Joint Modeling of Longitudinal Change and Survival (original) (raw)
Related papers
Joint longitudinal-survival models are useful when repeated measures and event time data are available and possibly associated. The application of this joint model in aging research is relatively rare, albeit particularly useful, when there is the potential for nonrandom dropout. In this article we illustrate the method and discuss some issues that may arise when fitting joint models of this type. Using prose recall scores from the Swedish OCTO-Twin Longitudinal Study of Aging, we fitted a joint longitudinal-survival model to investigate the association between risk of mortality and individual differences in rates of change in memory. A model describing change in memory scores as following an accelerating decline trajectory and a Weibull survival model was identified as the best fitting. This model adjusted for random effects representing individual variation in initial memory performance and change in rate of decline as linking terms between the longitudinal and survival models. Me...
Joint modelling of survival and cognitive decline in the Australian Longitudinal Study of Ageing
Journal of the Royal Statistical Society Series C, 2011
The paper describes the use of a longitudinal tobit model to characterize cognitive decline over a 13-year period in a cohort of 2087 elderly Australians. Use of a tobit formulation allows for the so-called 'ceiling effect' wherein many subjects achieve perfect test scores. A Bayesian hierarchical joint model is presented that allows for random subject-specific intercepts and slopes, as well as for informative dropout. Results suggest several potential areas of intervention. For example, there is a clear dose-response effect of exercise whereby increasing levels of exercise are associated with higher cognitive scores.
Frontiers in public health, 2014
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...
Frontiers in Psychology, 2021
With aging populations worldwide, there is growing interest in links between cognitive decline and elevated mortality risk—and, by extension, analytic approaches to further clarify these associations. Toward this end, some researchers have compared cognitive trajectories of survivors vs. decedents while others have examined longitudinal changes in cognition as predictive of mortality risk. A two-stage modeling framework is typically used in this latter approach; however, several recent studies have used joint longitudinal-survival modeling (i.e., estimating longitudinal change in cognition conditionally on mortality risk, and vice versa). Methodological differences inherent to these approaches may influence estimates of cognitive decline and cognition-mortality associations. These effects may vary across cognitive domains insofar as changes in broad fluid and crystallized abilities are differentially sensitive to aging and mortality risk. We compared these analytic approaches as app...
Joint Modelling of Longitudinal and Survival Data: A comparison of Joint and Independent Models
2011
In recent years, the interest in longitudinal data analysis has grown rapidly through the development of new methods and the increase in computational power to aid and further develop this field of research. One such method is the joint modelling of longitudinal and survival data. It is commonly found in the collection of medical longitudinal data that both repeated measures and time-to-event data are collected. These processes are typically correlated, where both types of data are associated through unobserved random effects. Due to this association, joint models were developed to enable a more accurate method to model both processes simultaneously. When these processes are correlated, the use of independent models can cause biased estimates [3, 6, 7], with joint models resulting in a reduction in the standard error of estimates. Thus, with more accurate parameter estimates, valid inferences concerning the effect of covariates on the longitudinal and survival processes can be obtai...
Extensions in the field of joint modeling of correlated data and dynamic predictions improve the development of prognosis research. The R package frailtypack provides estimations of various joint models for longitudinal data and survival events. In particular, it fits models for recurrent events and a terminal event (frailtyPenal), models for two survival outcomes for clustered data (frailtyPenal), models for two types of recurrent events and a terminal event (multivPenal), models for a longitudinal biomarker and a terminal event (longiPenal) and models for a longitudinal biomarker, recurrent events and a terminal event (trivPenal). The estimators are obtained using a standard and penalized maximum likelihood approach, each model function allows to evaluate goodness-of-fit analyses and provides plots of baseline hazard functions. Finally, the package provides individual dynamic predictions of the terminal event and evaluation of predictive accuracy. This paper presents the theoretical models with estimation techniques, applies the methods for predictions and illustrates frailtypack functions details with examples.
Applications of Survival Analysis to Aging Research
Experimental Aging Research, 1991
Many research questions in aging research treat time as the outcome variable. Researchers ask how much time must pass before a specific type of change or event occurs, and whether these times differ by characteristics of the subjects' background, training and treatment. Because of serious technical problems that arise when analyzing duration data, specially derived statistical methods – the methods of survival analysis – are required to answer the questions. In this paper, we introduce the conceptual framework of these new methodologies for analyzing duration data. We begin by identifying the types of research question that might appropriately treat time as an outcome. We then describe the new statistical methods for addressing such questions, provide a broad overview of their application, and identify relevant published sources containing additional background and technical information.
Longitudinal Data with Follow-up Truncated by Death: Match the Analysis Method to Research Aims
Statistical Science, 2009
Diverse analysis approaches have been proposed to distinguish data missing due to death from nonresponse, and to summarize trajectories of longitudinal data truncated by death. We demonstrate how these analysis approaches arise from factorizations of the distribution of longitudinal data and survival information. Models are illustrated using cognitive functioning data for older adults. For unconditional models, deaths do not occur, deaths are independent of the longitudinal response, or the unconditional longitudinal response is averaged over the survival distribution. Unconditional models, such as random effects models fit to unbalanced data, may implicitly impute data beyond the time of death. Fully conditional models stratify the longitudinal response trajectory by time of death. Fully conditional models are effective for describing individual trajectories, in terms of either aging (age, or years from baseline) or dying (years from death). Causal models (principal stratification) as currently applied are fully conditional models, since group differences at one timepoint are described for a cohort that will survive past a later timepoint. Partly conditional models summarize the longitudinal response in the dynamic cohort of survivors. Partly conditional models are serial cross-sectional snapshots of the response, reflecting the average response in survivors at a given timepoint rather than individual trajectories. Joint models of survival and longitudinal response describe the evolving health status of the entire cohort. Researchers using longitudinal data should consider which method of accommodating deaths is consistent with research aims, and use analysis methods accordingly.
Joint modelling of multivariate longitudinal profiles: pitfalls of the random-effects approach
Statistics in Medicine, 2004
A joint model based on a latent class approach is proposed to explore the association between correlated longitudinal quantitative markers and a time-to-event. A longitudinal latent class model describes latent profiles of evolution of the latent process underlying the correlated markers. The latent process is linked to the markers by nonlinear transformations including parameters to be estimated. A proportional hazard model describes the joint risk of event according to the latent classes and two specifications of the risk function are considered: a parametric function and a semi-parametric function based on splines. Depending on the chosen risk function, estimation is performed by a maximum likelihood or a maximum penalized likelihood approach. A simulation study validates the estimation procedure. As a latent class model relies on the strong assumption that the markers and the time-to-event are independent conditionally on the latent classes, a test of conditional independence is proposed using the residuals conditional on time-to-event. The procedure does not require any posterior classification and can be conducted using standard statistical softwares. The methodology is applied to describe profiles of cognitive decline in the elderly and their associated risk of dementia.
The quadratic hazard model for analyzing longitudinal data on aging, health, and the life span
Physics of life reviews, 2012
A better understanding of processes and mechanisms linking human aging with changes in health status and survival requires methods capable of analyzing new data that take into account knowledge about these processes accumulated in the field. In this paper, we describe an approach to analyses of longitudinal data based on the use of stochastic process models of human aging, health, and longevity which allows for incorporating state of the art advances in aging research into the model structure. In particular, the model incorporates the notions of resistance to stresses, adaptive capacity, and "optimal" (normal) physiological states. To capture the effects of exposure to persistent external disturbances, the notions of allostatic adaptation and allostatic load are introduced. These notions facilitate the description and explanation of deviations of individuals' physiological indices from their normal states, which increase the chances of disease development and death. Th...