Hypertabastic survival model

Time to event models, commonly known as survival or reliability models, have been studied and applied in a variety of scientific disciplines such as medicine, engineering and business. The Hosmer and Lemeshow [1], Lee and Wang [2], Kleinbaum and Klein [3], and Collet [4] books give a detailed overview of survival data modeling techniques. Non-parametric and semi-parametric survival models such as the Cox regression analysis have been the most widely used models in the analysis of time to event survival data [5]. On the other hand, if the assumption for parametric probability distribution is met for the data set under consideration, it will result in more efficient and easier to interpret estimates than non-parametric or semi parametric models. A comprehensive review was given by Efron [6] and Lee and Go [7].Parametric hazard functions can enable clinicians and researchers to model various disease scenarios, assess disease prognosis and progression, give valuable insights on the pattern of failure, and understand the pathogenesis of a chronic disease and how they are affected by different treatment effects [8-10]. Estimation of hazard function is also useful in the analysis of change-point hazard rate models. It helps policy makers with cost effective health care policy decisions [11]. Lundin et al. [12] estimated the survival probabilities in breast cancer patients and concluded that parametric survival estimates may be more precise than Kaplan-Meier estimates when there are few patients in a particular stratum. Royston and Parmar [13] modeled the baseline distribution function by restricted cubic regression spline. Kay et al. [14] discussed the use of hazard functions in breast cancer studies. They believe that the hazard function is an important tool in investigating disease curability and can help the clinician to express his ideas regarding disease progression and the biology of treatment effect. Foulkes et al. [15] used parametric modeling to assess the prognos