For the purpose of generalizing or extending an existing probability distribution, incorporation of additional parameter to it is very common in the statistical distribution theory and practice. In fact, in most of the times, such extensions provide better fit to the real life situations compared to the existing ones. In this article, we propose and study a two-parameter probability distribution, called quasi xgamma distribution, as an extension or generalization of xgamma distribution (Sen et al. 2016) for modeling lifetime data. Important distributional properties along with survival characteristics and distributions of order statistics are studied in detail. Method of maximum likelihood and method of moments are proposed and described for parameter estimation. A data generation algorithm is proposed supported by a Monte-Carlo simulation study to describe the mean square errors of estimates for different sample sizes. A bladder cancer survival data is used to illustrate the application and suitability of the proposed distribution as a potential survival model.
Abstract:In clinical studies, subjects or patients might be exposed to a succession of diagnostic tests or medication over time and interest is on determining whether there is progressive remission of conditions, disease or symptoms that have measured collectively as quality of life or outcome scores. In addition, subjects or study participants may be required, perhaps early in an experiment, to improve significantly in their performance rates at the current trial relative to an immediately preceding trial, otherwise the decision of withdrawal or dropping out is ineviTable. The common research interest would then be to determine some critical minimum marginal success rate to guide the management in decision making for implementing certain policies. Success rates lower than the minimum expected value would indicate a need for some remedial actions. In this article, a method of estimating these rates is proposed assuming the requirement is at the second trial of any particular study. Pairwise comparisons of proportions of success or failure by subjects is considered in repeated outcome measure situation to determine which subject or combinations is responsible for the rejection of the null hypothesis. The proposed method is illustrated with the help of a dataset on palliative care outcome scores (POS) of cancer patients.