Tackling dynamic prediction of death in patients with recurrent cardiovascular events

In the field of cardiovascular disease, recurrent events such as stroke or myocardial infarction (MI) are often encountered, leading to an increase in the risk of death. Accurately evaluating the prognosis of patients and dynamically predicting the risk of death by considering the historical recurrent events can improve medical decisions and lead to better health care outcomes. Recently proposed joint modeling approaches within the Bayesian framework have inspired the development of a dynamic prediction tool, which can be applied for subject-level prediction of death with implementation in software packages. The prediction model incorporates subject heterogeneity with subject-level random effects that account for unobserved time-invariant factors and an extra copula function capturing the part caused by unmeasured time-dependent factors. Thereafter, given the prespecified landmark timet ' $$ {t}^{\prime } $$ , the survival probability for a prediction horizon time of interestt $$ t $$ can be estimated for each individual. The prediction accuracy is assessed by time-dependent receiving operating characteristic curve and the area under the curve and the Brier score with calibration plots is compared to traditional joint frailty models. Finally, the tool is applied to patients with multiple attacks of stroke or MI in the Cardiovascular Health study and the Atherosclerosis Risk in Communities study for illustration.

Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched population comparison group

BACKGROUND

Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices.

METHODS

We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions.

RESULTS

Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable.

CONCLUSIONS

Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.

Socioeconomic status and its relation with breast cancer recurrence and survival in young women in the Netherlands

BACKGROUND

Associations between socioeconomic status (SES) and breast cancer survival are most pronounced in young patients. We further investigated the relation between SES, subsequent recurrent events and mortality in breast cancer patients < 40 years. Using detailed data on all recurrences that occur between date of diagnosis of the primary tumor and last observation, we provide a unique insight in the prognosis of young breast cancer patients according to SES.

METHODS

All women < 40 years diagnosed with primary operated stage I-III breast cancer in 2005 were selected from the nationwide population-based Netherlands Cancer Registry. Data on all recurrences within 10 years from primary tumor diagnosis were collected directly from patient files. Recurrence patterns and absolute risks of recurrence, contralateral breast cancer (CBC) and mortality - accounting for competing risks - were analysed according to SES. Relationships between SES, recurrence patterns and excess mortality were estimated using a multivariable joint model, wherein the association between recurrent events and excess mortality (expected mortality derived from the general population) was included.

RESULTS

We included 525 patients. The 10-year recurrence risk was lowest in high SES (18.1%), highest in low SES (29.8%). Death and CBC as first events were rare. In high, medium and low SES 13.2%, 15.3% and 19.1% died following a recurrence. Low SES patients had shorter median time intervals between diagnosis, first recurrence and 10-year mortality (2.6 and 2.7 years, respectively) compared to high SES (3.5 and 3.3 years, respectively). In multivariable joint modeling, high SES was significantly related to lower recurrence rates over 10-year follow-up, compared to low SES. A strong association between the recurrent event process and excess mortality was found.

CONCLUSIONS

High SES is associated with lower recurrence risks, less subsequent events and better prognosis after recurrence over 10 years than low SES. Breast cancer risk factors, adjuvant treatment adherence and treatment of recurrence may possibly play a role in this association.

Dynamic prediction of disease processes based on recurrent history and functional principal component analysis of longitudinal biomarkers: Application for ovarian epithelial cancer

Ovarian epithelial cancer is a gynecological tumor with a high risk of recurrence and death. In the clinical diagnosis of ovarian epithelial cancer, CA125 has become an important indicator of disease burden. To account for patient recurrence and death, a proper method is needed to integrate information from biomarkers and recurrence simultaneously. In the past 10 years, many methods have been proposed for joint modeling of longitudinal biomarkers and survival data, but few of them are applicable to longitudinal data and disease processes, including recurrence and death. In this article, we proposed a new joint frailty model based on functional principal component analysis for dynamic prediction of survival probabilities on the total time scale, which took recurrent history and longitudinal data into account simultaneously. The estimation of the joint frailty model is achieved by maximizing the penalized log-likelihood function. The simulation results demonstrated the advantages of our method in both discrimination and accuracy under different scenarios. To indicate the method's practicality, it is applied to an actual dataset of patients with ovarian epithelial cancer to predict survival dynamically using longitudinal data of biomarker CA125 and recurrent history data.

