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In this paper, we consider modifying the score statistic proposed by Prentice and Gloeckler [Prentice, R. L., & Gloeckler, L. A. (1978). Regression analysis of grouped data with applications to breast cancer data. Biometrics, 34, 5767] for the grouped data under the proportional hazards model. For this matter, we apply the likelihood method and derive the scores without re-parameterization as a discrete model. Then we illustrate the test with an example and compare the efficiency with the test of Prentice and Gloeckler's statistic by obtaining empirical powers through simulation study. Also we discuss some possible extension and estimated variances of the score statistic as concluding remarks.


In this paper, we consider modifying the score statistic proposed by Prentice and Gloeckler [Prentice, R. L., & Gloeckler, L. A. (1978). Regression analysis of grouped data with applications to breast cancer data. Biometrics, 34, 5767] for the grouped data under the proportional hazards model. For this matter, we apply the likelihood method and derive the scores without re-parameterization as a discrete model. Then we illustrate the test with an example and compare the efficiency with the test of Prentice and Gloeckler's statistic by obtaining empirical powers through simulation study. Also we discuss some possible extension and estimated variances of the score statistic as concluding remarks.