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

Weight calibration in the joint modelling of medical cost and mortality

Joint modelling of longitudinal and time-to-event data is a method that recognizes the dependency between the two data types, and combines the two outcomes into a single model, which leads to more precise estimates. These models are applicable when individuals are followed over a period of time, generally to monitor the progression of a disease or a medical condition, and also when longitudinal covariates are available. Medical cost datasets are often also available in longitudinal scenarios, but these datasets usually arise from a complex sampling design rather than simple random sampling and such complex sampling design needs to be accounted for in the statistical analysis. Ignoring the sampling mechanism can lead to misleading conclusions. This article proposes a novel approach to the joint modelling of complex data by combining survey calibration with standard joint modelling. This is achieved by incorporating a new set of equations to calibrate the sampling weights for the survival model in a joint model setting. The proposed method is applied to data on anti-dementia medication costs and mortality in people with diagnosed dementia in New Zealand.

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.

Disease progression joint model predicts time to type 1 diabetes onset: Optimizing future type 1 diabetes prevention studies

Clinical trials seeking type 1 diabetes prevention are challenging in terms of identifying patient populations likely to progress to type 1 diabetes within limited (i.e., short-term) trial durations. Hence, we sought to improve such efforts by developing a quantitative disease progression model for type 1 diabetes. Individual-level data obtained from the TrialNet Pathway to Prevention and The Environmental Determinants of Diabetes in the Young natural history studies were used to develop a joint model that links the longitudinal glycemic measure to the timing of type 1 diabetes diagnosis. Baseline covariates were assessed using a stepwise covariate modeling approach. Our study focused on individuals at risk of developing type 1 diabetes with the presence of two or more diabetes-related autoantibodies (AAbs). The developed model successfully quantified how patient features measured at baseline, including HbA1c and the presence of different AAbs, alter the timing of type 1 diabetes diagnosis with reasonable accuracy and precision (<30% RSE). In addition, selected covariates were statistically significant (p < 0.0001 Wald test). The Weibull model best captured the timing to type 1 diabetes diagnosis. The 2-h oral glucose tolerance values assessed at each visit were included as a time-varying biomarker, which was best quantified using the sigmoid maximum effect function. This model provides a framework to quantitatively predict and simulate the time to type 1 diabetes diagnosis in individuals at risk of developing the disease and thus, aligns with the needs of pharmaceutical companies and scientists seeking to advance therapies aimed at interdicting the disease process.

Using a Bayesian model of the joint distribution of pain and time on medication to decide on pain medication for neuropathy

The PAIN-CONTRoLS trial compared four medications in treating Cryptogenic sensory polyneuropathy. The primary outcome was a utility function that combined two outcomes, patients' pain score reduction and patients' quit rate. However, additional analysis of the individual outcomes could also be leveraged to inform selecting an optimal medication for future patients. We demonstrate how joint modeling of longitudinal and time-to-event data from PAIN-CONTRoLS can be used to predict the effects of medication in a patient-specific manner and helps to make patient-focused decisions. A joint model was used to evaluate the two outcomes while accounting for the association between the longitudinal process and the time-to-event processes. Results suggested no significant association between the patients' pain scores and time to the medication quit in the PAIN-CONTRoLS study, but the joint model still provided robust estimates and a better model fit. Using the model estimates, given patients' baseline characteristics, a drug profile on both the pain reduction and medication time could be obtained for each drug, providing information on how likely they would quit and how much pain reduction they should expect. Our analysis suggested that drugs viable for one patient may not be beneficial for others.

External validation and longitudinal application of the DO-GAP index to individualise survival prediction in idiopathic pulmonary fibrosis

Background

The Distance-Oxygen-Gender-Age-Physiology (DO-GAP) index has been shown to improve prognostication in idiopathic pulmonary fibrosis (IPF) compared to the Gender-Age-Physiology (GAP) score. We sought to externally validate the DO-GAP index compared to the GAP index for baseline risk assessment in patients with IPF. Additionally, we evaluated the utility of serial change in the DO-GAP index in predicting survival.

Methods

We performed an analysis of patients with IPF from the Pulmonary Fibrosis Foundation-Patient Registry (PFF-PR). Discrimination and calibration of the two models were assessed to predict transplant-free survival and IPF-related mortality. Joint longitudinal time-to-event modelling was utilised to individualise survival prediction based on DO-GAP index trajectory.

