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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.15599 |
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| _version_ | 1866912438488662016 |
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| author | Tsiatis, Anastasios A. Davidian, Marie |
| author_facet | Tsiatis, Anastasios A. Davidian, Marie |
| contents | Widely used methods and software for group
sequential tests of a null hypothesis of no treatment difference
that allow for early stopping of a clinical trial depend primarily
on the fact that sequentially-computed test statistics have the
independent increments property. However, there are many practical
situations where the sequentially-computed test statistics do not
possess this property. Key examples are in trials where the primary
outcome is a time to an event but where the assumption of
proportional hazards is likely violated, motivating consideration of
treatment effects such as the difference in restricted mean survival
time or the use of approaches that are alternatives to the familiar
logrank test, in which case the associated test statistics may not
possess independent increments. We show that, regardless of the
covariance structure of sequentially-computed test statistics, one
can always derive linear combinations of these test statistics
sequentially that do have the independent increments property. We
also describe how to best choose these linear combinations to target
specific alternative hypotheses, such as proportional or
non-proportional hazards or log odds alternatives. We thus derive
new, sequentially-computed test statistics that not only have the
independent increments property, supporting straightforward use of
existing methods and software, but that also have greater power
against target alternative hypotheses than do procedures based on
the original test statistics, regardless of whether or not the original
statistics have the independent increments property. We illustrate
with two examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Independent increments and group sequential tests Tsiatis, Anastasios A. Davidian, Marie Methodology Widely used methods and software for group sequential tests of a null hypothesis of no treatment difference that allow for early stopping of a clinical trial depend primarily on the fact that sequentially-computed test statistics have the independent increments property. However, there are many practical situations where the sequentially-computed test statistics do not possess this property. Key examples are in trials where the primary outcome is a time to an event but where the assumption of proportional hazards is likely violated, motivating consideration of treatment effects such as the difference in restricted mean survival time or the use of approaches that are alternatives to the familiar logrank test, in which case the associated test statistics may not possess independent increments. We show that, regardless of the covariance structure of sequentially-computed test statistics, one can always derive linear combinations of these test statistics sequentially that do have the independent increments property. We also describe how to best choose these linear combinations to target specific alternative hypotheses, such as proportional or non-proportional hazards or log odds alternatives. We thus derive new, sequentially-computed test statistics that not only have the independent increments property, supporting straightforward use of existing methods and software, but that also have greater power against target alternative hypotheses than do procedures based on the original test statistics, regardless of whether or not the original statistics have the independent increments property. We illustrate with two examples. |
| title | Independent increments and group sequential tests |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.15599 |