A joint model for repeated events of different types and multiple longitudinal outcomes with application to a follow-up study of patients after kidney transplant

Dynamic Prediction of Resectability for Patients with Advanced Ovarian Cancer Undergoing Neo-Adjuvant Chemotherapy: Application of Joint Model for Longitudinal CA-125 Levels

In patients with advanced ovarian cancer (AOC) receiving neoadjuvant chemotherapy (NAC), predicting the feasibility of complete interval cytoreductive surgery (ICRS) is helpful and may avoid unnecessary laparotomy. A joint model (JM) is a dynamic individual predictive model. The aim of this study was to develop a predictive JM combining CA-125 kinetics during NAC with patients' and clinical factors to predict resectability after NAC in patients with AOC. A retrospective study included 77 patients with AOC treated with NAC. A linear mixed effect (LME) sub-model was used to describe the evolution of CA-125 during NAC considering factors influencing the biomarker levels. A Cox sub-model screened the covariates associated with resectability. The JM combined the LME sub-model with the Cox sub-model. Using the LME sub-model, we observed that CA-125 levels were influenced by the number of NAC cycles and the performance of paracentesis. In the Cox sub-model, complete resectability was associated with Performance Status (HR = 0.57, [0.34-0.95], p = 0.03) and the presence of peritoneal carcinomatosis in the epigastric region (HR = 0.39, [0.19-0.80], p = 0.01). The JM accuracy to predict complete ICRS was 88% [82-100] with a predictive error of 2.24% [0-2.32]. Using a JM of a longitudinal CA-125 level during NAC could be a reliable predictor of complete ICRS.

Multivariate Longitudinal Assessment of Kidney Function Outcomes on Graft Survival after Kidney Transplantation Using Multivariate Joint Modeling Approach: A Retrospective Cohort Study

Background

The performance of a transplanted kidney is evaluated by monitoring variations in the value of the most important markers. These markers are measured longitudinally, and their variation is influenced by other factors. The simultaneous use of these markers increases the predictive power of the analytical model. This study aimed to determine the simultaneous longitudinal effect of serum creatinine and blood urea nitrogen (BUN) markers, and other risk factors on allograft survival after kidney transplantation.

Methods

In a retrospective cohort study, the medical records of 731 renal transplant patients, dated July 2000 to December 2013, from various transplant centers in Mashhad (Iran) were examined. Univariate and multivariate joint models of longitudinal and survival data were used, and the results from both models were compared. The R package joineRML was used to implement joint models. P values <0.05 were considered statistically significant.

Results

Results of the multivariate model showed that allograft rejection occurred more frequently in patients with elevated BUN levels (HR=1.68, 95% CI: 1.24-2.27). In contrast, despite a positive correlation between serum creatinine and allograft rejection (HR=1.49, 95% CI: 0.99-2.22), this relationship was not statistically significant.

Conclusion

Results of the multivariate model showed that longitudinal measurements of BUN marker play a more important role in the investigation of the allograft rejection.

Improved Landmark Dynamic Prediction Model to Assess Cardiovascular Disease Risk in On-Treatment Blood Pressure Patients: A Simulation Study and Post Hoc Analysis on SPRINT Data

