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

Bayesian two-stage modeling of longitudinal and time-to-event data with an integrated fractional Brownian motion covariance structure

It is difficult to characterize complex variations of biological processes, often longitudinally measured using biomarkers that yield noisy data. While joint modeling with a longitudinal submodel for the biomarker measurements and a survival submodel for assessing the hazard of events can alleviate measurement error issues, the continuous longitudinal submodel often uses random intercepts and slopes to estimate both between- and within-patient heterogeneity in biomarker trajectories. To overcome longitudinal submodel challenges, we replace random slopes with scaled integrated fractional Brownian motion (IFBM). As a more generalized version of integrated Brownian motion, IFBM reasonably depicts noisily measured biological processes. From this longitudinal IFBM model, we derive novel target functions to monitor the risk of rapid disease progression as real-time predictive probabilities. Predicted biomarker values from the IFBM submodel are used as inputs in a Cox submodel to estimate event hazard. This two-stage approach to fit the submodels is performed via Bayesian posterior computation and inference. We use the proposed approach to predict dynamic lung disease progression and mortality in women with a rare disease called lymphangioleiomyomatosis who were followed in a national patient registry. We compare our approach to those using integrated Ornstein-Uhlenbeck or conventional random intercepts-and-slopes terms for the longitudinal submodel. In the comparative analysis, the IFBM model consistently demonstrated superior predictive performance.

Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, samples are often selected at a later time, which results in delayed entry so that only individuals who have not yet experienced the terminal event will be included. In joint frailty models such left truncation has effects on the frailty distribution that need to be accounted for in both the recurrence process and the terminal event process, if the two are associated. We demonstrate, in a comprehensive simulation study, the effects that not adjusting for late entry can have and derive the correctly adjusted marginal likelihood, which can be expressed as a ratio of two integrals over the frailty distribution. We extend the estimation method of Liu and Huang (Stat Med 27:2665-2683, 2008. https://doi.org/10.1002/sim.3077 ) to include potential left truncation. Numerical integration is performed by Gaussian quadrature, the baseline intensities are specified as piecewise constant functions, potential covariates are assumed to have multiplicative effects on the intensities. We apply the method to estimate age-specific intensities of recurrent urinary tract infections and mortality in an older population.

Modeling unmeasured baseline information in observational time-to-event data subject to delayed study entry

Unmeasured baseline information in left-truncated data situations frequently occurs in observational time-to-event analyses. For instance, a typical timescale in trials of antidiabetic treatment is "time since treatment initiation", but individuals may have initiated treatment before the start of longitudinal data collection. When the focus is on baseline effects, one widespread approach is to fit a Cox proportional hazards model incorporating the measurements at delayed study entry. This has been criticized because of the potential time dependency of covariates. We tackle this problem by using a Bayesian joint model that combines a mixed-effects model for the longitudinal trajectory with a proportional hazards model for the event of interest incorporating the baseline covariate, possibly unmeasured in the presence of left truncation. The novelty is that our procedure is not used to account for non-continuously monitored longitudinal covariates in right-censored time-to-event studies, but to utilize these trajectories to make inferences about missing baseline measurements in left-truncated data. Simulating times-to-event depending on baseline covariates we also compared our proposal to a simpler two-stage approach which performed favorably. Our approach is illustrated by investigating the impact of baseline blood glucose levels on antidiabetic treatment failure using data from a German diabetes register.

Changes in Thoroughbred speed and stride characteristics over successive race starts and their association with musculoskeletal injury

BACKGROUND

Certain stride characteristics have been shown to affect changes in biomechanical factors that are associated with injuries in human athletes. Determining the relationship between stride characteristics and musculoskeletal injury (MSI) may be key in limiting injury occurrence in the racehorse.

OBJECTIVES

This study aimed to determine whether changes in race day speed and stride characteristics over career race starts are associated with an increased risk of MSI in racehorses.

STUDY DESIGN

Case-control study.

METHODS

Speed, stride length, and stride frequency data were obtained from the final 200 m sectional of n = 5660 race starts by n = 584 horses (case n = 146, control n = 438). Multivariable joint models, combining longitudinal and survival (time to injury) analysis, were generated. Hazard ratios and their 95% confidence intervals (CI) are presented.

