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, usually including biomarker repeated measurements. Several competing estimators have been proposed, 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. This paper aims to review the two approaches, precisely define the derived estimators of dynamic predictions and compare their performances notably in case of misspecification. The ultimate goal is to provide key elements for the use of individual dynamic predictions in clinical practice. Prediction of two competing causes of prostate cancer progression from the history of prostate-specific antigen is used as a motivated example. We formally define the quantity to estimate and its estimators, propose techniques to assess the uncertainty around predictions and validate them. We then conduct an in-depth simulation study compare the estimators in terms of prediction error, discriminatory power, efficiency and robustness to model assumptions. We show that prediction tools should be handled with care, in particular by properly specifying models and estimators.
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
and
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.
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