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Generalized log-rank tests for interval-censored failure time data. (English) Zbl 1092.62107

A class of tests is considered for the \(k\)-samples homogeneity hypothesis by interval censored failure time data. I.e., for each subject a random interval \((L_i,R_i)\) is observed to which its failure time belongs. The test statistics is \[ U_\xi=\sum_{i=1}^n x_i{ \xi(\widehat G_n(L_i))-\xi(\widehat G_n(R_i)) \over \widehat G_n(L_i)-\widehat G_n(R_i)}, \] where \(n\) is the number of subjects in the union of all samples, \(x_i\) is the vector of indicators of the sample (its \(l\)-th element equals 1 iff the \(i\)-th subject belongs to the \(l\)-th sample and is 0 otherwise), \(\widehat G_n(x)\) is a nonparametric estimator of the survival function under the null hypothesis (homogeneity), \(\xi\) is a fixed function. (E.g., for \(\xi(x)=x\log(x)\) this is the score statistics). The asymptotic normality of \(U_\xi\) under \(H_0\) is demonstrated. Simulation results and real breast cancer data application are considered.

MSC:

62N03 Testing in survival analysis and censored data
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
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References:

[1] Fleming T. R., Counting process and survival analysis (1991) · Zbl 0727.62096
[2] Finkelstein D. M., Biometrics 42 pp 845– (1986)
[3] Gentleman R., Biometrika 81 pp 618– (1994)
[4] Groeneboom P., Lecture Notes in Mathematics pp 1648– (1996)
[5] Groeneboom P., Information bounds and non-parametric maximum likelihood estimation (1992) · Zbl 0757.62017
[6] Huang J., Statist. Neerlandica 49 pp 153– (1995)
[7] Kalbfleisch J. D., The statistical analysis of failure time data, 2nd edn (2002) · Zbl 1012.62104
[8] Lagakos S. W., Appl. Statist. 37 pp 169– (1988)
[9] DOI: 10.1016/S0047-259X(02)00058-1 · Zbl 1025.62020
[10] Li L., Scand. J. Statist. 24 pp 531– (1997) · Zbl 1126.62366
[11] DOI: 10.1002/(SICI)1097-0258(20000115)19:1<1::AID-SIM296>3.0.CO;2-Q
[12] Peto R., J. Roy. Statist. Soc. Ser. A 135 pp 185– (1972)
[13] Rabinowitz D., Biometrika 82 pp 501– (1995)
[14] DOI: 10.1002/(SICI)1097-0258(19960715)15:13<1387::AID-SIM268>3.0.CO;2-R
[15] Sun J., Encyclopedia of Biostatistics pp 2090– (1998)
[16] DOI: 10.1111/1467-9868.00174 · Zbl 0913.62048
[17] Turnbull B. W., J. Roy. Statist. Soc. Ser. B 38 pp 290– (1976)
[18] Vaart A. W., Weak convergence and empirical processes (1996) · Zbl 0862.60002
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