Modeling and comparing data mining algorithms for prediction of recurrence of breast cancer

Breast cancer is the most common invasive cancer and the second leading cause of cancer death in women. and regrettably, this rate is increasing every year. One of the aspects of all cancers, including breast cancer, is the recurrence of the disease, which causes painful consequences to the patients. Moreover, the practical application of data mining in the field of breast cancer can help to provide some necessary information and knowledge required by physicians for accurate prediction of breast cancer recurrence and better decision-making. The main objective of this study is to compare different data mining algorithms to select the most accurate model for predicting breast cancer recurrence. This study is cross-sectional and data gathering of this research performed from June 2018 to June 2019 from the official statistics of Ministry of Health and Medical Education and the Iran Cancer Research Center for patients with breast cancer who had been followed for a minimum of 5 years from February 2014 to April 2019, including 5471 independent records. After initial pre-processing in dataset and variables, seven new and conventional data mining algorithms have been applied that each one represents one kind of data mining approach. Results show that the C5.0 algorithm possibly could be a helpful tool for the prediction of breast cancer recurrence at the stage of distant recurrence and nonrecurrence, especially in the first to third years. also, LN involvement rate, Her2 value, Tumor size, free or closed tumor margin were found to be the most important features in our dataset to predict breast cancer recurrence.

Assessment of death risk of breast cancer patients with joint frailty models

Objectives:

To investigate the effects of risk factors on recurrence and death in breast cancer patients, taking into account the dependence between recurrence and death as well as the heterogeneity among individuals. The other aim of this study was to make predictions of death risks with a dynamic model that includes patient’s history and different horizons.

Methods:

The data of 465 patients who had undergone surgery at the Istanbul University Oncology Institute, Istanbul, Turkey, between 2009 and 2016 were used. For data analysis in this retrospective study, the authors applied the joint frailty model, and the predictions were obtained using dynamic prediction methods that consider the patient’s history. The Brier score was used to evaluate the accuracy of the estimations.

Results:

A positive relationship was found between recurrence and death, and heterogeneity was found among patients (p<0.001, p=1.008, p=2.945). The effects of Cerb-B2, tumor type, remaining lymph nodes, neoadjuvant chemotherapy, and surgery type were statistically significant for death and recurrence (p<0.05, relative risk [death, recurrence] = [2.5, 11.86], [2.065, 2.798], [1.852, 3.113], [4.211, 9.366], [1.521,1.991]). The Brier score values used in the evaluation of the predictions obtained by the dynamic prediction methods were found to be below 0.30.

Conclusion:

The use of joint frailty models is recommended for the detection of heterogeneity effects and dependence between recurrence and death. Through models in survival analysis, researchers can obtain more accurate parameter estimates. A significant variance of frailty indicates different death risks for the same characteristics.

Design and analysis of nested case-control studies for recurrent events subject to a terminal event

The process by which patients experience a series of recurrent events, such as hospitalizations, may be subject to death. In cohort studies, one strategy for analyzing such data is to fit a joint frailty model for the intensities of the recurrent event and death, which estimates covariate effects on the two event types while accounting for their dependence. When certain covariates are difficult to obtain, however, researchers may only have the resources to subsample patients on whom to collect complete data: one way is using the nested case-control (NCC) design, in which risk set sampling is performed based on a single outcome. We develop a general framework for the design of NCC studies in the presence of recurrent and terminal events and propose estimation and inference for a joint frailty model for recurrence and death using data arising from such studies. We propose a maximum weighted penalized likelihood approach using flexible spline models for the baseline intensity functions. Two standard error estimators are proposed: a sandwich estimator and a perturbation resampling procedure. We investigate operating characteristics of our estimators as well as design considerations via a simulation study and illustrate our methods using two studies: one on recurrent cardiac hospitalizations in patients with heart failure and the other on local recurrence and metastasis in patients with breast cancer.

