Perspectives on Hazard Rate Functions: Concepts; Properties; Theories; Methods; Computations; and Application to Real-Life Data

A critical look at living organisms, devices, socio-economic units, and social units reveals that at any point in time of their survival, there will be a well-defined continuum of states: good ⇔ bad; healthy ⇔ unhealthy; and functional ⇔ dysfunctional. Recent studies have shown that, the hazard function plays a crucial role in depicting the aging process. It is in trying to investigate the underlying processes of the probability distributions of survival functions, and an attempt to understand intuitively the concept of hazard rate functions that informed the conduct of this study. Simulation design and real-life tertiary data were employed in this study. The plot for the cumulative hazard function for the Weibull model gave us an intercept on the Y-axis as -3.314 and the intercept on the time-axis as 1.397. The curve was approximately linear, this meant that the data used for the study fitted the model. The plot of the cumulative hazard function against time for the exponential model passed through the origin, implicitly, the data fitted the model. Further results revealed that as the hazard rates decreased from 0.061 ⇒ 0.051, survival probabilities increased from 0.941 ⇒ 0.950 respectively; and as the hazard rates increased from 1.098 ⇒ 1.609, survival probabilities decreased from 0.333 ⇒ 0.200 respectively. We noted again that, the risk of death was distributed among all four BMI groupings, the effect of the BMI was not readily seen. Gender and age appeared not to contribute significantly towards death due to heart attack. We also saw that the hazard rate for the first few days for all the four categories of BMIs was about constant, on the 3rd and 4th days there was a significant increase in the hazard rates especially for the female obese category. For the male category, we noted that there were stepwise increases in the hazards of three of the BMI categories; underweight, obese and healthy weights. This study has intuitively demonstrated, theorized, modelled, discussed and explored the relevance of the hazard model in assessing risk.