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Title: Flexible parametric joint modelling of longitudinal and survival data
Authors: Crowther, Michael J.
Abrams, Keith R.
Lambert, P. C.
First Published: 4-Oct-2012
Publisher: Wiley
Citation: Statistics in Medicine, 2012, 31 (30), pp. 4456-4471
Abstract: 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.
DOI Link: 10.1002/sim.5644
ISSN: 0277-6715
eISSN: 1097-0258
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2012 John Wiley & Sons, Ltd. This is the peer reviewed version of the following article: Crowther, M. J., Abrams, K. R. and Lambert, P. C. (2012), Flexible parametric joint modelling of longitudinal and survival data. Statist. Med., 31: 4456–4471, which has been published in final form at . This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Appears in Collections:Published Articles, Dept. of Health Sciences

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