On the Estimation of Survival and Death Probabilities under Myocardial Infarctions in the Presence of Competing Risks Based on an Illness-Death Model.

ABSTRACT

This paper is concerned with the development of an illness-death model for the study of survivability of heart patients. The Myocardial Infarctions (MI) experienced in heart disease have been categorized as fatal and nonfatal. Fatal MI’s are easily recognizable and identified and are always reported in the case history of the patient suffering from heart disease whereas non-fatal MI’s are not easily identified and are rarely reported in the case history of the patient. Also, in the case of human population, all individuals are not equally healthy and the chance of dying varies from one person to another. Moreover illness and death are two different types of events. Illness may be transient, repetitive and reversible, whereas death is an irreversible or absorbing state. Further complexity is introduced by competition among various risks of death. The probability of an individual dying from one cause is influenced by the presence of competition from other causes. Here in our problem we have taken two health states viz. normal state and illness state due to non-fatal MI’s, and two death states viz. death state due to fatal MI and death state due to competing risk. The study population of n individuals is divided into two groups viz. n individuals who are in the normal state and n individuals 1 2 who are in the illness state due to non-fatal MI’s, at the time of start of the study. The expressions for survival and death probabilities have been obtained by using the concep of crude probability of death under competing risks. The likelihood estimates of the survival and death probabilities have also been obtained. Application of the model is discussed.