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Peter J Diggle - One of the best experts on this subject based on the ideXlab platform.
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Joint Modelling of repeated measurement and time to event data an introductory tutorial
International Journal of Epidemiology, 2015Co-Authors: Ozgur Asar, James Ritchie, Philip A Kalra, Peter J DiggleAbstract:Backgound: The term ‘Joint Modelling’ is used in the statistical literature to refer to methods for simultaneously analysing longitudinal measurement outcomes, also called repeated measurement data, and time-to-event outcomes, also called survival data. A typical example from nephrology is a study in which the data from each participant consist of repeated estimated glomerular filtration rate (eGFR) measurements and time to initiation of renal replacement therapy (RRT). Joint models typically combine linear mixed effects models for repeated measurements and Cox models for censored survival outcomes. Our aim in this paper is to present an introductory tutorial on Joint Modelling methods, with a case study in nephrology. Methods: We describe the development of the Joint Modelling framework and compare the results with those obtained by the more widely used approaches of conducting separate analyses of the repeated measurements and survival times based on a linear mixed effects model and a Cox model, respectively. Our case study concerns a data set from the Chronic Renal Insufficiency Standards Implementation Study (CRISIS). We also provide details of our open-source software implementation to allow others to replicate and/or modify our analysis. Results: The results for the conventional linear mixed effects model and the longitudinal component of the Joint models were found to be similar. However, there were considerable differences between the results for the Cox model with time-varying covariate and the time-to-event component of the Joint model. For example, the relationship between kidney function as measured by eGFR and the hazard for initiation of RRT was significantly underestimated by the Cox model that treats eGFR as a time-varying covariate, because the Cox model does not take measurement error in eGFR into account. Conclusions: Joint models should be preferred for simultaneous analyses of repeated measurement and survival data, especially when the former is measured with error and the association between the underlying error-free measurement process and the hazard for survival is of scientific interest.
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Joint Modelling of repeated measurements and time to event outcomes flexible model specification and exact likelihood inference
Journal of The Royal Statistical Society Series B-statistical Methodology, 2015Co-Authors: Jessica K Barrett, Peter J Diggle, Robin Henderson, David TaylorrobinsonAbstract:Random effects or shared parameter models are commonly advocated for the analysis of combined repeated measurement and event history data, including dropout from longitudinal trials. Their use in practical applications has generally been limited by computational cost and complexity, meaning that only simple special cases can be fitted by using readily available software. We propose a new approach that exploits recent distributional results for the extended skew normal family to allow exact likelihood inference for a flexible class of random-effects models. The method uses a discretization of the timescale for the time-to-event outcome, which is often unavoidable in any case when events correspond to dropout. We place no restriction on the times at which repeated measurements are made. An analysis of repeated lung function measurements in a cystic fibrosis cohort is used to illustrate the method.
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joiner Joint Modelling of repeated measurements and time to event data
2012Co-Authors: Pete Philipson, Peter J Diggle, Ines Sousa, Paula R. Williamson, Ruwanthi Kolamunnagedona, Robin HendersonAbstract:The joineR package implements methods for analysing data from longitudinal studies in which the response from each subject consists of a time-sequence of repeated measurements and a possibly censored time-toevent outcome. The Modelling framework for the repeated measurements is the linear model with random effects and/or correlated error structure. The model for the time-to-event outcome is a Cox proportional hazards model with log-Gaussian frailty. Stochastic dependence is captured by allowing the Gaussian random effects of the linear model to be correlated with the frailty term of the Cox proportional hazards model.
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Joint Modelling of repeated measurements and time to event outcomes the fourth armitage lecture
Statistics in Medicine, 2008Co-Authors: Peter J Diggle, Ines Sousa, Amanda G ChetwyndAbstract:In many longitudinal studies, the outcomes recorded on each subject include both a sequence of repeated measurements at pre-specified times and the time at which an event of particular interest occurs: for example, death, recurrence of symptoms or drop out from the study. The event time for each subject may be recorded exactly, interval censored or right censored. The term Joint Modelling refers to the statistical analysis of the resulting data while taking account of any association between the repeated measurement and time-to-event outcomes. In this paper, we first discuss different approaches to Joint Modelling and argue that the analysis strategy should depend on the scientific focus of the study. We then describe in detail a particularly simple, fully parametric approach. Finally, we use this approach to re-analyse data from a clinical trial of drug therapies for schizophrenic patients, in which the event time is an interval-censored or right-censored time to withdrawal from the study due to adverse side effects.
