Power properties of classical test statistics in Weibull regression models with censoring and their applications to sample size calculation

Tiago M. Magalhães; Yolanda M. Gómez; Márcio A. Diniz; Osvaldo Venegas; Diego I. Gallardo; Tiago M. Magalhães; Yolanda M. Gómez; Márcio A. Diniz; Osvaldo Venegas; Diego I. Gallardo

doi:10.3934/math.2026528

AIMS Mathematics

2026, Volume 11, Issue 5: 12825-12865. doi: 10.3934/math.2026528

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Power properties of classical test statistics in Weibull regression models with censoring and their applications to sample size calculation

1.
Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora, 36036-900, Brazil
2.
Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
3.
Department of Population Health Science and Policy, Icahn School of Medicine at Mount Sinai, New York City, New York, USA
4.
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco, 4780000, Chile

Received: 09 February 2026 Revised: 03 April 2026 Accepted: 17 April 2026 Published: 08 May 2026
MSC : 62F03, 62F12

Regression models for time-to-event data are widely used in clinical and reliability studies, particularly in the presence of censoring. In this context, the Weibull regression model provides a flexible alternative to the proportional hazards model, allowing for a fully specified survival function and interpretable measures of treatment effects. However, inference based on classical test statistics may be unreliable in small or moderate samples. In this paper, we derive closed-form approximations for the non-null asymptotic distributions of the likelihood ratio, Wald, score, and gradient tests under Pitman alternatives in Weibull regression models for censored data. These results facilitate analytical evaluation of local power and provide a basis for comparing the performance of the four tests. The proposed approximations are assessed through simulation studies, which highlight their accuracy in moderate-to-large samples and illustrate the impact of censoring and model complexity. An application is presented to the design of Phase Ⅱ clinical trials to demonstrate how derived power functions can be used to estimate sample sizes. The results provide a computationally efficient tool for power analysis in censored Weibull regression models, although their use in practice should be complemented with simulation-based validation in small-sample or high-censoring scenarios.
- survival data,
- power function,
- sample size,
- gradient test,
- likelihood ratio test,
- score test,
- Wald test,
- Weibull model
Citation: Tiago M. Magalhães, Yolanda M. Gómez, Márcio A. Diniz, Osvaldo Venegas, Diego I. Gallardo. Power properties of classical test statistics in Weibull regression models with censoring and their applications to sample size calculation[J]. AIMS Mathematics, 2026, 11(5): 12825-12865. doi: 10.3934/math.2026528

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Abstract

Regression models for time-to-event data are widely used in clinical and reliability studies, particularly in the presence of censoring. In this context, the Weibull regression model provides a flexible alternative to the proportional hazards model, allowing for a fully specified survival function and interpretable measures of treatment effects. However, inference based on classical test statistics may be unreliable in small or moderate samples. In this paper, we derive closed-form approximations for the non-null asymptotic distributions of the likelihood ratio, Wald, score, and gradient tests under Pitman alternatives in Weibull regression models for censored data. These results facilitate analytical evaluation of local power and provide a basis for comparing the performance of the four tests. The proposed approximations are assessed through simulation studies, which highlight their accuracy in moderate-to-large samples and illustrate the impact of censoring and model complexity. An application is presented to the design of Phase Ⅱ clinical trials to demonstrate how derived power functions can be used to estimate sample sizes. The results provide a computationally efficient tool for power analysis in censored Weibull regression models, although their use in practice should be complemented with simulation-based validation in small-sample or high-censoring scenarios.

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