluate new opportunities arising from linked EHRs for improving quality of care and outcomes for patients at risk of or with coronary disease across the patient journey.

Design

Epidemiological cohort, health informatics, health economics and ethnographic approaches were used.

Setting

230 NHS hospitals and 226 general practices in England and Wales.

Participants

Up to 2 million initially healthy adults, 100,000 people with stable coronary artery disease (SCAD) and up to 300,000 patients with acute coronary syndrome.

Main outcome measures

Quality of care, fatal and non-fatal cardiovascular disease (CVD) events.

Data platform and methods

We created a novel research platform [ClinicAl disease research using LInked Bespoke studies and Electronic health Records (CALIBER)] based on linkage of four major sources of EHR data in primary care and national registries. We carried out 33 complementary studies within the CALIBER framework. We developed a web-based clinical decision support system (CDSS) in hospital chest pain clinics. We established a novel consented prognostic clinical cohort of SCAD patients.

Results

CALIBER was successfully established as a valid research platform based on linked EHR data in nearly 2 million adults with > 600 EHR phenotypes implemented on the web portal (seehttps://caliberresearch.org/portal). Despite national guidance, key opportunities for investigation and treatment were missed across the patient journey, resulting in a worse prognosis for patients in the UK compared with patients in health systems in other countries. Our novel, contemporary, high-resolution studies showed heterogeneous associations for CVD risk factors across CVDs. The CDSS did not alter the decision-making behaviour of clinicians in chest pain clinics. Prognostic models using real-world data validly discriminated risk of death and events, and were used in cost-effectiveness decision models.

Conclusions

Emerging ‘big data’ opportunities arising from the linkage of records at different stages of a patient’s journey are vital to the generation of actionable insights into the diagnosis, risk stratification and cost-effective treatment of people at risk of, or with, CVD.

Future work

The vast majority of NHS data remain inaccessible to research and this hampers efforts to improve efficiency and quality of care and to drive innovation. We propose three priority directions for further research. First, there is an urgent need to ‘unlock’ more detailed data within hospitals for the scale of the UK’s 65 million population. Second, there is a need for scaled approaches to using EHRs to design and carry out trials, and interpret the implementation of trial results. Third, large-scale, disease agnostic genetic and biological collections linked to such EHRs are required in order to deliver precision medicine and to innovate discovery.

Study registration

CALIBER studies are registered as follows: study 2 – NCT01569139, study 4 – NCT02176174 and NCT01164371, study 5 – NCT01163513, studies 6 and 7 – NCT01804439, study 8 – NCT02285322, and studies 26–29 – NCT01162187. Optimising the Management of Angina is registered as Current Controlled Trials ISRCTN54381840.

Funding

The National Institute for Health Research (NIHR) Programme Grants for Applied Research programme (RP-PG-0407-10314) (all 33 studies) and additional funding from the Wellcome Trust (study 1), Medical Research Council Partnership grant (study 3), Servier (study 16), NIHR Research Methods Fellowship funding (study 19) and NIHR Research for Patient Benefit (study 33).

Associations between community-level disaster exposure and individual-level changes in disability and risk of death for older Americans

Disasters occur frequently in the United States (US) and their impact on acute morbidity, mortality and short-term increased health needs has been well described. However, barring mental health, little is known about the medium or longer-term health impacts of disasters. This study sought to determine if there is an association between community-level disaster exposure and individual-level changes in disability and/or the risk of death for older Americans. Using the US Federal Emergency Management Agency's database of disaster declarations, 602 disasters occurred between August 1998 and December 2010 and were characterized by their presence, intensity, duration and type. Repeated measurements of a disability score (based on activities of daily living) and dates of death were observed between January 2000 and November 2010 for 18,102 American individuals aged 50-89 years, who were participating in the national longitudinal Health and Retirement Study. Longitudinal (disability) and time-to-event (death) data were modelled simultaneously using a 'joint modelling' approach. There was no evidence of an association between community-level disaster exposure and individual-level changes in disability or the risk of death. Our results suggest that future research should focus on individual-level disaster exposures, moderate to severe disaster events, or higher-risk groups of individuals.

Joint models for longitudinal and time-to-event data: a review of reporting quality with a view to meta-analysis

BACKGROUND

Joint models for longitudinal and time-to-event data are commonly used to simultaneously analyse correlated data in single study cases. Synthesis of evidence from multiple studies using meta-analysis is a natural next step but its feasibility depends heavily on the standard of reporting of joint models in the medical literature. During this review we aim to assess the current standard of reporting of joint models applied in the literature, and to determine whether current reporting standards would allow or hinder future aggregate data meta-analyses of model results.

