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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.
Reviewer: R. E. Maiboroda (Kyïv)

62N03Testing (survival analysis)
62G10Nonparametric hypothesis testing
62G20Nonparametric asymptotic efficiency
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