Results

There were 516 patients with IPF from the PFF-PR with available demographics, pulmonary function tests, 6-min walk test data and outcomes included in this analysis. The DO-GAP index (C-statistic: 0.73) demonstrated improved discrimination in discerning transplant-free survival compared to the GAP index (C-statistic: 0.67). DO-GAP index calibration was adequate, and the model retained predictive accuracy to identify IPF-related mortality (C-statistic: 0.74). The DO-GAP index was similarly accurate in the subset of patients taking antifibrotic medications. Serial change in the DO-GAP index improved model discrimination (cross-validated area under the curve: 0.83) enabling the personalised prediction of disease trajectory in individual patients.

Conclusion

The DO-GAP index is a simple, validated, multidimensional score that accurately predicts transplant-free survival in patients with IPF and can be adapted longitudinally in individual patients. The DO-GAP may also find use in studies of IPF to risk stratify patients and possibly as a clinical trial end-point.

Joint modelling of longitudinal processes and time-to-event outcomes in heart failure: systematic review and exemplar examining the relationship between serum digoxin levels and mortality

BACKGROUND

Joint modelling combines two or more statistical models to reduce bias and increase efficiency. As the use of joint modelling increases it is important to understand how and why it is being applied to heart failure research.

METHODS

A systematic review of major medical databases of studies which used joint modelling within heart failure alongside an exemplar; joint modelling repeat measurements of serum digoxin with all-cause mortality using data from the Effect of Digoxin on Mortality and Morbidity in Patients with Heart Failure (DIG) trial.

RESULTS

Overall, 28 studies were included that used joint models, 25 (89%) used data from cohort studies, the remaining 3 (11%) using data from clinical trials. 21 (75%) of the studies used biomarkers and the remaining studies used imaging parameters and functional parameters. The exemplar findings show that a per unit increase of square root serum digoxin is associated with the hazard of all-cause mortality increasing by 1.77 (1.34-2.33) times when adjusting for clinically relevant covariates.

CONCLUSION

Recently, there has been a rise in publications of joint modelling being applied to heart failure. Where appropriate, joint models should be preferred over traditional models allowing for the inclusion of repeated measures while accounting for the biological nature of biomarkers and measurement error.

Joint modeling of longitudinal measures of pneumonia and time to convalescence among pneumonia patients: a comparison of separate and joint models

BACKGROUND

Globally, pneumonia is the leading cause of children under age five morbidity and mortality with 98% of deaths in developing countries.

OBJECTIVE

This study aimed to identify the determinants of longitudinal measures of pneumonia and time to convalescence or recovery of under five admitted pneumonia patients at Felege Hiwot Referral Hospital, Bahir Dar, Ethiopia.

METHODS

A prospective cohort study was conducted among a randomly selected sample of 101 pneumonia patients using simple random sampling who were on follow up from December 2019 to February 2020. A Linear mixed effect model were used for the longitudinal outcomes and joint model for modeling both longitudinal and time to event outcomes jointly respectively.

RESULTS

The significant values of shared parameters in the survival sub model shows that the use of joint modeling of multivariate longitudinal outcomes with the time to event outcome is the best model compared to separate models. The estimated values of the association parameters: - 0.297(p-value = 0.0021), - 0.121) (p-value = < 0.001) and 0.5452 (p-value = 0.006) indicates association of respiratory rate, pulse rate and oxygen saturation respectively with time to recovery. The significant values show that there is an evidence to say that there is a negative relationship between longitudinal measures of respiratory rate and pulse rate with time to recovery and there is positive relationship between longitudinal measures of oxygen saturation with time to recovery. Variables age, birth order, dangerous signs, severity and visit time were significant factors on the longitudinal measure of pulse rate. The significant factors related to longitudinal measures of oxygen saturation were birth order, severity and visit. From this we can conclude that birth order, severity and visit were significant variables that simultaneously affect the longitudinal measures of respiratory rate, pulse rate and oxygen saturation of patients at 5% level of significance.

CONCLUSION

Results of multivariate joint analysis shows that severity was significant variable that jointly affects the three longitudinal measures and time to recovery of pneumonia patients and we can conclude that patients with severe pneumonia have high values of respiratory rate and pulse rate as well as less amount of oxygen saturation and they need longer time to recover from the disease.

Analysis of Recurrent Times-to-Clinical Malaria Episodes and Plasmodium falciparum Parasitemia: A Joint Modeling Approach Applied to a Cohort Data

Background

Recurrent clinical malaria episodes due to Plasmodium falciparum parasite infection are common in endemic regions. With each infection, acquired immunity develops, making subsequent disease episodes less likely. To capture the effect of acquired immunity to malaria, it may be necessary to model recurrent clinical disease episodes jointly with P. falciparum parasitemia data. A joint model of longitudinal parasitemia and time-to-first clinical malaria episode (single-event joint model) may be inaccurate because acquired immunity is lost when subsequent episodes are excluded. This study's informativeness assessed whether joint modeling of recurrent clinical malaria episodes and parasitemia is more accurate than a single-event joint model where the subsequent episodes are ignored.