Joint nested frailty models for clustered recurrent and terminal events: An application to colonoscopy screening visits and colorectal cancer risks in Lynch Syndrome families

Joint models for recurrent and terminal events have not been yet developed for clustered data. The goals of our study are to develop a statistical framework for modelling clustered recurrent and terminal events and to perform dynamic predictions of the terminal event in family studies. We propose a joint nested frailty model for colonoscopy screening visits and colorectal cancer onset in Lynch Syndrome families. The screening and disease processes could each depend on individuals' screening history and other measured covariates and be correlated within families; our approach allows for familial correlations to affect both the visit process and the terminal event and the dependence between the two processes is specified through frailty distributions. We provide dynamic predictions of colorectal cancer risk for an individual conditional on his/her own screening history, his/her family history of screening and disease and other important clinical covariates. We apply our model to 18 Lynch Syndrome families from Newfoundland for individualized dynamic predictions of colorectal cancer risks. We demonstrate that the screening visits are non-ignorable for estimating the disease risks, and the joint nested frailty model improves dynamic prediction accuracies compared to existing joint frailty models after accounting for familial and individual screening and cancer histories.

A flexible and robust method for assessing conditional association and conditional concordance

When analyzing bivariate outcome data, it is often of scientific interest to measure and estimate the association between the bivariate outcomes. In the presence of influential covariates for one or both of the outcomes, conditional association measures can quantify the strength of association without the disturbance of the marginal covariate effects, to provide cleaner and less-confounded insights into the bivariate association. In this work, we propose estimation and inferential procedures for assessing the conditional Kendall's tau coefficient given the covariates, by adopting the quantile regression and quantile copula framework to handle marginal covariate effects. The proposed method can flexibly accommodate right censoring and be readily applied to bivariate survival data. It also facilitates an estimator of the conditional concordance measure, namely, a conditional C index, where the unconditional C index is commonly used to assess the predictive capacity for survival outcomes. The proposed method is flexible and robust and can be easily implemented using standard software. The method performed satisfactorily in extensive simulation studies with and without censoring. Application of our methods to two real-life data examples demonstrates their desirable practical utility.

Dynamic prediction of repeated events data based on landmarking model: application to colorectal liver metastases data

BACKGROUND

In some clinical situations, patients experience repeated events of the same type. Among these, cancer recurrences can result in terminal events such as death. Therefore, here we dynamically predicted the risks of repeated and terminal events given longitudinal histories observed before prediction time using dynamic pseudo-observations (DPOs) in a landmarking model.

METHODS

The proposed DPOs were calculated using Aalen-Johansen estimator for the event processes described in the multi-state model. Furthermore, in the absence of a terminal event, a more convenient approach without matrix operation was described using the ordering of repeated events. Finally, generalized estimating equations were used to calculate probabilities of repeated and terminal events, which were treated as multinomial outcomes.

RESULTS

Simulation studies were conducted to assess bias and investigate the efficiency of the proposed DPOs in a finite sample. Little bias was detected in DPOs even under relatively heavy censoring, and the method was applied to data from patients with colorectal liver metastases.

CONCLUSIONS

The proposed method enabled intuitive interpretations of terminal event settings.

Explained variation of excess hazard models

The availability of longstanding collection of detailed cancer patient information makes multivariable modelling of cancer-specific hazard of death appealing. We propose to report variation in survival explained by each variable that constitutes these models. We adapted the ranks explained (RE) measure to the relative survival data setting, ie, when competing risks of death are accounted for through life tables from the general population. RE is calculated at each event time. We introduce weights for each death reflecting its probability to be a cancer death. RE varies between -1 and +1 and can be reported at given times in the follow-up and as a time-varying measure from diagnosis onward. We present an application for patients diagnosed with colon or lung cancer in England. The RE measure shows reasonable properties and is comparable in both relative and cause-specific settings. One year after diagnosis, RE for the most complex excess hazard models reaches 0.56, 95% CI: 0.54 to 0.58 (0.58 95% CI: 0.56-0.60) and 0.69, 95% CI: 0.68 to 0.70 (0.67, 95% CI: 0.66-0.69) for lung and colon cancer men (women), respectively. Stage at diagnosis accounts for 12.4% (10.8%) of the overall variation in survival among lung cancer patients whereas it carries 61.8% (53.5%) of the survival variation in colon cancer patients. Variables other than performance status for lung cancer (10%) contribute very little to the overall explained variation. The proportion of the variation in survival explained by key prognostic factors is a crucial information toward understanding the mechanisms underpinning cancer survival. The time-varying RE provides insights into patterns of influence for strong predictors.

