Averaged non-parametric regression in analysis of transformation models

One-sided semiparametric transformation models provide a common tool for analysis of failure time data. These models assume that conditionally on a vector of covariates Z, the failure time T has distribution function of the form F(Gamma(t),theta \ Z), where F(.,theta \ z) is a parametric family of distribution functions supported on the positive half-line and Gamma is an a.e. increasing transformation mapping the support of a continuous failure time T onto R+. Special cases include the proportional hazard, proportional odds and frailty models. The function Gamma can be in general interpreted in terms of conditional Q - Q plots. In this paper we discuss construction and properties of ad hoc estimates of the pair (theta,Gamma) based on a pseudo-profile likelihood obtained by averaging a nonparametric regression estimate of the conditional cumulative hazard function.