Methods

The single event joint model comprised Cox Proportional Hazards (PH) sub-model for time-to-first clinical malaria episode and Negative Binomial (NB) mixed-effects sub-model for the longitudinal parasitemia. The recurrent events joint model extends the survival sub-model to a Gamma shared frailty model to include all recurrent clinical episodes. The models were applied to cohort data from Malawi. Simulations were also conducted to assess the performance of the model under different conditions.

Results

The recurrent events joint model, which yielded higher hazard ratios of clinical malaria, was more precise and in most cases produced smaller standard errors than the single-event joint model; hazard ratio (HR) = 1.42, [95% confidence interval [CI]: 1.22, 2.03] vs. HR = 1.29, [95% CI:1.60, 2.45] among participants who reported not to use LLINs every night compared to those who used the nets every night; HR = 0.96, [ 95% CI: 0.94, 0.98] vs. HR = 0.81, [95% CI: 0.75, 0.88] for each 1-year increase in participants' age; and HR = 1.36, [95% CI: 1.05, 1.75] vs. HR = 1.10, [95% CI: 0.83, 4.11] for observations during the rainy season compared to the dry season.

Conclusion

The recurrent events joint model in this study provides a way of estimating the risk of recurrent clinical malaria in a cohort where the effect of immunity on malaria disease acquired due to P. falciparum parasitemia with aging is captured. The simulation study has shown that if correctly specified, the recurrent events joint model can give risk estimates with low bias.

Efficient Algorithms and Implementation of a Semiparametric Joint Model for Longitudinal and Competing Risk Data: With Applications to Massive Biobank Data

Semiparametric joint models of longitudinal and competing risk data are computationally costly, and their current implementations do not scale well to massive biobank data. This paper identifies and addresses some key computational barriers in a semiparametric joint model for longitudinal and competing risk survival data. By developing and implementing customized linear scan algorithms, we reduce the computational complexities from O(n 2) or O(n 3) to O(n) in various steps including numerical integration, risk set calculation, and standard error estimation, where n is the number of subjects. Using both simulated and real-world biobank data, we demonstrate that these linear scan algorithms can speed up the existing methods by a factor of up to hundreds of thousands when n > 104, often reducing the runtime from days to minutes. We have developed an R package, FastJM, based on the proposed algorithms for joint modeling of longitudinal and competing risk time-to-event data and made it publicly available on the Comprehensive R Archive Network (CRAN).

Impact of lung function decline on time to hospitalisation events in systemic sclerosis-associated interstitial lung disease (SSc-ILD): a joint model analysis

BACKGROUND

Interstitial lung disease (ILD) is a common organ manifestation in systemic sclerosis (SSc) and is the leading cause of death in patients with SSc. A decline in forced vital capacity (FVC) is an indicator of ILD progression and is associated with mortality in patients with SSc-associated ILD (SSc-ILD). However, the relationship between FVC decline and hospitalisation events in patients with SSc-ILD is largely unknown. The objective of this post hoc analysis was to investigate the relationship between FVC decline and clinically important hospitalisation endpoints.

METHODS

We used data from SENSCIS®, a phase III trial investigating the efficacy and safety of nintedanib in patients with SSc-ILD. Joint models for longitudinal and time-to-event data were used to assess the association between rate of decline in FVC% predicted and hospitalisation-related endpoints (including time to first all-cause hospitalisation or death; time to first SSc-related hospitalisation or death; and time to first admission to an emergency room [ER] or admission to hospital followed by admission to intensive care unit [ICU] or death) during the treatment period, over 52 weeks in patients with SSc-ILD.

RESULTS

There was a statistically significant association between FVC decline and the risk of all-cause (n = 78) and SSc-related (n = 42) hospitalisations or death (both P < 0.0001). A decrease of 3% in FVC corresponded to a 1.43-fold increase in risk of all-cause hospitalisation or death (95% confidence interval [CI] 1.24, 1.65) and a 1.48-fold increase in risk of SSc-related hospitalisation or death (95% CI 1.23, 1.77). No statistically significant association was observed between FVC decline and admission to ER or to hospital followed by admission to ICU or death (n = 75; P = 0.15). The estimated slope difference for nintedanib versus placebo in the longitudinal sub-model was consistent with the primary analysis in SENSCIS®.

