A class of transformation models that generalizes both the proportional hazards model and the proportional odds model was studied. The transformation model has the property that an increasing transformation of the survival time is linearly related to the covariate with a specified error distribution. Estimation of the unknown regression parameter, and the increasing transformation function in the transformation model was of interest when failure times are subject to double censoring.
A modified likelihood with the property of log-concavity was adapted. An algorithm for computing maximum likelihood estimators of the regression parameter and the increasing transformation function was proposed. Computation of the semi-parametric information of the regression parameter was described. Asymptotic consistency of the estimators of the regression parameter and the increasing transformation function was established. Large-sample behavior of the estimator of the regression parameter was also studied using numerical simulation. The approximate variance of the estimator and confidence intervals of the regression parameter were constructed using information estimation and bootstrap methods.
|