Landmark model (LM) is a dynamic prediction model that uses a longitudinal biomarker in time-to-event data to make prognosis prediction. This study was designed to improve this model and to apply it to assess the cardiovascular risk in on-treatment blood pressure patients. A frailty parameter was used in LM, landmark frailty model (LFM), to account the frailty of the patients and measure the correlation between different landmarks. The proposed model was compared with LM in different scenarios respecting data missing status, sample size (100, 200, and 400), landmarks (6, 12, 24, and 48), and failure percentage (30, 50, and 100%). Bias of parameter estimation and mean square error as well as deviance statistic between models were compared. Additionally, discrimination and calibration capability as the goodness of fit of the model were evaluated using dynamic concordance index (DCI), dynamic prediction error (DPE), and dynamic relative prediction error (DRPE). The proposed model was performed on blood pressure data, obtained from systolic blood pressure intervention trial (SPRINT), in order to calculate the cardiovascular risk. Dynpred, coxme, and coxphw packages in the R.3.4.3 software were used. It was proved that our proposed model, LFM, had a better performance than LM. Parameter estimation in LFM was closer to true values in comparison to that in LM. Deviance statistic showed that there was a statistically significant difference between the two models. In the landmark numbers 6, 12, and 24, the LFM had a higher DCI over time and the three landmarks showed better performance in discrimination. Both DPE and DRPE in LFM were lower in comparison to those in LM over time. It was indicated that LFM had better calibration in comparison to its peer. Moreover, real data showed that the structure of prognostic process was predicted better in LFM than in LM. Accordingly, it is recommended to use the LFM model for assessing cardiovascular risk due to its better performance.

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

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

Frailty modelling for multitype recurrent events in clinical trials

Recurrent event outcomes are ubiquitous among clinical trial data which encourages a conventional approach to analysis. Yet a common feature of these data has received less attention, that is, survival times often comprise multiple types of events that may imply a disparity in cost and disease severity. Typically, we neglect this feature of the data by combining event-types or analyzing each type separately, thus ignoring any interdependence among them. This practice may reflect a dearth of readily available methods and software that more appropriately acknowledge the true data structure. We provide a review of the literature on multitype recurrent events and frailty modelling which reflects a renewed interest in the topic over the past decade and the emergence of software for estimation. Thus, a review of available methods seems timely, if not overdue.

Joint analysis of longitudinal and survival AIDS data with a spatial fraction of long-term survivors: A Bayesian approach

A typical survival analysis with time-dependent covariates usually does not take into account the possible random fluctuations or the contamination by measurement errors of the variables. Ignoring these sources of randomness may cause bias in the estimates of the model parameters. One possible way for overcoming that limitation is to consider a longitudinal model for the time-varying covariates jointly with a survival model for the time to the event of interest, thereby taking advantage of the complementary information flowing between these two-model outcomes. We employ here a Bayesian hierarchical approach to jointly model spatial-clustered survival data with a fraction of long-term survivors along with the repeated measurements of CD4⁺ T lymphocyte counts for a random sample of 500 HIV/AIDS individuals collected in all the 27 states of Brazil during the period 2002-2006. The proposed Bayesian joint model comprises two parts: on the one hand, a flexible model using Penalized Splines to better capture the nonlinear behavior of the different CD4 profiles over time; on the other hand, a spatial cure model to cope with the set of long-term survivor individuals. Our findings show that joint models considering this set of patients were the ones with the best performance comparatively to the more traditional survival approach. Moreover, the use of spatial frailties allowed us to map the heterogeneity in the disease risk among the Brazilian states.

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

Background

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

Methods

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

Results

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

Conclusion

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

Electronic supplementary material

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

Dynamic prediction of recurrent events data by landmarking with application to a follow-up study of patients after kidney transplant

This paper extends dynamic prediction by landmarking to recurrent event data. The motivating data comprised post-kidney transplantation records of repeated infections and repeated measurements of multiple markers. At each landmark time point ts, a Cox proportional hazards model with a frailty term was fitted using data of individuals who were at risk at landmark s. This model included the time-updated marker values at ts as time-fixed covariates. Based on a stacked data set that merged all landmark data sets, we considered supermodels that allow parameters to depend on the landmarks in a smooth fashion. We described and evaluated four ways to parameterize the supermodels for recurrent event data. With both the study data and simulated data sets, we compared supermodels that were fitted on stacked data sets that consisted of either overlapping or non-overlapping landmark periods. We observed that for recurrent event data, the supermodels may yield biased estimates when overlapping landmark periods are used for stacking. Using the best supermodel amongst the ones considered, we dynamically estimated the probability to remain infection free between ts and a prediction horizon thor, conditional on the information available at ts.