Factors associated with breast cancer recurrences or mortality and dynamic prediction of death using history of cancer recurrences: the French E3N cohort

BACKGROUND

In addition to tumor characteristics and lifestyle factors, cancer relapses are often related to the risk of death but have not been jointly studied. We investigate the prognostic factors of recurrent events and death after a diagnosis of breast cancer and predict individual deaths including a history of recurrences.

METHODS

The E3N (Etude Epidémiologique auprès de Femmes de la Mutuelle Générale de l'Education Nationale) study is a prospective cohort study that was initiated in 1990 to investigate factors associated with the most common types of cancer. Overall survival and three types of recurrent events were considered: locoregional recurrence, metastasis, and second primary breast cancer. Recurrent events and death were analyzed using a joint frailty model.

RESULTS

The analysis included 4926 women from the E3N cohort diagnosed with a first primary invasive breast cancer between June 1990 and June 2008; during the follow-up, 1334 cases had a recurrence (median time of follow-up is 7.2 years) and 469 women died. Cases with high grade, large tumor size, axillary nodal involvement, and negative estrogen and progesterone receptors had a higher risk of recurrence or death. Furthermore, smoking increased the risk of relapse. For cases with a medium risk profile in terms of tumor characteristics and lifestyle factors, the probability of dying between 5 and 10 years after diagnosis was 6, 20 and 36% for 0, 1 or 2 recurrences within the first 5 years after diagnosis, respectively.

CONCLUSIONS

Our study showed the importance of considering baseline lifestyle characteristics and history of relapses to dynamically predict the risk of death in breast cancer cases. Medical experience coupled with an estimate of a patient's survival probability that considers all available information for this patient would enable physicians to make better informed decisions regarding their actions and thus improve clinical output.

Bayesian analysis of multi-type recurrent events and dependent termination with nonparametric covariate functions

Multi-type recurrent event data occur frequently in longitudinal studies. Dependent termination may occur when the terminal time is correlated to recurrent event times. In this article, we simultaneously model the multi-type recurrent events and a dependent terminal event, both with nonparametric covariate functions modeled by B-splines. We develop a Bayesian multivariate frailty model to account for the correlation among the dependent termination and various types of recurrent events. Extensive simulation results suggest that misspecifying nonparametric covariate functions may introduce bias in parameter estimation. This method development has been motivated by and applied to the lipid-lowering trial component of the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial.

Effect of coinfection with hepatitis C virus on survival of individuals with HIV-1 infection

PURPOSE OF REVIEW

Hepatitis C virus (HCV) coinfection is a common and an important comorbidity in HIV infection. We review current trends in mortality and the potential for early combination antiretroviral therapy (cART) and HCV therapy to improve survival in coinfected patients.

RECENT FINDINGS

HIV/HCV coinfection increases risk of death from all causes, and from liver disease and harmful drug use in particular. There is growing evidence for a direct role of HIV in liver fibrogenesis and for cART to decrease the risk of dying from liver disease in coinfected persons. Sustained virologic responses after HCV treatment greatly impact mortality by reducing rates of hepatic decompensation, hepatocellular carcinoma and death from liver-related and nonliver-related causes by at least 50%, but treatment uptake has been low so far. Recent epidemiologic studies do suggest that liver-related mortality is declining in recent calendar periods; however, methodological limitations of currently available studies are important.

SUMMARY

Early cART and wider HCV treatment have the potential to markedly reduce HCV-related mortality and thus increase survival overall for HIV-infected populations. However, HCV treatment will need to be greatly scaled up. Given the complex nature of the populations affected, future studies will need to be carefully designed and controlled to rigorously evaluate the impact of these revolutionary therapies on survival.