RESULTS

The risk of MSI increased by 1.18 (95% CI 1.09, 1.28; P < 0.001) for each 0.1 m/s decrease in speed and by 1.11 (95% CI 1.02, 1.21; P = 0.01) for each 10 cm decrease in stride length over time (career race starts). A more marked rate of decline in speed and stride length was observed approximately 6 races prior to injury. Risk of MSI was highest early in the horse's racing career.

MAIN LIMITATIONS

Only final sectional stride characteristics were assessed in the model. The model did not account for time between race starts.

CONCLUSIONS

Decreasing speed and stride length over multiple races is associated with MSI in racehorses. Monitoring stride characteristics over time may be beneficial for the early detection of MSI.

Using marginal structural joint models to estimate the effect of a time-varying treatment on recurrent events and survival: An application on arrhythmogenic cardiomyopathy

In many clinical applications to evaluate the effect of a treatment, randomized control trials are difficult to carry out. On the other hand, clinical observational registries are often available and they contain longitudinal data regarding clinical parameters, drug therapies, and outcomes. In the past, much research has addressed causal methods to estimate treatment effects from observational studies. In the context of time-varying treatments, marginal structural models are often used. However, most analyses have focused on binary outcomes or time-to-the-first event analyses. The novelty of our approach is to combine the marginal structural methodology with the case where correlated recurrent events and survival are the outcomes of interest. Our work focuses on solving the nontrivial problem of defining the measures of effect, specifying the model for the time-dependent weights and the model to estimate the outcome, implementing them, and finally estimating the final treatment effects in this life-history setting. Our approach provides a strategy that allows obtaining treatment effect estimates both on the recurrent events and the survival with a clear causal and clinical interpretation. At the same time, the strategy we propose is based on flexible modeling choices such as the use of joint models to capture the correlation within events from the same subject and the specification of time-dependent treatment effects. The clinical problem which motivated our work is the evaluation of the treatment effect of beta-blockers in arrhythmogenic right ventricular cardiomyopathy (ARVC/D), and the dataset comes from the Trieste Heart Muscle Disease Registry.

Longitudinal tumor fraction trajectories predict risk of progression in metastatic HR+ breast cancer patients undergoing CDK4/6 treatment

Despite improved clinical outcomes, intrinsic or acquired resistance to CDK4/6 inhibitor treatment has limited the success of this treatment in HR+ HER2- metastatic breast cancer patients. Biomarkers are urgently needed, and longitudinal biomarker measurements may harbor more dynamic predictive and prognostic information compared to single time point measurements. The aim of this study was to explore the longitudinal evolution of circulating tumor fractions within cell-free DNA assessed by an untargeted sequencing approach during CDK4/6 therapy and to quantify the potential association between longitudinal z-score measurements and clinical outcome by using joint models. Forty-nine HR+ HER2- metastatic breast cancer patients were enrolled, and z-score levels were measured at baseline and during 132 follow-up visits (median number of measurements per patient = 3, 25th -75th percentile: 3-5, range: 1-8). We observed higher baseline z-score levels (estimated difference 0.57, 95% CI: 0.147-0.983, P-value = 0.008) and a constant increase of z-score levels over follow-up time (overall P-value for difference in log z-score over time = 0.024) in patients who developed progressive disease. Importantly, the joint model revealed that elevated z-score trajectories were significantly associated with higher progression risk (HR of log z-score at any time of follow-up = 3.3, 95% CI, 1.44-7.55, P = 0.005). In contrast, single z-score measurement at CDK4/6 inhibitor treatment start did not predict risk of progression. In this prospective study, we demonstrate proof-of-concept that longitudinal z-score trajectories rather than single time point measurements may harbor important dynamic information on the development of disease progression in HR+ HER2- breast cancer patients undergoing CDK4/6 inhibitor treatment.

