DB - Optimal Criterion Design to Estimate the Parameters of Some Proportional Hazards Model with Minimal Variance with Practical Application

Abstract

Proportional hazards models represent a set of models that have been widely used in survival data analysis through the hazards function to study the effect of a vector of specific values of explanatory variables on survival times. The main assumption of these models is that the hazards function is proportional, that is, the explanatory variables of the model have multiple effect on the hazards function. In other words, at any time of survival (t>0) the hazards function of a particular singular with a particular vector of explanatory variable values is proportional to the hazards function of another singular.The survival analysis is one of the modern methods of analysis that is based on the fact that the dependent variable represents the time until the event concerned in the study (survival times) occurs. There are many survival models that deal with the study of the effects of explanatory factors on survival time; the parametric that depends on distribution of survival time, such as Exponential Model, Weibull Model, Log-logistic Model, and the semi-parametric which does not depend on the distribution of the survival time, and given the importance of these models in the practical life, many researchers studied these models from many different perspectives including the interest of researchers' to study these models still exists. The idea of the research is to study the effect of a set of factors represented by the explanatory variables on the survival times represented by the dependent variable for patients with myocardial infarction, a condition that is common occurrence and a threat to the lives of people, and is considered as a leading cause of death in the world, where myocardial infarction happens because blood supply to the heart muscles is blocked.