  In modeling survival data with a cure fraction, flexible modeling of
covariate effects on the probability of cure has important medical
implications, which aids investigators in identifying better treatments to
cure. This paper studies a semiparametric form of the Yakovlev promotion time
cure model that allows for nonlinear effects of a continuous covariate. We
adopt the local polynomial approach and use the local likelihood criterion to
derive nonlinear estimates of covariate effects on cure rates, assuming that
the baseline distribution function follows a parametric form. This way we adopt
a flexible method to estimate the cure rate locally, the important part in cure
models, and a convenient way to estimate the baseline function globally. An
algorithm is proposed to implement estimation at both the local and global
scales. Asymptotic properties of local polynomial estimates, the nonparametric
part, are investigated in the presence of both censored and cured data, and the
parametric part is shown to be root-n consistent. The proposed methods are
illustrated by simulated and real data.
