The generalized order statistics arising from three populations with the lower truncated proportional hazard rate models and its application to the sensitivity to the early disease stage.

In this paper, we present some results to make inference about the parameters of lower truncated proportional hazard rate models with the same baseline distributions based on three independent generalized order statistics samples. Then, especially by considering the results of the diagnostic tests for the non-diseased, early-diseased stage and fully diseased populations, we make inference about sensitivity to the early disease stage parameter. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for different structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence/credible intervals and two competitors. We use two real datasets to illustrate the proposed methods.