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A note on confidence intervals for the restricted mean survival time based on transformations in small sample size
Hiroya Hashimoto1, Akiko Kada2
1Core Laboratory, Nagoya City University Graduate School of Medical Sciences, Nagoya, Japan.
Pharmaceutical Statistics
|September 22, 2021
Summary
For small clinical trials, restricted mean survival time (RMST) confidence intervals can be inaccurate. Logit transformation of RMST with Greenwood
Area of Science:
- Biostatistics
- Clinical Trial Methodology
- Survival Analysis
Background:
- Restricted Mean Survival Time (RMST) is a key metric for time-to-event data in clinical trials.
- The distribution of RMST differences often deviates from normal, especially in small sample sizes, impacting confidence interval accuracy.
- Existing methods for RMST confidence intervals may exhibit poor performance under specific conditions.
Purpose of the Study:
- To evaluate the performance of various confidence intervals for RMST in small sample size scenarios.
- To compare different variance estimation methods and variable transformations for improving RMST confidence intervals.
- To identify optimal methods for constructing reliable RMST confidence intervals in challenging trial settings.
Main Methods:
- Conducted numerical simulations using Weibull distribution for one-sample survival time.
- Assessed eight confidence interval variations: two variance types (Greenwood's formula, Kaplan-Meier correction) and four transformations (none, arcsine square root, logit, complementary log-log).
- Evaluated performance based on coverage probability and error probabilities (over/underestimation).
Main Results:
- Untransformed RMST confidence intervals showed low coverage and overestimation with small sample sizes and low event rates.
- Kaplan-Meier variance correction improved coverage.
- Logit and complementary log-log transformations significantly enhanced coverage and reduced overestimation, with logit transformation being particularly effective.
Conclusions:
- Logit transformation combined with Greenwood's variance formula is recommended for constructing RMST confidence intervals in small sample size trials.
- Variable transformations are crucial for improving the accuracy of RMST confidence intervals.
- The findings provide practical guidance for biostatisticians and researchers in survival data analysis.
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