A Bayesian joint model for zero-inflated integers and left-truncated event times with a time-varying association: Applications to senior health care

Population aging in most industrialized societies has led to a dramatic increase in emergency medical demand among the elderly. In the context of private health care, an optimal allocation of the medical resources for seniors is commonly done by forecasting their life spans. Accounting for each subject's particularities is therefore indispensable, so the available data must be processed at an individual level. We use a large and unique dataset of insured parties aged 65 and older to appropriately relate the emergency care usage with mortality risk. Longitudinal and time-to-event processes are jointly modeled, and their underlying relationship can therefore be assessed. Such an application, however, requires some special features to also be considered. First, longitudinal demand for emergency services exhibits a nonnegative integer response with an excess of zeros due to the very nature of the data. These subject-specific responses are handled by a zero-inflated version of the hierarchical negative binomial model. Second, event times must account for the left truncation derived from the fact that policyholders must reach the age of 65 before they may begin to be observed. Consequently, a delayed entry bias arises for those individuals entering the study after this age threshold. Third, and as the main challenge of our analysis, the association parameter between both processes is expected to be age-dependent, with an unspecified association structure. This is well-approximated through a flexible functional specification provided by penalized B-splines. The parameter estimation of the joint model is derived under a Bayesian scheme.

Developmental considerations in survival models as applied to substance use research

Survival analysis is a class of models that are ideal for evaluating questions of timing of events, which makes them well-suited for modeling the development of a process such as initiation of substance use, development of addiction, or post-treatment recovery. The focus of this review paper is to demonstrate how survival models operate in a broader developmental framework and to offer guidance on selecting the appropriate model on the basis of the research question at hand. We provide a basic overview of survival models and then identify several key issues, explain how they pertain to research in the addiction field, and describe studies that utilize survival models to address questions about timing. We discuss the importance of carefully selecting the metric and origin of the time scale that corresponds to developmental process under investigation and we describe types of censoring/truncation. We describe the value of modeling covariates as time-invariant versus time-varying, and make the distinction between time-varying covariates and time-varying effects of covariates. We also explain how to test for substantive differences due to the timing of the assessment of the predictor. We finish the paper with a presentation of relatively novel extensions of survival models, including models that integrate standard statistical mediational analysis with discrete-time survival analysis, models that simultaneously consider order and timing of multiple events, and models that involve joint modeling of longitudinal and survival data. We also present our own substantive examples of various models in an Appendix containing annotated syntax and output.

Exposure to vitamin k antagonists and kidney function decline in patients with atrial fibrillation and chronic kidney disease

BACKGROUND

Exposure to vitamin K antagonists (VKA) has been suggested to accelerate progression of chronic kidney disease (CKD) but robust clinical data are currently lacking.

METHODS

We retrospectively evaluated the impact of VKA exposure on kidney function in patients with atrial fibrillation (AF) and CKD stage 3/4. Patients were prospectively followed within a primary care electronic database (median follow-up of 1.45 years). The kidney function trajectory over time, defined as the annualized change in estimated glomerular filtration rate (eGFR), was analyzed with linear mixed-effects regression including propensity score adjustment.

RESULTS

14 432 patients (median age 78 years, median CHA 2 DS 2-VASc score 4 points) contributed 97 792 eGFR measurements (mean 6.8 measurements/patient; range: 1-197). Mean baseline eGFR was 50.3 mL/min/1.73 m2; and declined by 1.10 mL/min/1.73 m2/year (95% CI: 0.91-1.28, P < 0.0001). In 7409 patients with VKA exposure, CKD progression was significantly faster compared to patients without VKA exposure (5-year absolute eGFR loss from baseline: 6.0 mL/min/1.73 m2 vs 4.5 mL/min/1.73 m2, for an absolute 5-year excess eGFR decline with VKA exposure of 1.5 mL/min/1.73 m2 (95% CI: 0.4-2.7, P = 0.002). These results prevailed upon adjusting for CHA 2 DS 2-VASc score and other potential imbalances in prognostic variables, and in several sensitivity analyses. In the group without documented VKA exposure, 1775 VKA patients (24%) and 1012 patients (14%) developed a 30% decline in eGFR during follow-up (P < 0.0001).

CONCLUSIONS

In patients with AF and CKD, VKA use is associated with accelerated eGFR decline. Within the limitations of a retrospective analysis, this finding supports the "VKA-renal-calcification hypothesis." However, although statistically significant, the excess loss in eGFR over 5 years with VKA was modest.

