Comparison of a time-varying covariate model and a joint model of time-to-event outcomes in the presence of measurement error and interval censoring: application to kidney transplantation

Modeling multiple correlated end-organ disease trajectories: A tutorial for multistate and joint models with applications in diabetes complications

State-of-the-art biostatistics methods allow for the simultaneous modeling of several correlated non-fatal disease processes over time, but there is no clear guidance on the optimal analysis in most settings. An example occurs in diabetes, where it is not known with certainty how microvascular complications of the eyes, kidneys, and nerves co-develop over time. In this article, we propose and contrast two general model frameworks for studying complications (sequential state and parallel trajectory frameworks) and review multivariate methods for their analysis, focusing on multistate and joint modeling. We illustrate these methods in a tutorial format using the long-term follow-up from the Diabetes Control and Complications Trial and Epidemiology of Diabetes Interventions and Complications study public data repository. A formal comparison of prediction error and discrimination is included. Multistate models are particularly advantageous for determining the order and timing of complications, but require discretization of the longitudinal outcomes and possibly a very complex state space process. Intermittent observation of the states must be accounted for, and discretization is a probable disadvantage in this setting. In contrast, joint models can account for variations of continuous biomarkers over time and are particularly designed for modeling complex association structures between the complications and for performing dynamic predictions of an outcome of interest to inform clinical decisions (eg, a late-stage complication). We found that both models have helpful features that can better-inform our understanding of the complex trajectories that complications may take and can therefore help with decision making for patients presenting with diabetes complications.

A multivariate joint model to adjust for random measurement error while handling skewness and correlation in dietary data in an epidemiologic study of mortality

PURPOSE

A substantial proportion of global deaths is attributed to unhealthy diets, which can be assessed at baseline or longitudinally. We demonstrated how to simultaneously correct for random measurement error, correlations, and skewness in the estimation of associations between dietary intake and all-cause mortality.

METHODS

We applied a multivariate joint model (MJM) that simultaneously corrected for random measurement error, skewness, and correlation among longitudinally measured intake levels of cholesterol, total fat, dietary fiber, and energy with all-cause mortality using US National Health and Nutrition Examination Survey linked to the National Death Index mortality data. We compared MJM with the mean method that assessed intake levels as the mean of a person's intake.

RESULTS

The estimates from MJM were larger than those from the mean method. For instance, the logarithm of hazard ratio for dietary fiber intake increased by 14 times (from -0.04 to -0.60) with the MJM method. This translated into a relative hazard of death of 0.55 (95% credible interval: 0.45, 0.65) with the MJM and 0.96 (95% credible interval: 0.95, 0.97) with the mean method.

CONCLUSIONS

MJM adjusts for random measurement error and flexibly addresses correlations and skewness among longitudinal measures of dietary intake when estimating their associations with death.

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

Background

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

Methods

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

Results

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

Conclusions

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

Development and validation of a dynamic survival prediction model for patients with acute-on-chronic liver failure

Background & Aims

Acute-on-chronic liver failure (ACLF) is usually associated with a precipitating event and results in the failure of other organ systems and high short-term mortality. Current prediction models fail to adequately estimate prognosis and need for liver transplantation (LT) in ACLF. This study develops and validates a dynamic prediction model for patients with ACLF that uses both longitudinal and survival data.

Methods

Adult patients on the UNOS waitlist for LT between 11.01.2016-31.12.2019 were included. Repeated model for end-stage liver disease-sodium (MELD-Na) measurements were jointly modelled with Cox survival analysis to develop the ACLF joint model (ACLF-JM). Model validation was carried out using separate testing data with area under curve (AUC) and prediction errors. An online ACLF-JM tool was created for clinical application.

Results

In total, 30,533 patients were included. ACLF grade 1 to 3 was present in 16.4%, 10.4% and 6.2% of patients, respectively. The ACLF-JM predicted survival significantly (p <0.001) better than the MELD-Na score, both at baseline and during follow-up. For 28- and 90-day predictions, ACLF-JM AUCs ranged between 0.840-0.871 and 0.833-875, respectively. Compared to MELD-Na, AUCs and prediction errors were improved by 23.1%-62.0% and 5%-37.6% respectively. Also, the ACLF-JM could have prioritized patients with relatively low MELD-Na scores but with a 4-fold higher rate of waiting list mortality.

Conclusions

The ACLF-JM dynamically predicts outcome based on current and past disease severity. Prediction performance is excellent over time, even in patients with ACLF-3. Therefore, the ACLF-JM could be used as a clinical tool in the evaluation of prognosis and treatment in patients with ACLF.

Lay summary

Acute-on-chronic liver failure (ACLF) progresses rapidly and often leads to death. Liver transplantation is used as a treatment and the sickest patients are treated first. In this study, we develop a model that predicts survival in ACLF and we show that the newly developed model performs better than the currently used model for ranking patients on the liver transplant waiting list.

•

ACLF is a dynamic disease that can rapidly change over time, which greatly influences patient survival without LT.

•

Currently, the MELD-Na score is used to prioritize patients for LT, but MELD-Na underestimates ACLF disease severity.