Joint model imputation to estimate the treatment effect on long-term survival using auxiliary events

Clinical trial duration may be a concern in clinical research, especially in cancer trials where the endpoint is overall survival. A surrogate endpoint can be used as an auxiliary variable to analyze the treatment effect earlier. At an early time point, the high number of censored observations can be compensated by the imputation of the unobserved deaths times. We propose to use predictions of the risk of death from a joint model for a recurrent event and a terminal event, which account for disease relapse information. Two imputation methods were compared: sampling from the estimated parametric distribution of the survival time and sampling using its nonparametric estimation. The treatment effect and its standard error were estimated via multiple imputations. The performances of the two methods were compared in terms of bias in the estimates, standard errors, and coverage probability. Both methods were then retrospectively applied to two randomized clinical trials studying the effect of adjuvant chemotherapy in breast cancer patients.

Personalized dynamic prediction of death according to tumour progression and high-dimensional genetic factors: Meta-analysis with a joint model

Developing a personalized risk prediction model of death is fundamental for improving patient care and touches on the realm of personalized medicine. The increasing availability of genomic information and large-scale meta-analytic data sets for clinicians has motivated the extension of traditional survival prediction based on the Cox proportional hazards model. The aim of our paper is to develop a personalized risk prediction formula for death according to genetic factors and dynamic tumour progression status based on meta-analytic data. To this end, we extend the existing joint frailty-copula model to a model allowing for high-dimensional genetic factors. In addition, we propose a dynamic prediction formula to predict death given tumour progression events possibly occurring after treatment or surgery. For clinical use, we implement the computation software of the prediction formula in the joint.Cox R package. We also develop a tool to validate the performance of the prediction formula by assessing the prediction error. We illustrate the method with the meta-analysis of individual patient data on ovarian cancer patients.

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.

Joint model for left-censored longitudinal data, recurrent events and terminal event: Predictive abilities of tumor burden for cancer evolution with application to the FFCD 2000-05 trial

In oncology, the international WHO and RECIST criteria have allowed the standardization of tumor response evaluation in order to identify the time of disease progression. These semi-quantitative measurements are often used as endpoints in phase II and phase III trials to study the efficacy of new therapies. However, through categorization of the continuous tumor size, information can be lost and they can be challenged by recently developed methods of modeling biomarkers in a longitudinal way. Thus, it is of interest to compare the predictive ability of cancer progressions based on categorical criteria and quantitative measures of tumor size (left-censored due to detection limit problems) and/or appearance of new lesions on overall survival. We propose a joint model for a simultaneous analysis of three types of data: a longitudinal marker, recurrent events, and a terminal event. The model allows to determine in a randomized clinical trial on which particular component treatment acts mostly. A simulation study is performed and shows that the proposed trivariate model is appropriate for practical use. We propose statistical tools that evaluate predictive accuracy for joint models to compare our model to models based on categorical criteria and their components. We apply the model to a randomized phase III clinical trial of metastatic colorectal cancer, conducted by the Fédération Francophone de Cancérologie Digestive (FFCD 2000-05 trial), which assigned 410 patients to two therapeutic strategies with multiple successive chemotherapy regimens.

A joint frailty-copula model between tumour progression and death for meta-analysis

Dependent censoring often arises in biomedical studies when time to tumour progression (e.g., relapse of cancer) is censored by an informative terminal event (e.g., death). For meta-analysis combining existing studies, a joint survival model between tumour progression and death has been considered under semicompeting risks, which induces dependence through the study-specific frailty. Our paper here utilizes copulas to generalize the joint frailty model by introducing additional source of dependence arising from intra-subject association between tumour progression and death. The practical value of the new model is particularly evident for meta-analyses in which only a few covariates are consistently measured across studies and hence there exist residual dependence. The covariate effects are formulated through the Cox proportional hazards model, and the baseline hazards are nonparametrically modeled on a basis of splines. The estimator is then obtained by maximizing a penalized log-likelihood function. We also show that the present methodologies are easily modified for the competing risks or recurrent event data, and are generalized to accommodate left-truncation. Simulations are performed to examine the performance of the proposed estimator. The method is applied to a meta-analysis for assessing a recently suggested biomarker CXCL12 for survival in ovarian cancer patients. We implement our proposed methods in R joint.Cox package.