CONCLUSIONS

The association of lung function decline with an increased risk of hospitalisation suggests that slowing FVC decline in patients with SSc-ILD may prevent hospitalisations. Our findings also provide evidence that FVC decline may serve as a surrogate endpoint for clinically relevant hospitalisation-associated endpoints.

TRIAL REGISTRATION

ClinicalTrials.gov NCT02597933 . Registered on 8 October 2015.

Congestive Heart Failure Patients’ Pulse Rate Progression and Time to Death at Debre Tabor Referral Hospital, Ethiopia

Background. Heart failure is a progressive condition marked by worsening symptoms such as shortness of breath, coughing, exhaustion and lethargy, fluid retention with swelling of the legs and abdomen, and a reduced ability to exercise. As a result, this study aims to use a joint model application to determine the joint risk factors of longitudinal change in pulse rate and time to death of congestive heart failure patients and their association admitted to a hospital. Methods. A retrospective study was undertaken on congestive heart failure patients admitted to the Debre Tabor Referral Hospital from January 2016 to December 2019. A statistical joint modeling strategy was employed to match the repeated biomarker pulse rate and a survival outcome at the same time. A total of 271 patients with congestive heart failure were chosen. Data were analyzed with R statistical software via joineRML. Results. According to the findings, the association between longitudinal changes in pulse rate and time to death in heart failure patients is statistically significant. Sex, residence, left ventricular injection fraction, New York Heart Association class, and diabetes mellitus were all found to be significant risk factors for congestive heart failure patients’ short survival time to death. Age, sex, residence, hypertension, left ventricular injection fraction, congestive heart failure, diabetes mellitus, tuberculosis, and etiology were all significant contributors in pulse rate progression. Conclusion. The computed association parameters revealed subject-specific values. The subject-specific linear time slope of PR measurement was positively related to the hazard rate of time to death of CHF patients in the study area. To reduce the risk level of CHF, health professionals, governmental organizations, and nongovernmental organizations must promote and allocate a suitable amount of budget for the treatment of CHF patients.

Dynamic prediction models improved the risk classification of type 2 diabetes compared with classical static models

OBJECTIVE

Dynamic prediction models use the repeated measurements of predictors to estimate coefficients that link the longitudinal predictors to a static model (i.e. Cox regression). This study aims to develop and validate a dynamic prediction for incident type 2 diabetes (T2DM) as the outcome.

STUDY DESIGN AND SETTING

Data from the Tehran lipid and glucose study was used to develop (n = 5291 individuals; phases 1 to 3) and validate (n = 3147 individuals; phases 3 to 6) the dynamic prediction model among individuals aged ≥ 20 years. We used repeated measurements of fasting plasma glucose (FPG) or waist circumference (WC) in the framework of the joint modeling (JM) of longitudinal and time-to-event analysis.

RESULTS

Compared with the Cox which used just baseline data, JM showed the same discrimination, better calibration, and higher clinical usefulness (i.e. with a net benefit considering both true and false positive decisions); all were shown with repeated measurements of FPG/WC. Additionally, in our study, the dynamic models improve the risk reclassification (net reclassification index 33% for FPG and 24% for WC model).

CONCLUSION

Dynamic prediction models, compared with the static one could yield significant improvements in the prediction of T2DM. The complexity of the dynamic models could be addressed by using decision support systems.

Predicting Biologic Therapy Outcome of Patients With Spondyloarthritis: Joint Models for Longitudinal and Survival Analysis

BACKGROUND

Rheumatic diseases are one of the most common chronic diseases worldwide. Among them, spondyloarthritis (SpA) is a group of highly debilitating diseases, with an early onset age, which significantly impacts patients' quality of life, health care systems, and society in general. Recent treatment options consist of using biologic therapies, and establishing the most beneficial option according to the patients' characteristics is a challenge that needs to be overcome. Meanwhile, the emerging availability of electronic medical records has made necessary the development of methods that can extract insightful information while handling all the challenges of dealing with complex, real-world data.

OBJECTIVE

The aim of this study was to achieve a better understanding of SpA patients' therapy responses and identify the predictors that affect them, thereby enabling the prognosis of therapy success or failure.

METHODS

A data mining approach based on joint models for the survival analysis of the biologic therapy failure is proposed, which considers the information of both baseline and time-varying variables extracted from the electronic medical records of SpA patients from the database, Reuma.pt.

