Semiparametric transformation models for point processes

In this article we propose a family of semiparametric transformation models for point. processes with positive jumps of arbitrary sizes. These models offer great flexibilities in formulating the effects of covariates on the mean function of the point process while leaving the stochastic structure completely unspecified. We develop a class of estimating equations for the baseline mean function and the vector-valued regression parameter based on censored point processes and covariate data. These equations can be solved easily by the standard Newton-Raphson algorithm. The resultant estimator of the regression parameter is consistent and asymptotically normal with a covariance matrix that can be estimated consistently Furthermore, the estimator of the baseline mean function is uniformly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process with an easily estimated covariance function. We demonstrate through extensive simulation studies that the proposed inference procedures are appropriate for practical use. The data on recurrent pulmonary exacerbations from a cystic fibrosis clinical trial are provided for illustration.