Modelling cancer outcomes of bone metastatic patients: combining survival data with N-Telopeptide of type I collagen (NTX) dynamics through joint models

Background

Joint models (JM) have emerged as a promising statistical framework to concurrently analyse survival data and multiple longitudinal responses. This is particularly relevant in clinical studies where the goal is to estimate the association between time-to-event data and the biomarkers evolution. In the context of oncological data, JM can indeed provide interesting prognostic markers for the event under study and thus support clinical decisions and treatment choices. However, several problems arise when dealing with this type of data, such as the high-dimensionality of the covariates space, the lack of knowledge about the function structure of the time series and the presence of missing data, facts that may hamper the accurate estimation of the JM.

Methods

We propose to apply JM for the analysis of bone metastatic patients and infer the association of their survival with several covariates, in particular the N-Telopeptide of Type I Collagen (NTX) dynamics. This biomarker has been identified as a relevant prognostic factor in patients with metastatic cancer, but only using static information in some specific time points.

Results

We extended this analysis using the full NTX time series for a larger cohort of patients with bone metastasis, and compared the results obtained by the JM and the extended Cox regression model. Imputation based on fuzzy clustering was used to deal with missing values and several functions for NTX evolution were compared, such as rational, exponential and cubic splines.

Conclusions

The JM obtained confirm the association between NTX values and patients’ response, attesting the importance of this time series, and additionally provide a deep understanding of the key survival covariates.

Joint modeling of multivariate longitudinal data and survival data in several observational studies of Huntington's disease

BACKGROUND

Joint modeling is appropriate when one wants to predict the time to an event with covariates that are measured longitudinally and are related to the event. An underlying random effects structure links the survival and longitudinal submodels and allows for individual-specific predictions. Multiple time-varying and time-invariant covariates can be included to potentially increase prediction accuracy. The goal of this study was to estimate a multivariate joint model on several longitudinal observational studies of Huntington's disease, examine external validity performance, and compute individual-specific predictions for characterizing disease progression. Emphasis was on the survival submodel for predicting the hazard of motor diagnosis.

METHODS

Data from four observational studies was analyzed: Enroll-HD, PREDICT-HD, REGISTRY, and Track-HD. A Bayesian approach to estimation was adopted, and external validation was performed using a time-varying AUC measure. Individual-specific cumulative hazard predictions were computed based on a simulation approach. The cumulative hazard was used for computing predicted age of motor onset and also for a deviance residual indicating the discrepancy between observed diagnosis status and model-based status.

RESULTS

The joint model trained in a single study had very good performance in discriminating among diagnosed and pre-diagnosed participants in the remaining test studies, with the 5-year mean AUC = .83 (range .77-.90), and the 10-year mean AUC = .86 (range .82-.92). Graphical analysis of the predicted age of motor diagnosis showed an expected strong relationship with the trinucleotide expansion that causes Huntington's disease. Graphical analysis of the deviance-type residual revealed there were individuals who converted to a diagnosis despite having relatively low model-based risk, others who had not yet converted despite having relatively high risk, and the majority falling between the two extremes.

CONCLUSIONS

Joint modeling is an improvement over traditional survival modeling because it considers all the longitudinal observations of covariates that are predictive of an event. Predictions from joint models can have greater accuracy because they are tailored to account for individual variability. These predictions can provide relatively accurate characterizations of individual disease progression, which might be important in the timing of interventions, determining the qualification for appropriate clinical trials, and general genotypic analysis.

Survival models and health sequences

Survival studies often generate not only a survival time for each patient but also a sequence of health measurements at annual or semi-annual check-ups while the patient remains alive. Such a sequence of random length accompanied by a survival time is called a survival process. Robust health is ordinarily associated with longer survival, so the two parts of a survival process cannot be assumed independent. This paper is concerned with a general technique-reverse alignment-for constructing statistical models for survival processes, here termed revival models. A revival model is a regression model in the sense that it incorporates covariate and treatment effects into both the distribution of survival times and the joint distribution of health outcomes. The revival model also determines a conditional survival distribution given the observed history, which describes how the subsequent survival distribution is determined by the observed progression of health outcomes.

The CHA2DS2-VASc score strongly correlates with glomerular filtration rate and predicts renal function decline over time in elderly patients with atrial fibrillation and chronic kidney disease

BACKGROUND

The decline of renal function affects stroke risk in patients with atrial fibrillation (AF). Here, we aim to study the predictive value of the CHA₂DS₂-VASc score, a stroke-risk stratification model in AF, for renal function and renal decline in patients with AF and chronic kidney disease (CKD).

