Empirical Likelihood Based Test for Equality of Cumulative Incidence Functions
- PDF / 339,354 Bytes
- 10 Pages / 439.37 x 666.142 pts Page_size
- 26 Downloads / 213 Views
RESEARCH ARTICLE
Empirical Likelihood Based Test for Equality of Cumulative Incidence Functions Asokan Mulayath Variyath1 • P. G. Sankaran2 Accepted: 18 September 2020 Ó The Indian Society for Probability and Statistics (ISPS) 2020
Abstract An empirical likelihood based test for comparing the incidence functions for multiple competing risks is proposed, without making any assumptions on the distribution of the failure times. The performance of the proposed method is assessed based on large number of simulations and compared with existing method. Simulation studies shows that the proposed method has comparable performance when there is no censoring and has better performance where there is heavy censoring. We applied our proposed method in a well known data set. Keywords Cumulative incidence functions Competing risks data Empirical likelihood Cause-specific hazard rates
1 Introduction In survival studies, the term competing risks refers to the situations in which a subject is exposed to two or more risks of failure, but its eventual failure can be attributed to exactly one of these risks of failure. Examples of competing risks data in different scenarios are available in Hoel (1972) and Hinds (1996), among many others. Competing risks data consists of failures time and the associated causes of failure. Assume that the failure time T has an absolutely continuous distribution function F(t) and survival function SðtÞ ¼ 1 FðtÞ. The failure of the subject may be due to any one of k causes. The analysis of competing risks data is carried out using one the following two formulations; & P. G. Sankaran [email protected] Asokan Mulayath Variyath [email protected] 1
Department of Mathematics and Statistics, Memorial University, St. John’s, NL A1C 5S7, USA
2
Department of Statistics, Cochin University of Science and Technology, Cochin, India
123
Journal of the Indian Society for Probability and Statistics
(1)
Cause-specific hazard rate function ðkðtÞÞ formulation, where Pðt T\t þ Dt; c ¼ jjT tÞ ; Dt!0 Dt
kj ðtÞ ¼ lim (2)
j ¼ 1; 2; . . .; k
Cumulative incidence function ðFj ðtÞÞ formulations where Fj ðtÞ ¼ PðT t; C ¼ jÞ;
j ¼ 1; 2; . . .; k
Crowder (2001), Kalbfleisch and Prentice (2002) and Lawless (2003) provide review of literature on competing risks analysis using (1) and (2). In many applications, it is often great interest to compare various risks of failure. The comparison of the risks can be done either by kj ðtÞ or by Fj ðtÞ. This problem had earlier been studied by several researchers in literature. Aly et al. (1998) and El Barmi (2004) have employed Kolmogrove–Smirnov type tests to compare two risks problem without censoring while El Barmi and Kochar (2002) developed a likelihood ratio test for the same problem in the discrete or groups lifetime data set up. Sun (2001) developed generalized nonparametric test procedures using cause specific hazard rates. The comparison of k-risks were discussed in El Barmi and Mukerjee (2006) and El Barmi et al. (2006). Sankaran et al. (2010) developed
Data Loading...
