Inference on the Loglogistic Model with Right Censored Data

Survival Analysis Methods are commonly used to analyze clinical trial data. In most clinical studies, the time until the occurrence of an event is the main outcome of significance. Clinical trials are conducted to assess the worth of new treatment regimens. The major events that the trial subjects seek to determine are either death, development of an undesirable reaction, relapse from remission, or the progress of a new disease entity. In order to model timeto- event data or clinical trials data, a parametric distribution can be assumed. We have in this study assumed that the data follow a log-logistic distribution. To estimate the parameters of this lifetime distribution, the Bayesian estimation approach is considered under the assumption of informative (gamma) priors as well as the frequentist estimation method. The Bayes estimators cannot be obtained in close forms; therefore, approximate Bayesian estimates are computed using the idea of Lindley. The clinical trial data considered in this study is either randomly or non-informatively censored. These types of data occur when each subject has a censoring time that is statistically independent of their failure times. A simulation study is carried out and also three different sets of real data have been analyzed in order to examine our methods. The Bayesian methods are considered under squared error and linear exponential loss functions.