Confidence Intervals Estimation for Survival Function in Log-Logistic Distribution and Proportional Odds Regression Based on Censored Survival Time Data

Abstract

Log-logistic and Weibull distributions have both accelerated survival time property. The log-logistic distribution has also proportional odds property. Log-logistic distribution has unimodal hazard curve which changes direction. Link [6,7] presented a confidence interval estimate of survival function using Cox\'s proportional hazard model with covariates. Her idea more recently extended by [1] to the exponential distribution and [2] to exponential proportional hazard model, respectively. The same idea has been extended to the Weibull proportional hazard regression model by [3]. In this study, it is formed on confidence interval for log-logistic distribution survival function for any values of the time provided that the survival times have a log-logistic distributed random variable. It is also extended the same results to the proportional odds regression. A Real time data and a simulation data examples are also considered in the study for illustration the discussed confidence interval.