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.


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