RESULTS

Our results show that being a male, starting biologic therapy at an older age, having a larger time interval between disease start and initiation of the first biologic drug, and being human leukocyte antigen (HLA)-B27 positive are indicators of a good prognosis for the biological drug survival; meanwhile, having disease onset or biologic therapy initiation occur in more recent years, a larger number of education years, and higher values of C-reactive protein or Bath Ankylosing Spondylitis Functional Index (BASFI) at baseline are all predictors of a greater risk of failure of the first biologic therapy.

CONCLUSIONS

Among this Portuguese subpopulation of SpA patients, those who were male, HLA-B27 positive, and with a later biologic therapy starting date or a larger time interval between disease start and initiation of the first biologic therapy showed longer therapy adherence. Joint models proved to be a valuable tool for the analysis of electronic medical records in the field of rheumatic diseases and may allow for the identification of potential predictors of biologic therapy failure.

Comparison of Joint and Landmark Modeling for Predicting Cancer Progression in Men With Castration-Resistant Prostate Cancer: A Secondary Post Hoc Analysis of the PREVAIL Randomized Clinical Trial

IMPORTANCE

Dynamic prediction models may help predict radiographic disease progression in advanced prostate cancer.

OBJECTIVE

To assess whether dynamic prediction models aid prognosis of radiographic progression risk, using ongoing longitudinal prostate-specific antigen (PSA) assessments.

DESIGN, SETTING, AND PARTICIPANTS

This prognostic study used data from the PREVAIL study to compare dynamic models for predicting disease progression. The PREVAIL study was a phase 3, multinational, double-blind, placebo-controlled randomized clinical trial of enzalutamide for prostate cancer conducted from September 2010 to September 2012. A total of 773 men with metastatic castration-resistant prostate cancer (CRPC) who had never received chemotherapy and had no baseline visceral disease were treated with enzalutamide. For illustration, 4 patients were selected based on PSA kinetics or PSA response in case studies. Data were analyzed from July 2018 to September 2019.

MAIN OUTCOMES AND MEASURES

Landmark and joint models were applied to dynamically predict radiographic progression-free survival (PFS) using longitudinal PSA profile, baseline PSA, lactate dehydrogenase, and hemoglobin levels. The main outcome was radiographic PFS as predicted using landmark and joint models. Current PSA and PSA change were considered longitudinal biomarkers possibly associated with radiographic PFS. Predictive performance was evaluated using Brier score for overall prediction errors (PEs) and area under the curve (AUC) for model discriminative capability. Case studies were illustrated using dynamic prediction plots.

RESULTS

A total of 763 men with metastatic CRPC treated with enzalutamide (mean [SD] age, 71.2 [8.5] years; mean [SD] body mass index [calculated as weight in kilograms divided by height in meters squared], 28.4 [4.6]) were included in the analysis. Current PSA and PSA change were associated with radiographic PFS in all models. Adding the PSA slope, compared with the landmark models using current PSA alone, improved the prediction of 5-month prospect of radiographic progression, with relative gains of 5.7% in prediction (PE [SE], 0.132 [0.008] vs 0.140 [0.008]) and 7.7% in discrimination (AUC [SE], 0.800 [0.018] vs 0.743 [0.018]) at month 10. In joint models with linear vs nonlinear PSA, prediction of 5-month risk of radiographic progression was improved when PSA trajectories were not assumed to be linear, with 8.0% relative gain in prediction (PE [SE], 0.150 [0.006] vs 0.138 [0.005]) and 19.4% relative gain in discrimination (AUC [SE], 0.653 [0.022] vs 0.780 [0.016]) at month 10. Predictions were affected by amount of marker information accumulated and prespecified assumptions. PSA changes affected progression risk more strongly at later vs earlier follow-up.

CONCLUSIONS AND RELEVANCE

This prognostic study found that prediction of radiographic PFS was improved when longitudinal PSA information was added to baseline variables. In a population of patients with metastatic CRPC, dynamic predictions using landmark or joint models may help identify patients at risk of progression.

Cognitive reserve in amyotrophic lateral sclerosis (ALS): a population-based longitudinal study

BACKGROUND

Amyotrophic lateral sclerosis (ALS) is often associated with cognitive and/or behavioural impairment. Cognitive reserve (CR) may play a protective role in offsetting cognitive impairment. This study examined the relationship between CR and longitudinal change in cognition in an Irish ALS cohort.

METHODS

Longitudinal neuropsychological assessment was carried out on 189 patients over 16 months using the Edinburgh cognitive and behavioural ALS screen (ECAS) and an additional battery of neuropsychological tests. CR was measured by combining education, occupation and physical activity data. Joint longitudinal and time-to-event models were fitted to investigate the associations between CR, performance at baseline and decline over time while controlling for non-random drop-out.

