Saddlepoint p-values for a class of nonparametric tests for the current status and panel count data under generalized permuted block design

Abd El-Raheem M. Abd El-Raheem; Mona Hosny; Abd El-Raheem M. Abd El-Raheem; Mona Hosny

doi:10.3934/math.2023960

AIMS Mathematics

2023, Volume 8, Issue 8: 18866-18880. doi: 10.3934/math.2023960

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Saddlepoint p-values for a class of nonparametric tests for the current status and panel count data under generalized permuted block design

Abd El-Raheem M. Abd El-Raheem ^{1
,
,},
Mona Hosny ²

1.
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt
2.
Department of Mathematics, Faculty of Science for Girls, King Khalid University, Abha 61413, Saudi Arabia

Received: 19 March 2023 Revised: 17 May 2023 Accepted: 25 May 2023 Published: 05 June 2023
MSC : 92B15, 62P10, 62E17, 62G10

Current status and panel count data appear in many applied fields, including medicine, clinical trials, epidemiology, econometrics, demography, engineering and public health. Therefore, in this article, we use the saddlepoint approximation method to approximate the exact p-value of a number of nonparametric tests for the current status and panel count data under a generalized permuted block design. The saddlepoint approximation is referred to as higher-order approximation and it is more accurate than the methods that lead to approximations that are accurate to the first order, such as the asymptotic normal approximation method. To verify the accuracy and efficiency of the saddlepoint approximation method, a simulation study is conducted. The simulation study results confirm that the saddlepoint approximation method is more powerful than the existing approximation method. Furthermore, number of real current status and panel count data sets are analyzed and displayed as illustrative examples.
- approximating exact p-value,
- saddlepoint approximation,
- current status data,
- panel count data,
- permuted block design,
- two-sample tests
Citation: Abd El-Raheem M. Abd El-Raheem, Mona Hosny. Saddlepoint p-values for a class of nonparametric tests for the current status and panel count data under generalized permuted block design[J]. AIMS Mathematics, 2023, 8(8): 18866-18880. doi: 10.3934/math.2023960

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Abstract

Current status and panel count data appear in many applied fields, including medicine, clinical trials, epidemiology, econometrics, demography, engineering and public health. Therefore, in this article, we use the saddlepoint approximation method to approximate the exact p-value of a number of nonparametric tests for the current status and panel count data under a generalized permuted block design. The saddlepoint approximation is referred to as higher-order approximation and it is more accurate than the methods that lead to approximations that are accurate to the first order, such as the asymptotic normal approximation method. To verify the accuracy and efficiency of the saddlepoint approximation method, a simulation study is conducted. The simulation study results confirm that the saddlepoint approximation method is more powerful than the existing approximation method. Furthermore, number of real current status and panel count data sets are analyzed and displayed as illustrative examples.

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