Semiparametric Efficient Estimation for a Class of Generalized Proportional Odds Cure Models

We present a mixture cure model with the survival time of the "uncured" group coming from a class of linear transformation models, which is an extension of the proportional odds model. This class of model, first proposed by Dabrowska and Doksum (1988), which we term "generalized proportional odds model," is well suited for the mixture cure model setting due to a clear separation between long-term and short-term effects. A standard expectation-maximization algorithm can be employed to locate the nonparametric maximum likelihood estimators, which are shown to be consistent and semiparametric efficient. However, there are difficulties in the M-step due to the nonparametric component. We overcome these difficulties by proposing two different algorithms. The first is to employ an majorize-minimize (MM) algorithm in the M-step instead of the usual Newton-Raphson method, and the other is based on an alternative form to express the model as a proportional hazards frailty model. The two new algorithms are compared in a simulation study with an existing estimating equation approach by Lu and Ying (2004). The MM algorithm provides both computational stability and efficiency. A case study of leukemia data is conducted to illustrate the proposed procedures.