DBMS: dynamic borrowing method for frequentist hybrid control designs based on historical-current data similarity
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Masahiro Kojima
Abstract
Information borrowing from historical data is gaining increasing attention in clinical trials for rare and pediatric diseases, where small sample sizes may lead to insufficient statistical power for confirming efficacy. While Bayesian information borrowing methods are well established, recent frequentist approaches, such as the test-then-pool and equivalence-based test-then-pool methods, have been proposed to determine whether historical data should be incorporated into statistical hypothesis testing. Depending on the outcome of these hypothesis tests, historical data may or may not be utilized. This paper introduces a dynamic borrowing method for leveraging historical information based on the similarity between current and historical data. Similar to Bayesian dynamic borrowing, our proposed method adjusts the degree of information borrowing dynamically, ranging from 0 to 100 %. We present two approaches to measure similarity: one using the density function of the t-distribution and the other employing a logistic function. The performance of the proposed methods is evaluated through Monte Carlo simulations. Additionally, we demonstrate the utility of dynamic information borrowing by reanalyzing data from an actual clinical trial.
Acknowledgements
We are grateful to the editor, associate editor, and reviewers for their valuable comments and helpful suggestions.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: The authors have accepted responsibility for the entire content of thismanuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: Nothing to declare.
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Data availability: Not applicable.
A Appendix
A.1 Sensitivity analysis simulations
We performed the supplemental simulations according to Table 3. The number of simulations in each scenario was 10,000. The number of bootstrap sets was 5,000 due to the computing cost (Figures 5–9).
Parameter setting for supplemental simulation.
| Scenario | n t | n c | n h | μ t | μ c | μ h | σ t = σ c = σ h |
|---|---|---|---|---|---|---|---|
| S1 | 50 | 25 | 25 | 0 | 0 | −1 | 5 |
| S2 | 50 | 50 | 50 | 0 | 0 | −1 | 5 |
| S3 | 100 | 50 | 50 | 0 | 0 | −1 | 5 |
| S4 | 100 | 100 | 100 | 0 | 0 | −1 | 5 |
| S5 | 50 | 25 | 25 | 2 | 0 | 0 | 8 |
| S6 | 50 | 50 | 50 | 2 | 0 | 0 | 8 |
| S7 | 100 | 50 | 50 | 2 | 0 | 0 | 8 |
| S8 | 100 | 100 | 100 | 2 | 0 | 0 | 8 |
| S9 | 50 | 25 | 25 | 2 | 0 | 1 | 8 |
| S10 | 50 | 50 | 50 | 2 | 0 | 1 | 8 |
| S11 | 100 | 50 | 50 | 2 | 0 | 1 | 8 |
| S12 | 100 | 100 | 100 | 2 | 0 | 1 | 8 |
| S13 | 50 | 25 | 25 | 2 | 0 | −1 | 8 |
| S14 | 50 | 50 | 50 | 2 | 0 | −1 | 8 |
| S15 | 100 | 50 | 50 | 2 | 0 | −1 | 8 |
| S16 | 100 | 100 | 100 | 2 | 0 | −1 | 8 |
| S17 | 50 | 25 | 25 | 2 | −1 | 0 | 8 |
| S18 | 50 | 50 | 50 | 2 | −1 | 0 | 8 |
| S19 | 100 | 50 | 50 | 2 | −1 | 0 | 8 |
| S20 | 100 | 100 | 100 | 2 | −1 | 0 | 8 |
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The type-1 error rates and powers are shown below.
Type-1 error rates in supplemental simulation. DB-T is the dynamic borrowing method based on the density function of the t-distribution, DB-L1 is the dynamic borrowing based on the logistic function with β0 = −7.379 and β1 = 4.472, DB-L2 is the dynamic borrowing based on the logistic function with β0 = −7.374 and β1 = 3.747, TTP1 is the original TTP (test-then-pool) method under αh1 = 0.05, TTP2 is the original TTP (test-then-pool) method under αh1 = 0.10, EQ1 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.05, and EQ2 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.10, Gray line is 2.5 %.
Powers of scenarios 5–8 in supplemental simulation. DB-T is the dynamic borrowing method based on the density function of the t-distribution, DB-L1 is the dynamic borrowing based on the logistic function with β0 = −7.379 and β1 = 4.472, DB-L2 is the dynamic borrowing based on the logistic function with β0 = −7.374 and β1 = 3.747, TTP1 is the original TTP (test-then-pool) method under αh1 = 0.05, TTP2 is the original TTP (test-then-pool) method under αh1 = 0.10, EQ1 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.05, and EQ2 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.10, Gray line is 2.5 %.
Powers of scenarios 9–12 in supplemental simulation. DB-T is the dynamic borrowing method based on the density function of the t-distribution, DB-L1 is the dynamic borrowing based on the logistic function with β0 = −7.379 and β1 = 4.472, DB-L2 is the dynamic borrowing based on the logistic function with β0 = −7.374 and β1 = 3.747, TTP1 is the original TTP (test-then-pool) method under αh1 = 0.05, TTP2 is the original TTP (test-then-pool) method under αh1 = 0.10, EQ1 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.05, and EQ2 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.10, Gray line is 2.5 %.
Powers of scenarios 13–16 in supplemental simulation. DB-T is the dynamic borrowing method based on the density function of the t-distribution, DB-L1 is the dynamic borrowing based on the logistic function with β0 = −7.379 and β1 = 4.472, DB-L2 is the dynamic borrowing based on the logistic function with β0 = −7.374 and β1 = 3.747, TTP1 is the original TTP (test-then-pool) method under αh1 = 0.05, TTP2 is the original TTP (test-then-pool) method under αh1 = 0.10, EQ1 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.05, and EQ2 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.10, Gray line is 2.5 %.
Powers of scenarios 17–20 in supplemental simulation. DB-T is the dynamic borrowing method based on the density function of the t-distribution, DB-L1 is the dynamic borrowing based on the logistic function with β0 = −7.379 and β1 = 4.472, DB-L2 is the dynamic borrowing based on the logistic function with β0 = −7.374 and β1 = 3.747, TTP1 is the original TTP (test-then-pool) method under αh1 = 0.05, TTP2 is the original TTP (test-then-pool) method under αh1 = 0.10, EQ1 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.05, and EQ2 is the equivalence-based TTP (test-then-pool) method under αh2 = 0.10, Gray line is 2.5 %.
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Supplementary Material
This article contains supplementary material (https://doi.org/10.1515/ijb-2024-0051).
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