METHODS

Two electronic health record cohorts with AF and CKD stage III/IV were evaluated (Cohort #1 (IMS-DA, Germany): 18,539 patients with 125,149 estimated glomerular filtration rate (eGFR) measurements; Cohort #2 (IMS-THIN, United Kingdom): 18,240 patients with 133,676 eGFR measurements). The eGFR trajectories were analysed with multi-level mixed-effects regression and joint models for longitudinal and survival data.

RESULTS

In IMS-DA, the mean baseline eGFR was 52.0ml/min/1.73m², and declined by 1.03ml/min/1.73m²/year (95%CI: 0.86-1.19, p<0.0001). In IMS-THIN, the mean baseline eGFR was 48.0ml/min/1.73m², and declined by 0.44ml/min/1.73m²/year (95%CI: 0.37-0.51, p<0.0001). In both datasets, higher CHA₂DS₂-VASc scores (median: 4 points) were strongly associated with both lower baseline eGFR (p<0.0001) and faster progression of CKD (p=0.002). Mean baseline eGFR values were higher in patients with a CHA₂DS₂-VASc score of 0 compared to patients with a score of 8 points. Conversely, the annual declines in eGFR were lower in patients with a score of 0 compared to patients with a score of 8 points in both databases.

CONCLUSION

The CHA₂DS₂-VASc score can identify AF patient subgroups with lower baseline eGFR and a higher risk of CKD progression, which has important implications for the management of anticoagulation in these patients.

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.

The current application of the Royston-Parmar model for prognostic modeling in health research: a scoping review

BACKGROUND

Prognostic models incorporating survival analysis predict the risk (i.e., probability) of experiencing a future event over a specific time period. In 2002, Royston and Parmar described a type of flexible parametric survival model called the Royston-Parmar model in Statistics in Medicine, a model which fits a restricted cubic spline to flexibly model the baseline log cumulative hazard on the proportional hazards scale. This feature permits absolute measures of effect (e.g., hazard rates) to be estimated at all time points, an important feature when using the model. The Royston-Parmar model can also incorporate time-dependent effects and be used on different scales (e.g., proportional odds, probit). These features make the Royston-Parmar model attractive for prediction, yet their current uptake for prognostic modeling is unknown. Thus, the objectives were to conduct a scoping review of how the Royston-Parmar model has been applied to prognostic models in health research, to raise awareness of the model, to identify gaps in current reporting, and to offer model building considerations and reporting suggestions for other researchers.

METHODS

Five electronic databases and gray literature indexed in web sources from 2001 to 2016 were searched to identify articles for inclusion in the scoping review. Two reviewers independently screened 1429 articles, and after applying exclusion criteria through a two-step screening process, data from 12 studies were abstracted.

RESULTS

Since 2001, only 12 studies were identified that used the Royston-Parmar model in some capacity for prognostic modeling, 10 of which used the model as the basis for their prognostic model. The restricted cubic spline varied across studies in the number of interior knots (range 1 to 6), and only three studies reported knot placement. Three studies provided details about the baseline function, with two studies using a figure and the third providing coefficients. However, no studies provided adequate information on their restricted cubic spline to permit others to validate or completely use the model.

CONCLUSIONS

Despite the advantages of the Royston-Parmar model for prognostic models, they are not widely used in health research. Better reporting of details about the restricted cubic spline is needed, so the prognostic model can be used and validated by others.

REGISTRATION

The protocol was registered with Open Science Framework (https://osf.io/r3232/).

Flexible semiparametric joint modeling: an application to estimate individual lung function decline and risk of pulmonary exacerbations in cystic fibrosis

Background

Epidemiologic surveillance of lung function is key to clinical care of individuals with cystic fibrosis, but lung function decline is nonlinear and often impacted by acute respiratory events known as pulmonary exacerbations. Statistical models are needed to simultaneously estimate lung function decline while providing risk estimates for the onset of pulmonary exacerbations, in order to identify relevant predictors of declining lung function and understand how these associations could be used to predict the onset of pulmonary exacerbations.

Methods

Using longitudinal lung function (FEV₁) measurements and time-to-event data on pulmonary exacerbations from individuals in the United States Cystic Fibrosis Registry, we implemented a flexible semiparametric joint model consisting of a mixed-effects submodel with regression splines to fit repeated FEV₁ measurements and a time-to-event submodel for possibly censored data on pulmonary exacerbations. We contrasted this approach with methods currently used in epidemiological studies and highlight clinical implications.

