Survival Analysis Competing Risk using Fine-Gray Subdistribution Model with the Maximum Partial Likelihood Estimation Method

Abstract

Survival analysis is a statistical method which the variable of concern is the time until the event occurs. In survival analysis, there is a situation where an individual can experience more than one type of event and the occurrence of these events prevents the occurrence of other types of events. This situation is called competing risk. The situation causes the Kaplan Meier method, which is a method of estimating the survival function, cannot be used. The Cumulative Incidence Function method is proposed as a solution to solve competing risk events uses the probability of each type of event. The Cox regression model is also modified to allow for competing risk is called the Fine-Gray subdistribution model using the Maximum Partial Likelihood Estimation. This study examines the estimation of parameter Fine-Gray subdistribution model and applies it to melanoma case. Melanoma is a type skin cancer that can spread to other organs in the body. In the case of death, melanoma patients who experience death with other causes are called a competing risks and death with melanoma are considered as the event of interest. Study showed that factors that influence melanoma mortality are age, sex, tumor thickness, and cultured epidermal autografts. Patients death with melanoma was 1.400 times higher risk than death with other causes.