Dynamic prediction models for clustered and interval-censored outcomes: Investigating the intra-couple correlation in the risk of dementia

The use of settings such as cohorts or clinical trials with interval-censored data and clustered event times are increasingly popular designs. First, the observed outcomes cannot be considered as independent and random effects survival models were introduced. Second, the failure time is not known exactly but it is only known to have occurred within a certain interval. We propose here an extension of shared frailty models to handle simultaneously the interval censoring, the clustering and also left truncation due to delayed entry in the cohort. A simulation study to evaluate the proposed method was conducted. The estimated results are used to obtain dynamic predictions for clustered patients, with interval-censored failure times and with a given history. We apply our method to the Three-City study, a prospective cohort with periodic follow-up in order to study prognostic factors of dementia. In this application scheme, couples are natural clusters and an intra-couple correlation might be present with a possible increased risk for dementia for subjects whose partner already developed incident dementia. No significant intra-couple correlation for the risk of dementia was observed before and after adjustments for covariates. We also present individual predictions of dementia underlining the usefulness of dynamic prognostic tools that can take into account the clustering. The consideration of frailty models for interval-censoring data and left-truncated data permits useful analysis of very complex clustered data. It could help to improve estimation of the impact of proposed prognostic features in a study with clustering. We proposed here a tractable model and a dynamic prediction tool that can easily be implemented using the R package Frailtypack.

Validation of death prediction after breast cancer relapses using joint models

BACKGROUND

Cancer relapses may be useful to predict the risk of death. To take into account relapse information, the Landmark approach is popular. As an alternative, we propose the joint frailty model for a recurrent event and a terminal event to derive dynamic predictions of the risk of death.

METHODS

The proposed prediction settings can account for relapse history or not. In this work, predictions developed on a French hospital series of patients with breast cancer are externally validated on UK and Netherlands registry data. The performances in terms of prediction error and calibration are compared to those from a Landmark Cox model.

RESULTS

The error of prediction was reduced when relapse information was taken into account. The prediction was well-calibrated, although it was developed and validated on very different populations. Joint modelling and Landmark approaches had similar performances.

CONCLUSIONS

When predicting the risk of death, accounting for relapses led to better prediction performance. Joint modelling appeared to be suitable for such prediction. Performance was similar to the landmark Cox model, while directly quantifying the correlation between relapses and death.

Joint Analyses of Longitudinal and Time-to-Event Data in Research on Aging: Implications for Predicting Health and Survival

Longitudinal data on aging, health, and longevity provide a wealth of information to investigate different aspects of the processes of aging and development of diseases leading to death. Statistical methods aimed at analyses of time-to-event data jointly with longitudinal measurements became known as the "joint models" (JM). An important point to consider in analyses of such data in the context of studies on aging, health, and longevity is how to incorporate knowledge and theories about mechanisms and regularities of aging-related changes that accumulate in the research field into respective analytic approaches. In the absence of specific observations of longitudinal dynamics of relevant biomarkers manifesting such mechanisms and regularities, traditional approaches have a rather limited utility to estimate respective parameters that can be meaningfully interpreted from the biological point of view. A conceptual analytic framework for these purposes, the stochastic process model of aging (SPM), has been recently developed in the biodemographic literature. It incorporates available knowledge about mechanisms of aging-related changes, which may be hidden in the individual longitudinal trajectories of physiological variables and this allows for analyzing their indirect impact on risks of diseases and death. Despite, essentially, serving similar purposes, JM and SPM developed in parallel in different disciplines with very limited cross-referencing. Although there were several publications separately reviewing these two approaches, there were no publications presenting both these approaches in some detail. Here, we overview both approaches jointly and provide some new modifications of SPM. We discuss the use of stochastic processes to capture biological variation and heterogeneity in longitudinal patterns and important and promising (but still largely underused) applications of JM and SPM to predictions of individual and population mortality and health-related outcomes.