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Joint Modelling of longitudinal measurements and event time data
Biostatistics, 2000Co-Authors: Robin Henderson, Peter J Diggle, Angela DobsonAbstract:SUMMARY This paper formulates a class of models for the Joint behaviour of a sequence of longitudinal measurements and an associated sequence of event times, including single-event survival data. This class includes and extends a number of specific models which have been proposed recently, and, in the absence of association, reduces to separate models for the measurements and events based, respectively, on a normal linear model with correlated errors and a semi-parametric proportional hazards or intensity model with frailty. Special cases of the model class are discussed in detail and an estimation procedure which allows the two components to be linked through a latent stochastic process is described. Methods are illustrated using results from a clinical trial into the treatment of schizophrenia.
Cecile Proustlima - One of the best experts on this subject based on the ideXlab platform.
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individual dynamic predictions using landmarking and Joint Modelling validation of estimators and robustness assessment
Statistical Methods in Medical Research, 2019Co-Authors: Loic Ferrer, Hein Putter, Cecile ProustlimaAbstract:After the diagnosis of a disease, one major objective is to predict cumulative probabilities of events such as clinical relapse or death from the individual information collected up to a prediction...
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individual dynamic predictions using landmarking and Joint Modelling validation of estimators and robustness assessment
arXiv: Applications, 2017Co-Authors: Loic Ferrer, Hein Putter, Cecile ProustlimaAbstract:After the diagnosis of a disease, one major objective is to predict cumulative probabilities of events such as clinical relapse or death from the individual information collected up to a prediction time, including usually biomarker repeated measurements. Several competing estimators have been proposed to calculate these individual dynamic predictions, mainly from two approaches: Joint Modelling and landmarking. These approaches differ by the information used, the model assumptions and the complexity of the computational procedures. It is essential to properly validate the estimators derived from the Joint models and the landmark models, quantify their variability and compare them in order to provide key elements for the development and use of individual dynamic predictions in clinical follow-up of patients. Motivated by the prediction of two competing causes of progression of prostate cancer from the history of prostate-specific antigen, we conducted an in-depth simulation study to validate and compare the dynamic predictions derived from these two methods. Specifically, we formally defined the quantity to estimate and its estimators, proposed techniques to assess the uncertainty around predictions and validated them. We also compared the individual dynamic predictions derived from Joint models and landmark models in terms of accuracy of prediction, efficiency and robustness to model assumptions. We show that these prediction tools should be handled with care, in particular by properly specifying models and estimators.
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Joint Modelling of longitudinal and multi state processes application to clinical progressions in prostate cancer
Statistics in Medicine, 2016Co-Authors: Loic Ferrer, Virginie Rondeau, James J Dignam, Tom Pickles, Helene Jacqmingadda, Cecile ProustlimaAbstract:Joint Modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate-specific antigen (PSA) and time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post-radiotherapy, or to predict the risk of one specific type of clinical recurrence post-radiotherapy, from the PSA history. In this context, we present a Joint model for a longitudinal process and a multi-state process, which is divided into two sub-models: a linear mixed sub-model for longitudinal data and a multi-state sub-model with proportional hazards for transition times, both linked by a function of shared random effects. Parameters of this Joint multi-state model are estimated within the maximum likelihood framework using an EM algorithm coupled with a quasi-Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer. Thanks to the classical covariates available at baseline and the repeated PSA measurements, we are able to assess the biomarker's trajectory, define the risks of transitions between health states and quantify the impact of the PSA dynamics on each transition intensity. Copyright © 2016 John Wiley & Sons, Ltd.
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Joint Modelling of longitudinal and multi state processes application to clinical progressions in prostate cancer
arXiv: Applications, 2015Co-Authors: Loic Ferrer, Virginie Rondeau, James J Dignam, Tom Pickles, Helene Jacqmingadda, Cecile ProustlimaAbstract:Joint Modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate-specific antigen (PSA) and the time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post-radiotherapy, or to predict the risk of one specific type of clinical recurrence post-radiotherapy, from the PSA history. In this context, we present a Joint model for a longitudinal process and a multi-state process which is divided into two sub-models: a linear mixed sub-model for longitudinal data, and a multi-state sub-model with proportional hazards for transition times, both linked by shared random effects. Parameters of this Joint multi-state model are estimated within the maximum likelihood framework using an EM algorithm coupled to a quasi-Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending the mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer and treated by radiotherapy. Thanks to the classical covariates available at baseline and the PSA measurements collected repeatedly during the follow-up, we are able to assess the biomarker's trajectory, define the risks of transitions between health states, and quantify the impact of the PSA dynamics on each transition intensity.
