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Summary Consideration is given to the piecewise smooth estimation of hazard functions given by Cox's (1972) proportional hazards model. The smoothest estimate available hitherto is a step-function which is not continuous. The method used is penalized maximum likelihood estimation introduced by Good and Gaskins (1971) and developed by Silverman (1978). This gives a quadratic spline with discontinuities in the slope at the times of death. The knot points are at times of death and censoring. The hazard function and corresponding survival curves are estimated for a group of 51 women with carcinoma of the vulva. The estimated survival curve is compared with those given by Breslow's (1972) and Kalbfleisch and Prentice's (1973) methods.
Anderson et al. (Tue,) studied this question.