RESULTS

CR was a significant predictor of baseline neuropsychological performance, with high CR patients performing better than those with medium or low CR. Better cognitive performance in high CR individuals was maintained longitudinally for ECAS, social cognition, executive functioning and confrontational naming. Patients displayed little cognitive decline over the course of the study, despite controlling for non-random drop-out.

CONCLUSIONS

These findings suggest that CR plays a role in the presentation of cognitive impairment at diagnosis but is not protective against cognitive decline. However, further research is needed to examine the interaction between CR and other objective correlates of cognitive impairment in ALS.

Bayesian inference using Hamiltonian Monte-Carlo algorithm for nonlinear joint modeling in the context of cancer immunotherapy

Treatment evaluation in advanced cancer mainly relies on overall survival and tumor size dynamics. Both markers and their association can be simultaneously analyzed by using joint models, and these approaches are supported by many softwares or packages. However, these approaches are essentially limited to linear models for the longitudinal part, which limit their biological interpretation. More biological models of tumor dynamics can be obtained by using nonlinear models, but they are limited by the fact that parameter identifiability require rich dataset. In that context Bayesian approaches are particularly suited to incorporate the biological knowledge and increase the information available, but they are limited by the high computing cost of Monte-Carlo by Markov Chains algorithms. Here, we aimed to assess the performances of the Hamiltonian Monte-Carlo (HMC) algorithm implemented in Stan for inference in a nonlinear joint model. The method was validated on simulated data where HMC provided proper posterior distributions and credibility intervals in a reasonable computational time. Then the association between tumor size dynamics and survival was assessed in patients with advanced or metastatic bladder cancer treated with atezolizumab, an immunotherapy agent. HMC confirmed limited sensitivity to prior distributions. A cross-validation approach was developed and identified the current slope of tumor size dynamics as the most relevant driver of survival. In summary, HMC is an efficient approach to perform nonlinear joint models in a Bayesian framework, and opens the way for the use of nonlinear models to characterize both the rapid dynamics and the intersubject variability observed during cancer immunotherapy treatment.

Assessing Importance of Biomarkers: a Bayesian Joint Modeling Approach of Longitudinal and Survival Data with Semicompeting Risks

Longitudinal biomarkers such as patient-reported outcomes (PROs) and quality of life (QOL) are routinely collected in cancer clinical trials or other studies. Joint modeling of PRO/QOL and survival data can provide a comparative assessment of patient-reported changes in specific symptoms or global measures that correspond to changes in survival. Motivated by a head and neck cancer clinical trial, we develop a class of trajectory-based models for longitudinal and survival data with disease progression. Specifically, we propose a class of mixed effects regression models for longitudinal measures, a cure rate model for the disease progression time (T _P ), and a Cox proportional hazards model with time-varying covariates for the overall survival time (T _D ) to account for T _P and treatment switching. Under the semi-competing risks framework, the disease progression is the nonterminal event, the occurrence of which is subject to a terminal event of death. The properties of the proposed models are examined in detail. Within the Bayesian paradigm, we derive the decompositions of the deviance information criterion (DIC) and the logarithm of the pseudo marginal likelihood (LPML) to assess the fit of the longitudinal component of the model and the fit of each survival component, separately. We further develop ΔDIC as well as ΔLPML to determine the importance and contribution of the longitudinal data to the model fit of the T _P and T _D data.

Do Longitudinally Collected Symptom Scores Predict Time to Death in Advanced Breast Cancer: A Joint Modeling Analysis

CONTEXT

Patients with advanced breast cancer have low rates of survival that can be associated with symptom burden.

OBJECTIVES

This study seeks to characterize the effect of longitudinally collected symptom scores on predicting time to death for patients with advanced breast cancer.

METHODS

A cohort of 993 Stage IV breast cancer patients was constructed using linked population-level health administrative databases that captured longitudinally collected symptom data using the Edmonton Symptom Assessment System. Data were captured on individual symptom scores (20,371 assessments) for pain, tiredness, drowsiness, nausea, appetite, dyspnea, depression, anxiety, and wellbeing, as well as three summative scores of total symptom distress score, physical subscore, and psychological subscore. A joint modeling approach was undertaken to simultaneously model repeated-measures longitudinal data and time-to-event data.

RESULTS

Of patients who died in the study, 56.11% survived for a mean time of less than three years and had lower mean symptom scores for all symptoms except shortness of breath, in comparison with patients who lived for more than three years. Symptom burden was predictive of patient time to death for all symptoms, with risk of death increasing with worsening symptom scores. For total symptom distress score, age at diagnosis (0.009; P < 0.05), chemotherapy (-0.63; P < 0.001), and palliative care (3.15; P < 0.001) were significant predictors of patient time to death.