METHODS

We undertook a literature review of non-methodological studies that involved joint modelling of longitudinal and time-to-event medical data. Study characteristics were extracted and an assessment of whether separate meta-analyses for longitudinal, time-to-event and association parameters were possible was made.

RESULTS

The 65 studies identified used a wide range of joint modelling methods in a selection of software. Identified studies concerned a variety of disease areas. The majority of studies reported adequate information to conduct a meta-analysis (67.7% for longitudinal parameter aggregate data meta-analysis, 69.2% for time-to-event parameter aggregate data meta-analysis, 76.9% for association parameter aggregate data meta-analysis). In some cases model structure was difficult to ascertain from the published reports.

CONCLUSIONS

Whilst extraction of sufficient information to permit meta-analyses was possible in a majority of cases, the standard of reporting of joint models should be maintained and improved. Recommendations for future practice include clear statement of model structure, of values of estimated parameters, of software used and of statistical methods applied.

Performance of joint modelling of time-to-event data with time-dependent predictors: an assessment based on transition to psychosis data

Joint modelling has emerged to be a potential tool to analyse data with a time-to-event outcome and longitudinal measurements collected over a series of time points. Joint modelling involves the simultaneous modelling of the two components, namely the time-to-event component and the longitudinal component. The main challenges of joint modelling are the mathematical and computational complexity. Recent advances in joint modelling have seen the emergence of several software packages which have implemented some of the computational requirements to run joint models. These packages have opened the door for more routine use of joint modelling. Through simulations and real data based on transition to psychosis research, we compared joint model analysis of time-to-event outcome with the conventional Cox regression analysis. We also compared a number of packages for fitting joint models. Our results suggest that joint modelling do have advantages over conventional analysis despite its potential complexity. Our results also suggest that the results of analyses may depend on how the methodology is implemented.

Time-dependent efficacy of longitudinal biomarker for clinical endpoint

Joint modelling of longitudinal biomarker and event-time processes has gained its popularity in recent years as they yield more accurate and precise estimates. Considering this modelling framework, a new methodology for evaluating the time-dependent efficacy of a longitudinal biomarker for clinical endpoint is proposed in this article. In particular, the proposed model assesses how well longitudinally repeated measurements of a biomarker over various time periods (0,t) distinguish between individuals who developed the disease by time t and individuals who remain disease-free beyond time t. The receiver operating characteristic curve is used to provide the corresponding efficacy summaries at various t based on the association between longitudinal biomarker trajectory and risk of clinical endpoint prior to each time point. The model also allows detecting the time period over which a biomarker should be monitored for its best discriminatory value. The proposed approach is evaluated through simulation and illustrated on the motivating dataset from a prospective observational study of biomarkers to diagnose the onset of sepsis.

Joint modelling of longitudinal and multi-state processes: application to clinical progressions in prostate cancer

Joint modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate-specific antigen (PSA) and time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post-radiotherapy, or to predict the risk of one specific type of clinical recurrence post-radiotherapy, from the PSA history. In this context, we present a joint model for a longitudinal process and a multi-state process, which is divided into two sub-models: a linear mixed sub-model for longitudinal data and a multi-state sub-model with proportional hazards for transition times, both linked by a function of shared random effects. Parameters of this joint multi-state model are estimated within the maximum likelihood framework using an EM algorithm coupled with a quasi-Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer. Thanks to the classical covariates available at baseline and the repeated PSA measurements, we are able to assess the biomarker's trajectory, define the risks of transitions between health states and quantify the impact of the PSA dynamics on each transition intensity. Copyright © 2016 John Wiley & Sons, Ltd.

Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues

Background

Available methods for the joint modelling of longitudinal and time-to-event outcomes have typically only allowed for a single longitudinal outcome and a solitary event time. In practice, clinical studies are likely to record multiple longitudinal outcomes. Incorporating all sources of data will improve the predictive capability of any model and lead to more informative inferences for the purpose of medical decision-making.

Methods

We reviewed current methodologies of joint modelling for time-to-event data and multivariate longitudinal data including the distributional and modelling assumptions, the association structures, estimation approaches, software tools for implementation and clinical applications of the methodologies.

Results

We found that a large number of different models have recently been proposed. Most considered jointly modelling linear mixed models with proportional hazard models, with correlation between multiple longitudinal outcomes accounted for through multivariate normally distributed random effects. So-called current value and random effects parameterisations are commonly used to link the models. Despite developments, software is still lacking, which has translated into limited uptake by medical researchers.