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Joint Modelling of repeated multivariate cognitive measures and competing risks of dementia and death a latent process and latent class approach
arXiv: Applications, 2014Co-Authors: Cecile Proustlima, Jeanfrancois Dartigues, Helene JacqmingaddaAbstract:Joint models initially dedicated to a single longitudinal marker and a single time-to-event need to be extended to account for the rich longitudinal data of cohort studies. Multiple causes of clinical progression are indeed usually observed, and multiple longitudinal markers are collected when the true latent trait of interest is hard to capture (e.g. quality of life, functional dependency, cognitive level). These multivariate and longitudinal data also usually have nonstandard distributions (discrete, asymmetric, bounded,...). We propose a Joint model based on a latent process and latent classes to analyze simultaneously such multiple longitudinal markers of different natures, and multiple causes of progression. A latent process model describes the latent trait of interest and links it to the observed longitudinal outcomes using flexible measurement models adapted to different types of data, and a latent class structure links the longitudinal and the cause-specific survival models. The Joint model is estimated in the maximum likelihood framework. A score test is developed to evaluate the assumption of conditional independence of the longitudinal markers and each cause of progression given the latent classes. In addition, individual dynamic cumulative incidences of each cause of progression based on the repeated marker data are derived. The methodology is validated in a simulation study and applied on real data about cognitive aging coming from a large population-based study. The aim is to predict the risk of dementia by accounting for the competing death according to the profiles of semantic memory measured by two asymmetric psychometric tests.
Paul C Lambert - One of the best experts on this subject based on the ideXlab platform.
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Joint Modelling of longitudinal and survival data incorporating delayed entry and an assessment of model misspecification
Statistics in Medicine, 2016Co-Authors: Michael J Crowther, Keith R Abrams, Paul C Lambert, Therese M L Andersson, Keith HumphreysAbstract: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. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
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flexible parametric Joint Modelling of longitudinal and survival data
Statistics in Medicine, 2012Co-Authors: Michael J Crowther, Keith R Abrams, Paul C LambertAbstract:The Joint Modelling of longitudinal and survival data is a highly active area of biostatistical research. The submodel for the longitudinal biomarker usually takes the form of a linear mixed effects model. We describe a flexible parametric approach for the survival submodel that models the log baseline cumulative hazard using restricted cubic splines. This approach overcomes limitations of standard parametric choices for the survival submodel, which can lack the flexibility to effectively capture the shape of the underlying hazard function. Numerical integration techniques, such as Gauss–Hermite quadrature, are usually required to evaluate both the cumulative hazard and the overall Joint likelihood; however, by using a flexible parametric model, the cumulative hazard has an analytically tractable form, providing considerable computational benefits. We conduct an extensive simulation study to assess the proposed model, comparing it with a B-spline formulation, illustrating insensitivity of parameter estimates to the baseline cumulative hazard function specification. Furthermore, we compare non-adaptive and fully adaptive quadrature, showing the superiority of adaptive quadrature in evaluating the Joint likelihood. We also describe a useful technique to simulate survival times from complex baseline hazard functions and illustrate the methods using an example data set investigating the association between longitudinal prothrombin index and survival of patients with liver cirrhosis, showing greater flexibility and improved stability with fewer parameters under the proposed model compared with the B-spline approach. We provide user-friendly Stata software. Copyright © 2012 John Wiley & Sons, Ltd.
Aruna Sivakumar - One of the best experts on this subject based on the ideXlab platform.
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a framework for Joint Modelling of activity choice duration and productivity while travelling
Transportation Research Part B-methodological, 2017Co-Authors: Jacek Pawlak, John W Polak, Aruna SivakumarAbstract:Abstract Recent developments in mobile information and communication technologies (ICT), vehicle automation, and the associated debates on the implications for the operation of transport systems and for the appraisal of investment has heightened the importance of understanding how people spend travel time and how productive they are while travelling. To date, however, no approach has been proposed that incorporates the Joint Modelling of in-travel activity type, activity duration and productivity behaviour. To address this critical gap, we draw on a recently developed PPS framework (Pawlak et al., 2015) to develop a new Joint model of activity type choice, duration and productivity. In our framework, we use copulas to provide a flexible link between a discrete choice model of activity type choice, a hazard-based model for activity duration, and a log-linear model of productivity. Our model is readily amenable to estimation, which we demonstrate using data from the 2008 UK Study of Productive Use of Rail Travel-time. We hence show how journey-, respondent-, attitude-, and ICT-related factors are related to expected in-travel time allocation to work and non-work activities, and the associated productivity. To the best of our knowledge, this is the first framework that both captures the effects of different factors on activity choice, duration and productivity, and models links between these aspects of behaviour. Furthermore, the convenient interpretation of the parameters in the form of semi-elasticities enables the comparison of effects associated with the presence of on-board facilities (e.g., workspace, connectivity) or equipment use, facilitating use of the model outputs in applied contexts.