•

The ACLF joint model (ACLF-JM) was developed to dynamically predict survival.

•

The ACLF-JM significantly outperformed the MELD-Na score for the prediction of mortality on the LT waiting list.

•

The ACLF-JM can be used online to predict survival in individual patients.

Joint modeling of liver transplant candidates outperforms the model for end-stage liver disease: The effect of disease development over time on patient outcome

Liver function is measured regularly in liver transplantation (LT) candidates. Currently, these previous disease development data are not used for survival prediction. By constructing and validating joint models (JMs), we aimed to predict the outcome based on all available data, using both disease severity and its rate of change over time. Adult LT candidates listed in Eurotransplant between 2007 and 2018 (n = 16 283) and UNOS between 2016 and 2019 (n = 30 533) were included. Patients with acute liver failure, exception points, or priority status were excluded. Longitudinal MELD(-Na) data were modeled using spline-based mixed effects. Waiting list survival was modeled with Cox proportional hazards models. The JMs combined the longitudinal and survival analysis. JM 90-day mortality prediction performance was compared to MELD(-Na) in the validation cohorts. MELD(-Na) score and its rate of change over time significantly influenced patient survival. The JMs significantly outperformed the MELD(-Na) score at baseline and during follow-up. At baseline, MELD-JM AUC and MELD AUC were 0.94 (0.92-0.95) and 0.87 (0.85-0.89), respectively. MELDNa-JM AUC was 0.91 (0.89-0.93) and MELD-Na AUC was 0.84 (0.81-0.87). The JMs were significantly (p < .001) more accurate than MELD(-Na). After 90 days, we ranked patients for LT based on their MELD-Na and MELDNa-JM survival rates, showing that MELDNa-JM-prioritized patients had three times higher waiting list mortality.

Random survival forests for dynamic predictions of a time-to-event outcome using a longitudinal biomarker

BACKGROUND

Risk prediction models for time-to-event outcomes play a vital role in personalized decision-making. A patient's biomarker values, such as medical lab results, are often measured over time but traditional prediction models ignore their longitudinal nature, using only baseline information. Dynamic prediction incorporates longitudinal information to produce updated survival predictions during follow-up. Existing methods for dynamic prediction include joint modeling, which often suffers from computational complexity and poor performance under misspecification, and landmarking, which has a straightforward implementation but typically relies on a proportional hazards model. Random survival forests (RSF), a machine learning algorithm for time-to-event outcomes, can capture complex relationships between the predictors and survival without requiring prior specification and has been shown to have superior predictive performance.

METHODS

We propose an alternative approach for dynamic prediction using random survival forests in a landmarking framework. With a simulation study, we compared the predictive performance of our proposed method with Cox landmarking and joint modeling in situations where the proportional hazards assumption does not hold and the longitudinal marker(s) have a complex relationship with the survival outcome. We illustrated the use of the RSF landmark approach in two clinical applications to assess the performance of various RSF model building decisions and to demonstrate its use in obtaining dynamic predictions.

RESULTS

In simulation studies, RSF landmarking outperformed joint modeling and Cox landmarking when a complex relationship between the survival and longitudinal marker processes was present. It was also useful in application when there were several predictors for which the clinical relevance was unknown and multiple longitudinal biomarkers were present. Individualized dynamic predictions can be obtained from this method and the variable importance metric is useful for examining the changing predictive power of variables over time. In addition, RSF landmarking is easily implementable in standard software and using suggested specifications requires less computation time than joint modeling.

CONCLUSIONS

RSF landmarking is a nonparametric, machine learning alternative to current methods for obtaining dynamic predictions when there are complex or unknown relationships present. It requires little upfront decision-making and has comparable predictive performance and has preferable computational speed.

Dynamic prediction based on variability of a longitudinal biomarker

BACKGROUND

Tacrolimus is given post-kidney transplant to suppress the immune system, and the amount of drug in the body is measured frequently. Higher variability over time may be indicative of poor drug adherence, leading to more adverse events. It is important to account for the variation in Tacrolimus, not just the average change over time.

METHODS

Using data from the University of Colorado, we compare methods of assessing how the variability in Tacrolimus influences the hazard of de novo Donor Specific Antibodies (dnDSA), an early warning sign of graft failure. We compare multiple joint models in terms of fit and predictive ability. We explain that the models that account for the individual-specific variability over time have the best predictive performance. These models allowed each patient to have an individual-specific random error term in the longitudinal Tacrolimus model, and linked this to the hazard of dnDSA model.

RESULTS

The hazard for the variance and coefficient of variation (CV) loading parameter were greater than 1, indicating that higher variability of Tacrolimus had a higher hazard of dnDSA. Introducing the individual-specific variability improved the fit, leading to more accurate predictions about the individual-specific time-to-dnDSA.

CONCLUSIONS

We showed that the individual's variability in Tacrolimus is an important metric in predicting long-term adverse events in kidney transplantation. This is an important step in personalizing the dosage of TAC post-transplant to improve outcomes post-transplant.