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Likelihood contour method for the calculation of asymptotic upper confidence limits on the risk function for
Summary
This study introduces the likelihood contour method (LCM) for calculating one-sided confidence limits in statistical models. The method simplifies calculations by using asymptotic expansions, improving the efficiency of statistical inference.
Area of Science:
- Statistical modeling
- Computational statistics
Background:
- Profile likelihood is a standard method for confidence limits.
- Existing methods can be computationally intensive and require good initial values.
Purpose of the Study:
- To develop a computationally and analytically convenient profile likelihood method.
- To introduce the likelihood contour method (LCM) for one-sided confidence limits.
- To address confidence limits for risk functions in dose-response models.
Main Methods:
- Developed the likelihood contour method (LCM) as a convenient form of profile likelihood.
- Replaced complex LCM equations with asymptotic expansions for explicit solutions.
- Applied the method to dose-response models with normally distributed responses.
Main Results:
- The simplified LCM equations provide explicit starting values for iterative solutions.
- Analytic simplification is possible for normally distributed responses, reducing to a one-dimensional root-finding problem.
- Simulation studies assess the small-sample coverage of the confidence limits.
Conclusions:
- The likelihood contour method offers a more accessible approach to calculating confidence limits.
- The method is particularly efficient for specific models like dose-response with normal data.
- Further simulation is needed to validate coverage properties across various scenarios.
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