Results

The semiparametric joint model had the best fit of all models examined based on deviance information criterion. Higher starting FEV₁ implied more rapid lung function decline in both separate and joint models; however, individualized risk estimates for pulmonary exacerbation differed depending upon model type. Based on shared parameter estimates from the joint model, which accounts for the nonlinear FEV₁ trajectory, patients with more positive rates of change were less likely to experience a pulmonary exacerbation (HR per one standard deviation increase in FEV₁ rate of change = 0.566, 95% CI 0.516–0.619), and having higher absolute FEV₁ also corresponded to lower risk of having a pulmonary exacerbation (HR per one standard deviation increase in FEV₁ = 0.856, 95% CI 0.781–0.937). At the population level, both submodels indicated significant effects of birth cohort, socioeconomic status and respiratory infections on FEV₁ decline, as well as significant effects of gender, socioeconomic status and birth cohort on pulmonary exacerbation risk.

Conclusions

Through a flexible joint-modeling approach, we provide a means to simultaneously estimate lung function trajectories and the risk of pulmonary exacerbations for individual patients; we demonstrate how this approach offers additional insights into the clinical course of cystic fibrosis that were not possible using conventional approaches.

Electronic supplementary material

The online version of this article (10.1186/s12982-017-0067-1) contains supplementary material, which is available to authorized users.

Using predictions from a joint model for longitudinal and survival data to inform the optimal time of intervention in an abdominal aortic aneurysm screening programme

Joint models of longitudinal and survival data can be used to predict the risk of a future event occurring based on the evolution of an endogenous biomarker measured repeatedly over time. This has led naturally to the use of dynamic predictions that update each time a new longitudinal measurement is provided. In this paper, we show how such predictions can be utilised within a fuller decision modelling framework, in particular to allow planning of future interventions for patients under a ‘watchful waiting’ care pathway. Through the objective of maximising expected life‐years, the predicted risks associated with not intervening (e.g. the occurrence of severe sequelae) are balanced against risks associated with the intervention (e.g. operative risks). Our example involves patients under surveillance in an abdominal aortic aneurysm screening programme where a joint longitudinal and survival model is used to associate longitudinal measurements of aortic diameter with the risk of aneurysm rupture. We illustrate how the decision to intervene, which is currently based on a diameter measurement greater than a certain threshold, could be made more personalised and dynamic through the application of a decision modelling approach.

Dynamics of Disease Progression and Gastrostomy Tube Placement in Children and Adolescents with Cystic Fibrosis: Application of Joint Models for Longitudinal and Time-to-Event Data

BACKGROUND

Previous small-sample studies have examined the effect of gastrostomy (g-) tube placement on weight, height, and lung function in adolescent patients with cystic fibrosis (CF), but there are no RCTs to date reporting efficacy. The goal of this study was to implement a dynamic prediction model to 1) understand the role of rapid lung function decline in g-tube placement in real-world clinical settings; 2) provide a prognostic tool with the potential to aid clinicians in optimizing the timing of g-tube placement, in relation to rate of lung function decline and current nutrition status.

METHODS

A dynamic prediction model was developed, utilizing data on patients 6-21 years of age from the Cystic Fibrosis Foundation Patient Registry (1997-2013). A joint model was implemented, which coupled a semiparametric mixed model to characterize rapid lung function decline with a time-to-event model to identify risk factors for g-tube initiation.

RESULTS

The 4,034 individuals (21.3%) who underwent g-tube placement during adolescence or young adulthood had poorer nutrition and lung function at baseline and initially had increased rates of pancreatic enzyme use, infection and gastroesophageal reflux disease, compared to those who did not receive g-tubes; these associations changed over follow up. Rapid lung function decline was associated with increased risk of g-tube supplementation.

CONCLUSIONS

By jointly modeling longitudinal patterns of lung function decline with g-tube delivery, it is possible to construct prognostic aids to evaluate treatment delivery in relation to the onset of rapid lung function decline and other important clinical markers. These algorithms have the potential to enable more effective monitoring of disease progression and promote more timely treatment delivery.

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.