Confidence Intervals for Parallel Systems with Covariates

Abstract

Exact confidence intervals for regression models with censored data are often not tractable, and hence approximate intervals are derived. The most common method of obtaining these approximate intervals is based on the asymptotic normal distribution of the maximum likelihood estimator. These intervals are easy to compute and they are used in most computer statistical packages. However, these intervals have some limitations. When the sample size is small or even moderate they tend to be anticonservative and have asymmetric upper and lower tail probabilities. An alternative method based on the asymptotics of the maximum likelihood estimator is to construct intervals from the inverted likelihood ratio tests. The performance of these intervals is investigated for the regression models based on parallel systems with covariates, and with randomly right censored data for finite samples. The simulation results show that the intervals based on the inverted likelihood ratio test have better performance. They have coverage probability that is close to the nominal one, and have nearly symmetric upper and lowel tail probabilities.