## 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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