Journal
STATISTICS IN MEDICINE
Volume 33, Issue 30, Pages 5280-5297Publisher
WILEY
DOI: 10.1002/sim.6300
Keywords
survival analysis; parametric modelling; Gaussian quadrature; maximum likelihood; splines; time-dependent effects; relative survival
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Funding
- National Institute for Health Research [DRF-2012-05-409]
- National Institute for Health Research [DRF-2012-05-409] Funding Source: researchfish
- National Institutes of Health Research (NIHR) [DRF-2012-05-409] Funding Source: National Institutes of Health Research (NIHR)
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Parametric survival models are being increasingly used as an alternative to the Cox model in biomedical research. Through direct modelling of the baseline hazard function, we can gain greater understanding of the risk profile of patients over time, obtaining absolute measures of risk. Commonly used parametric survival models, such as the Weibull, make restrictive assumptions of the baseline hazard function, such as monotonicity, which is often violated in clinical datasets. In this article, we extend the general framework of parametric survival models proposed by Crowther and Lambert (Journal of Statistical Software 53:12, 2013), to incorporate relative survival, and robust and cluster robust standard errors. We describe the general framework through three applications to clinical datasets, in particular, illustrating the use of restricted cubic splines, modelled on the log hazard scale, to provide a highly flexible survival modelling framework. Through the use of restricted cubic splines, we can derive the cumulative hazard function analytically beyond the boundary knots, resulting in a combined analytic/numerical approach, which substantially improves the estimation process compared with only using numerical integration. User-friendly Stata software is provided, which significantly extends parametric survival models available in standard software. Copyright (c) 2014 John Wiley & Sons, Ltd.
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