Selecting the smoothing parameter and knots for an extension of penalized splines to censored data

Abstract

The combination of P-splines and Kaplan–Meier weights provide a flexible approach to nonparametric modelling in the context of censored data. To apply this methodology, it is necessary to choose the smoothing parameter and the number and location of the knots. In this paper, we propose a new criterion for choosing the smoothing parameter adapted to the case of uncensored data. In addition, alternatives to the methods used in the literature on uncensored data are proposed for choosing the location and number of knots. Using a simulation study we analyse the effectiveness of the various alternatives proposed in situations with differences in the information available and show that their performance is quite satisfactory. A real dataset from Mayo Clinic Primary Biliary Cirrhosis data is also used to illustrate the methodology proposed. Finally, we offer some guidelines to help the user choose the parameters in the practical application of the methodology.