A study of a survival data using kernel estimates of hazard rate and aging intensity functions

Abstract

Analyzing survival (life-testing) data and drawing inferences about them is a part of engineering and health sciences. So far, various statistical tools, e.g., survival (reliability) function (s f ), probability density function (pd f ), and hazard rate function (HR) were available among decision-making scientists to handle time-to-event data (complete or censored). But because functions (pd f ) estimators were interval (window) based, they mostly gave qualitative ideas having pictorial representation resembling step functions, ordinate remain constant when abscissa vary over an interval, thereby giving incomplete information. However, it can be sorted out with the use of kernel estimates of the above mentioned functions, resulting into smooth estimators. Moreover, the metric based on aging intensity function (AI) gives an alternative way of studying lifetime or clinical datasets as it is a quantitative measure (not interval-based), thereby depicting a broader view of a given data. In our study, we primarily focus on AI and HR functions estimated using four different kernels. We apply them to a case study of patients with primary malignant tumors of sternum (cf. Daniel and Cross, 2014) with the right-censored data. Our result shows that kernel estimates of HR and AI functions for patients with high grade tumor (HGT) are higher than for patients with low grade tumor (LGT), as expected. Thus, the study opens up a new direction for applying AI and HR functions in health sciences and engineering studies.