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towards a microeconomic framework for Modelling the Joint choice of activity travel behaviour and ict use
Transportation Research Part A-policy and Practice, 2015Co-Authors: Jacek Pawlak, John W Polak, Aruna SivakumarAbstract:The rapid development of information and communication technologies (ICT) has been argued to affect time use patterns in a variety of ways, with consequent impacts on travel behaviour. While there exists a significant body of empirical studies documenting these effects, theoretical developments have lagged this empirical work and in particular, microeconomic time allocation models have not to date been fully extended to accommodate the implications of an increasingly digitised society. To address this gap, we present a Modelling framework, grounded in time allocation theories and the goods–leisure framework, for Joint Modelling of the choice of mode of activity (physical versus tele-activity), travel mode and route, and ICT bundle. By providing the expression for a conditional indirect utility function, we use hypothetical scenarios to demonstrate how our framework can conceptualise various activity–travel decision situations. In our scenarios we assume a variety of situations such as the implications of severe weather, the introduction of autonomous vehicles, and the interaction between multiple decision makers. Moreover, our approach lays the microeconomic foundations for deriving subjective values of ICT qualities such as broadband speed or connection reliability. Finally, we also demonstrate the means by which our framework could be linked to various data collection protocols (stated preference exercises, diaries of social interactions, laboratory experiments) and Modelling approaches (discrete choice Modelling, hazard-based duration models).
Andrew Mackinnon - One of the best experts on this subject based on the ideXlab platform.
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dynamic prediction of transition to psychosis using Joint Modelling
Schizophrenia Research, 2018Co-Authors: Hok Pan Yuen, Andrew Mackinnon, Jessica A Hartmann, G P Amminger, Connie Markulev, Suzie Lavoie, Miriam R Schafer, Andrea PolariAbstract:Abstract Considerable research has been conducted seeking risk factors and constructing prediction models for transition to psychosis in individuals at ultra-high risk (UHR). Nearly all such research has only employed baseline predictors, i.e. data collected at the baseline time point, even though longitudinal data on relevant measures such as psychopathology have often been collected at various time points. Dynamic prediction, which is the updating of prediction at a post-baseline assessment using baseline and longitudinal data accumulated up to that assessment, has not been utilized in the UHR context. This study explored the use of dynamic prediction and determined if it could enhance the prediction of frank psychosis onset in UHR individuals. An emerging statistical methodology called Joint Modelling was used to implement the dynamic prediction. Data from the NEURAPRO study (n = 304 UHR individuals), an intervention study with transition to psychosis study as the primary outcome, were used to investigate dynamic predictors. Compared with the conventional approach of using only baseline predictors, dynamic prediction using Joint Modelling showed significantly better sensitivity, specificity and likelihood ratios. As dynamic prediction can provide an up-to-date prediction for each individual at each new assessment post entry, it can be a useful tool to help clinicians adjust their prognostic judgements based on the unfolding clinical symptomatology of the patients. This study has shown that a dynamic approach to psychosis prediction using Joint Modelling has the potential to aid clinicians in making decisions about the provision of timely and personalized treatment to patients concerned.
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a new method for analysing transition to psychosis Joint Modelling of time to event outcome with time dependent predictors
International Journal of Methods in Psychiatric Research, 2018Co-Authors: Hok Pan Yuen, Andrew Mackinnon, Barnaby NelsonAbstract:An active area in psychosis research is the identification of predictors of transition to a psychotic state among those who are assessed as being at high risk of psychosis. Many of the potential predictors are time dependent in the sense that they may change over time and are measured at a number of assessment time points. Examples are various psychopathological measures such as negative symptoms, positive symptoms, depression, and anxiety. Most research in transition to psychosis has not made use of the dynamic nature of these measures, probably because suitable statistical methods and software have not been easily available. However, a relatively new statistical methodology is well suited to include such time-dependent predictors in transition to psychosis analysis. This methodology is called Joint Modelling and has recently been incorporated in mainstream statistical software. This paper describes this methodology and demonstrates its usefulness using data from one of the pioneering studies on transition to psychosis.
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Performance of Joint Modelling of time-to-event data with time-dependent predictors: an assessment based on transition to psychosis data.
PeerJ, 2016Co-Authors: Hok Pan Yuen, Andrew MackinnonAbstract:: Joint Modelling has emerged to be a potential tool to analyse data with a time-to-event outcome and longitudinal measurements collected over a series of time points. Joint Modelling involves the simultaneous Modelling of the two components, namely the time-to-event component and the longitudinal component. The main challenges of Joint Modelling are the mathematical and computational complexity. Recent advances in Joint Modelling have seen the emergence of several software packages which have implemented some of the computational requirements to run Joint models. These packages have opened the door for more routine use of Joint Modelling. Through simulations and real data based on transition to psychosis research, we compared Joint model analysis of time-to-event outcome with the conventional Cox regression analysis. We also compared a number of packages for fitting Joint models. Our results suggest that Joint Modelling do have advantages over conventional analysis despite its potential complexity. Our results also suggest that the results of analyses may depend on how the methodology is implemented.
