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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.03198 |
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| _version_ | 1866909013465104384 |
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| author | Bi, Yu Ghosh, Durbadal Selukar, Subodh |
| author_facet | Bi, Yu Ghosh, Durbadal Selukar, Subodh |
| contents | Time-to-event data with long-term survivors (L-TS), subjects who never experience the event, have been reported in multiple areas of oncology as therapies have improved. Conventional two-sample tests ignore L-TS, but alternatives have been developed in the cure models literature. Because L-TS can induce non-proportional hazards (non-PH), non-PH candidates also exist. However, there has not been a comprehensive comparison of these candidates. Additionally, follow-up is an important consideration for data with L-TS, but there has been limited study of the impact of follow-up time on performance of two-sample tests with L-TS. We conducted a neutral simulation study of the impact of sample size and follow-up time on type I error and power across varying effect sizes for conventional methods, methods adapted for non-PH, and a correctly-specified parametric model. When one or both groups lack L-TS, log-rank tests and one non-PH method typically have the highest power, but order varies. Surprisingly, when both groups have L-TS, these tests have non-monotonic power as a function of follow-up time, while parametric models have monotonic increasing power and the highest power at the longest follow-up time. While absolute power differs, patterns over follow-up are consistent across sample sizes. To address this for practitioners, we devise a numerical approach to predict the potential for non-monotonicity during study planning. We conclude that naïve use of conventional methods can have counterintuitive properties in settings with L-TS, and this work provides knowledge and a tool to anticipate and address these issues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03198 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A comparative study of two-sample hypothesis tests in the presence of long-term survivors Bi, Yu Ghosh, Durbadal Selukar, Subodh Methodology Time-to-event data with long-term survivors (L-TS), subjects who never experience the event, have been reported in multiple areas of oncology as therapies have improved. Conventional two-sample tests ignore L-TS, but alternatives have been developed in the cure models literature. Because L-TS can induce non-proportional hazards (non-PH), non-PH candidates also exist. However, there has not been a comprehensive comparison of these candidates. Additionally, follow-up is an important consideration for data with L-TS, but there has been limited study of the impact of follow-up time on performance of two-sample tests with L-TS. We conducted a neutral simulation study of the impact of sample size and follow-up time on type I error and power across varying effect sizes for conventional methods, methods adapted for non-PH, and a correctly-specified parametric model. When one or both groups lack L-TS, log-rank tests and one non-PH method typically have the highest power, but order varies. Surprisingly, when both groups have L-TS, these tests have non-monotonic power as a function of follow-up time, while parametric models have monotonic increasing power and the highest power at the longest follow-up time. While absolute power differs, patterns over follow-up are consistent across sample sizes. To address this for practitioners, we devise a numerical approach to predict the potential for non-monotonicity during study planning. We conclude that naïve use of conventional methods can have counterintuitive properties in settings with L-TS, and this work provides knowledge and a tool to anticipate and address these issues. |
| title | A comparative study of two-sample hypothesis tests in the presence of long-term survivors |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.03198 |