Long term survival analysis: the curability of breast cancer.
ABSTRACT Methods of survival analysis for long-term follow-up studies are illustrated by a study of mortality in 3878 breast cancer patients in Edinburgh followed for up to 20 years. The problems of life tables, advantages of hazard plots and difficulties in statistical modelling are demonstrated by studying the relationship between survival and both clinical stage and initial menopausal status at diagnosis. To assess the 'curability' of breast cancer, mortality by year of follow-up is compared with expected mortality using Scottish age-specific death rates. Techniques for analysing such relative survival data include age-corrected life tables, ratio of observed to expected deaths and excess death rates. Finally, an additive hazard model is developed to incorporate covariates in the analysis of relative survival and curability.
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ABSTRACT: Several omnibus tests of the proportional hazards assumption have been proposed in the literature. In the two-sample case, tests have also been developed against ordered alternatives like monotone hazard ratio and monotone ratio of cumulative hazards. Here we propose a natural extension of these partial orders to the case of continuous and potentially time varying covariates, and develop tests for the proportional hazards assumption against such ordered alternatives. The work is motivated by applications in biomedicine and economics where covariate effects often decay over lifetime. The proposed tests do not make restrictive assumptions on the underlying regression model, and are applicable in the presence of time varying covariates, multiple covariates and frailty. Small sample performance and an application to real data highlight the use of the framework and methodology to identify and model the nature of departures from proportionality.Journal of Statistical Planning and Inference 01/2011; 141(1-141):243-261. DOI:10.1016/j.jspi.2010.06.012 · 0.60 Impact Factor
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ABSTRACT: A two-component parametric mixture is proposed to model survival after an invasive treatment, when patients may experience different hazards regimes: a risk of early mortality directly related to the treatment and/or the treated condition, and a risk of late death influenced by several exogenous factors. The parametric mixture is based on Weibull distributions for both components. Different sets of covariates can affect the Weibull scale parameters and the probability of belonging to one of the two latent classes. A logarithmic function is used to link explanatory variables to scale parameters while a logistic link is assumed for the probability of the latent classes. Inference about unknown parameters is developed in a Bayesian framework: point and interval estimates are based on posterior distributions, whereas the Schwarz criterion is used for testing hypotheses. The advantages of the approach are illustrated by analyzing data from an aorta aneurysm study.Computational Statistics & Data Analysis 02/2010; 54(2):416-428. DOI:10.1016/j.csda.2009.09.007 · 1.15 Impact Factor
- Social History of Medicine 04/2011; 25(2):500-519. DOI:10.1093/shm/hkr151 · 0.40 Impact Factor