Proportional odds regression and sieve maximum likelihood estimation

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This paper introduces, under a censoring mechanism, an estimation procedure for the baseline function and the regression parameters in the proportional odds model based on the sieve maximum likelihood method. The procedure uses monotone splines of variable orders and knots as approximations for the baseline function and an approximately unbiased estimator of the comparative Kullback-Leibler risk to select the best approximation. The procedure adapts to various unknown structures of the baseline function such as spatial structures and smoothness of an unknown degree. The proposed procedure is implemented for right-censored and so-called Case 2 interval-censored data. The estimated regression parameters are shown to be asymptotically normal and efficient. The small sample operating characteristics of the proposed procedure are examined via simulations and are illustrated on a dataset from a study of breast cancer patients.