CONCLUSION

Patients with advanced breast cancer experience chronic ongoing low symptom burden, which predicts patient time to death. Future research should examine the mechanisms by which patient characteristics, treatment, and supportive and palliative care can have an impact on patient survival.

Assessing the Course of Organ Dysfunction Using Joint Longitudinal and Time-to-Event Modeling in the Vasopressin and Septic Shock Trial

Supplemental Digital Content is available in the text.

Non-mortality septic shock outcomes (e.g., Sequential Organ Failure Assessment score) are important clinical endpoints in pivotal sepsis trials. However, comparisons of observed longitudinal non-mortality outcomes between study groups can be biased if death is unequal between study groups or is associated with an intervention (i.e., informative censoring). We compared the effects of vasopressin versus norepinephrine on the Sequential Organ Failure Assessment score in the Vasopressin and Septic Shock Trial to illustrate the use of joint modeling to help minimize potential bias from informative censoring.

Genetics of physiological dysregulation: findings from the long life family study using joint models

Recently, Mahalanobis distance (D_M) was suggested as a statistical measure of physiological dysregulation in aging individuals. We constructed D_M variants using sets of biomarkers collected at the two visits of the Long Life Family Study (LLFS) and performed joint analyses of longitudinal observations of D_M and follow-up mortality in LLFS using joint models. We found that D_M is significantly associated with mortality (hazard ratio per standard deviation: 1.31 [1.16, 1.48] to 2.22 [1.84, 2.67]) after controlling for age and other covariates. GWAS of random intercepts and slopes of D_M estimated from joint models found a genome-wide significant SNP (rs12652543, p=7.2×10^-9) in the TRIO gene associated with the slope of D_M constructed from biomarkers declining in late life. Review of biological effects of genes corresponding to top SNPs from GWAS of D_M slopes revealed that these genes are broadly involved in cancer prognosis and axon guidance/synapse function. Although axon growth is mainly observed during early development, the axon guidance genes can function in adults and contribute to maintenance of neural circuits and synaptic plasticity. Our results indicate that decline in axons' ability to maintain complex regulatory networks may potentially play an important role in the increase in physiological dysregulation during aging.

Bayesian Individual Dynamic Predictions with Uncertainty of Longitudinal Biomarkers and Risks of Survival Events in a Joint Modelling Framework: a Comparison Between Stan, Monolix, and NONMEM

Given a joint model and its parameters, Bayesian individual dynamic prediction (IDP) of biomarkers and risk of event can be performed for new patients at different landmark times using observed biomarker values. The aim of the present study was to compare IDP, with uncertainty, using Stan 2.18, Monolix 2018R2 and NONMEM 7.4. Simulations of biomarker and survival were performed using a nonlinear joint model of prostate-specific antigen (PSA) kinetics and survival in metastatic prostate cancer. Several scenarios were evaluated, according to the strength of the association between PSA and survival. For various landmark times, a posteriori distribution of PSA kinetic individual parameters was estimated, given individual observations, with each software. Samples of individual parameters were drawn from the posterior distribution. Bias and imprecision of individual parameters as well as coverage of 95% credibility interval for PSA and risk of death were evaluated. All software performed equally well with small biases on individual parameters. Imprecision on individual parameters was comparable across software and showed marked improvements with increasing landmark time. In terms of coverage, results were also comparable and all software were able to well predict PSA kinetics and survival. As for computing time, Stan was faster than Monolix and NONMEM to obtain individual parameters. Stan 2.18, Monolix 2018R2 and NONMEM 7.4 are able to characterize IDP of biomarkers and risk of event in a nonlinear joint modelling framework with correct uncertainty and hence could be used in the context of individualized medicine.

Joint model robustness compared with the time-varying covariate Cox model to evaluate the association between a longitudinal marker and a time-to-event endpoint

BACKGROUND

The recent progress in medical research generates an increasing interest in the use of longitudinal biomarkers for characterizing the occurrence of an outcome. The present work is motivated by a study, where the objective was to explore the potential of the long pentraxin 3 (PTX3) as a prognostic marker of Acute Graft-versus-Host Disease (GvHD) after haematopoietic stem cell transplantation. Time-varying covariate Cox model was commonly used, despite its limiting assumptions that marker values are constant in time and measured without error. A joint model has been developed as a viable alternative; however, the approach is computationally intensive and requires additional strong assumptions, in which the impacts of their misspecification were not sufficiently studied.

