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Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification.

ABSTRACT: 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.

SUBMITTER: Crowther MJ

PROVIDER: S-EPMC5019272 | biostudies-literature | 2016 Mar

REPOSITORIES: biostudies-literature

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Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification.

Crowther Michael J MJ Andersson Therese M-L TM Lambert Paul C PC Abrams Keith R KR Humphreys Keith K

Statistics in medicine 20151029 7

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 t ...[more]

PMID: 26514596

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Project description:BackgroundImmuno-epidemiologists are often faced with multivariate outcomes, measured repeatedly over time. Such data are characterised by complex inter- and intra-outcome relationships which must be accounted for during analysis. Scientific questions of interest might include determining the effect of a treatment on the evolution of all outcomes together, or grouping outcomes that change in the same way. Modelling the different outcomes separately may not be appropriate because it ignores the underlying relationships between outcomes. In such situations, a joint modelling strategy is necessary. This paper describes a pairwise joint modelling approach and discusses its benefits over more simple statistical analysis approaches, with application to data from a study of the response to BCG vaccination in the first year of life, conducted in Entebbe, Uganda.MethodsThe study aimed to determine the effect of maternal latent Mycobacterium tuberculosis infection (LTBI) on infant immune response (TNF, IFN-γ, IL-13, IL-10, IL-5, IL-17A and IL-2 responses to PPD), following immunisation with BCG. A simple analysis ignoring the correlation structure of multivariate longitudinal data is first shown. Univariate linear mixed models are then used to describe longitudinal profiles of each outcome, and are then combined into a multivariate mixed model, specifying a joint distribution for the random effects to account for correlations between the multiple outcomes. A pairwise joint modelling approach, where all possible pairs of bivariate mixed models are fitted, is then used to obtain parameter estimates.ResultsUnivariate and pairwise longitudinal analysis approaches are consistent in finding that LTBI had no impact on the evolution of cytokine responses to PPD. Estimates from the pairwise joint modelling approach were more precise. Major advantages of the pairwise approach include the opportunity to test for the effect of LTBI on the joint evolution of all, or groups of, outcomes and the ability to estimate association structures of the outcomes.ConclusionsThe pairwise joint modelling approach reduces the complexity of analysis of high-dimensional multivariate repeated measures, allows for proper accounting for association structures and can improve our understanding and interpretation of longitudinal immuno-epidemiological data.

Project description:BACKGROUND:Joint modeling is appropriate when one wants to predict the time to an event with covariates that are measured longitudinally and are related to the event. An underlying random effects structure links the survival and longitudinal submodels and allows for individual-specific predictions. Multiple time-varying and time-invariant covariates can be included to potentially increase prediction accuracy. The goal of this study was to estimate a multivariate joint model on several longitudinal observational studies of Huntington's disease, examine external validity performance, and compute individual-specific predictions for characterizing disease progression. Emphasis was on the survival submodel for predicting the hazard of motor diagnosis. METHODS:Data from four observational studies was analyzed: Enroll-HD, PREDICT-HD, REGISTRY, and Track-HD. A Bayesian approach to estimation was adopted, and external validation was performed using a time-varying AUC measure. Individual-specific cumulative hazard predictions were computed based on a simulation approach. The cumulative hazard was used for computing predicted age of motor onset and also for a deviance residual indicating the discrepancy between observed diagnosis status and model-based status. RESULTS:The joint model trained in a single study had very good performance in discriminating among diagnosed and pre-diagnosed participants in the remaining test studies, with the 5-year mean AUC?=?.83 (range .77-.90), and the 10-year mean AUC?=?.86 (range .82-.92). Graphical analysis of the predicted age of motor diagnosis showed an expected strong relationship with the trinucleotide expansion that causes Huntington's disease. Graphical analysis of the deviance-type residual revealed there were individuals who converted to a diagnosis despite having relatively low model-based risk, others who had not yet converted despite having relatively high risk, and the majority falling between the two extremes. CONCLUSIONS:Joint modeling is an improvement over traditional survival modeling because it considers all the longitudinal observations of covariates that are predictive of an event. Predictions from joint models can have greater accuracy because they are tailored to account for individual variability. These predictions can provide relatively accurate characterizations of individual disease progression, which might be important in the timing of interventions, determining the qualification for appropriate clinical trials, and general genotypic analysis.

Dataset Information

Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification.

Publications

Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification.

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