Modelling of Recurrent Events in Survival Analysis

Abstract

Competing survival time was simulated as suggested by Jan Beyermann 2011 the proportion of Main event and Competing event was fixed with respect to different combinations namely 95% Main event Vs 5% Competing event; 90% Main event Vs 10% Competing event; 85% Main event Vs 15% Competing event; 80% Main event Vs 20% Competing event; 75% Main event Vs 25% Competing event; 70% Main event Vs 30% Competing event and 65% Main event Vs 35% Competing event respectively. Each proportion of competing event and main event was considered as Cause specific hazard function and survival time was simulated for sample of size 100,200 and 300. By literature 1-KM technique was always over estimating the incidence when compared with the Cumulative Incidence function, hence we assessed using various combinations of Main event and Competing Risk events and also with respect to sample size. 1-KM method was consistently over estimating the incidence with respect to each combination of main event and competing event and also with each sample size of 100, 200 and 300. However, there was a significant difference which was observed from 75% Vs 25% onwards in the two techniques namely 1-KM and CIF. The above mentioned criteria were reaffirmed based on increase in sample size which also rendered similar result. This implied that 1-KM estimate may be done without any loss of information at Competing Risk rate less than 25%. When comparing the proportion of Survival between Treatment and control group with respect to Log rank test and Gray s test which are different when the Main event rate is from 70% with a competing risk event rate at 30% and subsequently. However, this difference vanished by increasing the sample to 200 and 300 respectively. The Regression analysis gives us a comparison between the treatment and the control group with respect to sub distributional hazard model stating that there was no significant difference between the Treatment and the Control group less than 30% of competing event however it did not hold good with increased sample size.