HAZARD REGRESSION WITH INTERVAL-CENSORED DATA

In a recent paper, Kooperberg, Stone, and Truong (1995a) introduced ha zard regression (HARE), in which linear splines and their tensor produ cts 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 li kelihood estimation of the unknown coefficients, Rao and Wald statisti cs to carry out stepwise addition and deletion of basis functions, and the Bayesian Information Criterion (BIG) to select the final model. I n the present paper, the HARE methodology is extended to accommodate i nterval-censored data, time-dependent covariates, and cubic splines. T he presence of interval-censored data means that the log-likelihood fu nction may no longer be concave, presenting additional numerical chall enges. The extended methodology is applied to a data set containing bo th interval-censoring and time-dependent covariates. The new software will be available in a future release of S-Plus.