Hazard regression with interval-censored data

In a recent paper, Kooperberg, Stone, and Truong (1995a) introduced hazard regression (HARE), in which linear splines and their tensor products are used to estimate the conditional log-hazard function based on possibly censored, positive response data and one or more covariates. Model selection is carried out in an adaptive fashion using maximum likelihood estimation of the unknown coefficients, Rao and Wald statistics to carry out stepwise addition and deletion of basis functions, and the Bayesian Information Criterion (BIG) to select the final model. In the present paper, the HARE methodology is extended to accommodate interval-censored data, time-dependent covariates, and cubic splines. The presence of interval-censored data means that the log-likelihood function may no longer be concave, presenting additional numerical challenges. The extended methodology is applied to a data set containing both interval-censoring and time-dependent covariates. The new software will be available in a future release of S-Plus.