METHODS

We conduct an extensive simulation to clarify relevant assumptions for the understanding of joint models and assessment of its robustness under key model misspecifications. Further, we characterize the extent of bias introduced by the limiting assumptions of the time-varying covariate Cox model and compare its performance with a joint model in various contexts. We then present results of the two approaches to evaluate the potential of PTX3 as a prognostic marker of GvHD after haematopoietic stem cell transplantation.

RESULTS

Overall, we illustrate that a joint model provides an unbiased estimate of the association between a longitudinal marker and the hazard of an event in the presence of measurement error, showing improvement over the time-varying Cox model. However, a joint model is severely biased when the baseline hazard or the shape of the longitudinal trajectories are misspecified. Both the Cox model and the joint model correctly specified indicated PTX3 as a potential prognostic marker of GvHD, with the joint model providing a higher hazard ratio estimate.

CONCLUSIONS

Joint models are beneficial to investigate the capability of the longitudinal marker to characterize time-to-event endpoint. However, the benefits are strictly linked to the correct specification of the longitudinal marker trajectory and the baseline hazard function, indicating a careful consideration of assumptions to avoid biased estimates.

Review and Comparison of Computational Approaches for Joint Longitudinal and Time-to-Event Models

Joint models for longitudinal and time-to-event data are useful in situations where an association exists between a longitudinal marker and an event time. These models are typically complicated due to the presence of shared random effects and multiple submodels. As a consequence, software implementation is warranted that is not prohibitively time consuming. While methodological research in this area continues, several statistical software procedures exist to assist in the fitting of some joint models. We review the available implementation for frequentist and Bayesian models in the statistical programming languages R, SAS, and Stata. A description of each procedure is given including estimation techniques, input and data requirements, available options for customization, and some available extensions, such as competing risks models. The software implementations are compared and contrasted through extensive simulation, highlighting their strengths and weaknesses. Data from an ongoing trial on adrenal cancer patients is used to study different nuances of software fitting on a practical example.

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.

Prospective Associations between Single Foods, Alzheimer's Dementia and Memory Decline in the Elderly

Background: Evidence whether single &ldquo;cognitive health&rdquo; foods could prevent cognitive decline is limited. We investigated whether dietary intake of red wine, white wine, coffee, green tea, olive oil, fresh fish, fruits and vegetables, red meat and sausages, assessed by a single-food-questionnaire, would be associated with either incident Alzheimer&rsquo;s dementia (AD) or verbal memory decline. Methods: Participants aged 75+ of the German Study on Aging, Cognition and Dementia in Primary Care Patients (AgeCoDe) cohort were regularly followed over 10 years (n = 2622; n = 418 incident AD cases). Multivariable-adjusted joint modeling of repeated-measures and survival analysis was used, taking gender and Apolipoprotein E4 (APOE &epsilon;4) genotype into account as possible effect modifiers. Results: Only higher red wine intake was associated with a lower incidence of AD (HR = 0.92; P = 0.045). Interestingly, this was true only for men (HR = 0.82; P < 0.001), while in women higher red wine intake was associated with a higher incidence of AD (HR = 1.15; P = 0.044), and higher white wine intake with a more pronounced memory decline over time (HR = &minus;0.13; P = 0.052). Conclusion: We found no evidence for these single foods to be protective against cognitive decline, with the exception of red wine, which reduced the risk for AD only in men. Women could be more susceptible to detrimental effects of alcohol.

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 Proposed Approach for Joint Modeling of the Longitudinal and Time-To-Event Data in Heterogeneous Populations: An Application to HIV/AIDS's Disease

In recent years, the joint models have been widely used for modeling the longitudinal and time-to-event data simultaneously. In this study, we proposed an approach (PA) to study the longitudinal and survival outcomes simultaneously in heterogeneous populations. PA relaxes the assumption of conditional independence (CI). We also compared PA with joint latent class model (JLCM) and separate approach (SA) for various sample sizes (150, 300, and 600) and different association parameters (0, 0.2, and 0.5). The average bias of parameters estimation (AB-PE), average SE of parameters estimation (ASE-PE), and coverage probability of the 95% confidence interval (CP) among the three approaches were compared. In most cases, when the sample sizes increased, AB-PE and ASE-PE decreased for the three approaches, and CP got closer to the nominal level of 0.95. When there was a considerable association, PA in comparison with SA and JLCM performed better in the sense that PA had the smallest AB-PE and ASE-PE for the longitudinal submodel among the three approaches for the small and moderate sample sizes. Moreover, JLCM was desirable for the none-association and the large sample size. Finally, the evaluated approaches were applied on a real HIV/AIDS dataset for validation, and the results were compared.

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.