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A generalized Fleming and Harrington's class of tests for interval‐censored data
Author(s) -
Oller Ramon,
Gómez Guadalupe
Publication year - 2012
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11139
Subject(s) - permutation (music) , class (philosophy) , rank (graph theory) , interval (graph theory) , counting process , confidence interval , statistical hypothesis testing , analogy , log rank test , statistics , mathematics , lambda , survival analysis , econometrics , combinatorics , computer science , artificial intelligence , epistemology , philosophy , physics , acoustics , optics
The class $G^{\rho,\lambda }$ of weighted log‐rank tests proposed by Fleming & Harrington [Fleming & Harrington (1991) Counting Processes and Survival Analysis , Wiley, New York] has been widely used in survival analysis and is nowadays, unquestionably, the established method to compare, nonparametrically, k different survival functions based on right‐censored survival data. This paper extends the $G^{\rho,\lambda }$ class to interval‐censored data. First we introduce a new general class of rank based tests, then we show the analogy to the above proposal of Fleming & Harrington. The asymptotic behaviour of the proposed tests is derived using an observed Fisher information approach and a permutation approach. Aiming to make this family of tests interpretable and useful for practitioners, we explain how to interpret different choices of weights and we apply it to data from a cohort of intravenous drug users at risk for HIV infection. The Canadian Journal of Statistics 40: 501–516; 2012 © 2012 Statistical Society of Canada