Estimation in a semiparametric modulated renewal process

We consider parameter estimation in a regression model corresponding to an i.i.d. sequence of censored observations of a finite state modulated renewal process. The model assumes a similar form as in Cox regression except that the baseline intensities are functions of the backwards recurrence time of the process and a time dependent covariate. As a result of this it falls outside the class of multiplicative intensity counting process models. We use kernel estimation to construct estimates of the regression coefficients and baseline cumulative hazards. We give conditions for consistency and asymptotic normality of estimates. Data from a bone marrow transplant study are used to illustrate the results.