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Updated: Jun 18, 2026
05:37
An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
Bootstrap and second-order tests of risk difference.
1University of Melbourne, Carlton, Australia. c.lloyd@mbs.edu
Biometrics
|November 17, 2009
Summary
Bootstrap P-values are recommended for small sample clinical trial data. This method offers superior accuracy, power, and stability compared to standard approximate tests and higher-order asymptotics for noninferiority margin testing.
Area of Science:
- Biostatistics
- Clinical Trial Design
- Statistical Inference
Background:
- Standard approximate statistical tests (score, likelihood ratio) exhibit limitations in clinical trials with small count data.
- These limitations include discrepancies in results, inaccurate type-1 error rates, and non-monotonic inferences, even with large sample sizes.
- Existing exact inference methods can produce unstable confidence sets and are sensitive to null parameter values.
Purpose of the Study:
- To evaluate two modern approaches for small sample inference in clinical trials: higher-order asymptotics and parametric bootstrap.
- To compare these methods against standard tests for assessing if a difference in probabilities exceeds a noninferiority margin.
- To provide recommendations for the most reliable statistical inference method in challenging small sample scenarios.
Main Methods:
- Evaluation of higher-order asymptotics (Reid, 2003) involving adjustments to likelihood ratio statistics.
- Assessment of parametric bootstrap (Lee and Young, 2005) through exact significance calculations.
- Extensive numerical studies comparing the performance of these methods under various conditions.
Main Results:
- Bootstrap P-values demonstrated practical consistency across different test statistics.
- The bootstrap method exhibited excellent type-1 error accuracy and enhanced statistical power.
- Bootstrap P-values showed significantly less erratic variation concerning the null parameter (noninferiority margin).
Conclusions:
- Parametric bootstrap P-values are recommended as the superior method for small sample inference in clinical trials.
- This approach addresses the key limitations of standard approximate tests and higher-order asymptotics.
- The bootstrap method offers reliable and robust statistical inference for noninferiority testing with small count data.
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