Conclusion

Although, in an era of personalized medicine, the value of multivariate joint modelling has been established, researchers are currently limited in their ability to fit these models routinely. We make a series of recommendations for future research needs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-016-0212-5) contains supplementary material, which is available to authorized users.

Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification

A now common goal in medical research is to investigate the inter-relationships between a repeatedly measured biomarker, measured with error, and the time to an event of interest. This form of question can be tackled with a joint longitudinal-survival model, with the most common approach combining a longitudinal mixed effects model with a proportional hazards survival model, where the models are linked through shared random effects. In this article, we look at incorporating delayed entry (left truncation), which has received relatively little attention. The extension to delayed entry requires a second set of numerical integration, beyond that required in a standard joint model. We therefore implement two sets of fully adaptive Gauss-Hermite quadrature with nested Gauss-Kronrod quadrature (to allow time-dependent association structures), conducted simultaneously, to evaluate the likelihood. We evaluate fully adaptive quadrature compared with previously proposed non-adaptive quadrature through a simulation study, showing substantial improvements, both in terms of minimising bias and reducing computation time. We further investigate, through simulation, the consequences of misspecifying the longitudinal trajectory and its impact on estimates of association. Our scenarios showed the current value association structure to be very robust, compared with the rate of change that we found to be highly sensitive showing that assuming a simpler trend when the truth is more complex can lead to substantial bias. With emphasis on flexible parametric approaches, we generalise previous models by proposing the use of polynomials or splines to capture the longitudinal trend and restricted cubic splines to model the baseline log hazard function. The methods are illustrated on a dataset of breast cancer patients, modelling mammographic density jointly with survival, where we show how to incorporate density measurements prior to the at-risk period, to make use of all the available information. User-friendly Stata software is provided.

Joint longitudinal hurdle and time-to-event models: an application related to viral load and duration of the first treatment regimen in patients with HIV initiating therapy

Shared parameter joint models provide a framework under which a longitudinal response and a time to event can be modelled simultaneously. A common assumption in shared parameter joint models has been to assume that the longitudinal response is normally distributed. In this paper, we instead propose a joint model that incorporates a two-part 'hurdle' model for the longitudinal response, motivated in part by longitudinal response data that is subject to a detection limit. The first part of the hurdle model estimates the probability that the longitudinal response is observed above the detection limit, whilst the second part of the hurdle model estimates the mean of the response conditional on having exceeded the detection limit. The time-to-event outcome is modelled using a parametric proportional hazards model, assuming a Weibull baseline hazard. We propose a novel association structure whereby the current hazard of the event is assumed to be associated with the current combined (expected) outcome from the two parts of the hurdle model. We estimate our joint model under a Bayesian framework and provide code for fitting the model using the Bayesian software Stan. We use our model to estimate the association between HIV RNA viral load, which is subject to a lower detection limit, and the hazard of stopping or modifying treatment in patients with HIV initiating antiretroviral therapy. Copyright © 2016 John Wiley & Sons, Ltd.

Declines in Strength and Mortality Risk Among Older Mexican Americans: Joint Modeling of Survival and Longitudinal Data

BACKGROUND

Grip strength is a noninvasive method of risk stratification; however, the association between changes in strength and mortality is unknown. The purposes of this study were to examine the association between grip strength and mortality among older Mexican Americans and to determine the ability of changes in strength to predict mortality.

METHODS

Longitudinal data were included from 3,050 participants in the Hispanic Established Population for the Epidemiological Study of the Elderly. Strength was assessed using a hand-held dynamometer and normalized to body mass. Conditional inference tree analyses were used to identify sex- and age-specific weakness thresholds, and the Kaplan-Meier estimator was used to determine survival estimates across various strata. We also evaluated survival with traditional Cox proportional hazard regression for baseline strength, as well as with joint modeling of survival and longitudinal strength change trajectories.

RESULTS

Survival estimates were lower among women who were weak at baseline for only 65- to 74-year-olds (11.93 vs 16.69 years). Survival estimates were also lower among men who were weak at baseline for only ≥75-year-olds (5.80 vs 7.39 years). Lower strength at baseline (per 0.1 decrement) was significantly associated with mortality (hazard ratio [HR]: 1.10; 95% confidence interval [CI]: 1.01-1.19) for women only. There was a strong independent, longitudinal association between strength decline and early mortality, such that each 0.10 decrease in strength, within participants over time, resulted in a HR of 1.12 (95% CI: 1.00-1.25) for women and a HR of 1.15 (95% CI: 1.04-1.28) for men.

CONCLUSIONS

Longitudinal declines in strength are significantly associated with all-cause mortality in older Mexican Americans.