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Though Cox’s model is the most frequently employed regression tool for survival data, fully parametric models (e.g., exponential, Weibull, log-normal, log-logistic) may lead to more efficient parameter estimates in certain circumstances (e.g., for parameter values far from zero, follow-up depending on covariates, strong time dependencies of covariate effects), and also permit extrapolation in time. However, there is the added requirement of checking the appropriateness of the chosen family of distributions. For this purpose Nardi and Schemper 2003 have suggested plots of normal-deviate residuals (already developed for Cox’s model by Nardi and Schemper, 1999). If the chosen type of parametric model fits the data well, the density of these residuals follows that of the standard normal distribution. The SAS macro COMPASS (Comparison of parametric survival models) alleviates the task of choosing the right parametric model by providing kernel-based density plots of the residuals for the common types of parametric models and Cox’s model. The plots may also indicate that none of the parametric models fits the data well or that the fit by two different types of models is equally satisfactory.


Nardi, A., Schemper, M. (2003): "Comparing Cox and Parametric Models in Clinical Studies", Statistics in Medicine 22, 3597 - 3610
Nardi, A., Schemper, M. (1999): "New Residuals for Cox Regression and Their Application to Outlier Screening", Biometrics 55, 523 - 529


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