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 m ean function of the point process while leaving the stochastic structure co mpletely unspecified. We develop a class of estimating equations for the ba seline mean function and the vector-valued regression parameter based on ce nsored point processes and covariate data. These equations can be solved ea sily by the standard Newton-Raphson algorithm. The resultant estimator of t he regression parameter is consistent and asymptotically normal with a cova riance matrix that can be estimated consistently Furthermore, the estimator of the baseline mean function is uniformly consistent and, upon proper nor malization, 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 practic al use. The data on recurrent pulmonary exacerbations from a cystic fibrosi s clinical trial are provided for illustration.