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Confidence intervals after multiple imputation: combining profile likelihood information from logistic regressions
Georg Heinze1, Meinhard Ploner, Jan Beyea
1Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria.
Statistics in Medicine
|July 23, 2013
Summary
This study introduces a new method, Combination of Likelihood Profiles (CLIP), for analyzing Alzheimer's disease data with missing values. CLIP offers more reliable confidence intervals than traditional methods, especially for small datasets.
Area of Science:
- Statistics
- Biostatistics
- Computational Biology
Background:
- Missing data in logistic regression for Alzheimer's disease studies necessitates multiple imputation.
- Traditional methods like Rubin's Rules (RR) for combining imputed data may yield unreliable confidence intervals due to unmet normality assumptions, especially in small or sparse datasets.
- Existing alternatives like Bayesian methods do not leverage penalized profile likelihoods.
Purpose of the Study:
- To introduce and evaluate the Combination of Likelihood Profiles (CLIP) method for analyzing multiply imputed data in logistic regression.
- To address the limitations of Rubin's Rules in small, sparse, or nearly separated datasets.
- To provide a reliable alternative that utilizes penalized profile likelihoods for bias reduction and guaranteed convergence.
Main Methods:
- Developed CLIP by expressing penalized likelihood profiles as posterior cumulative distribution functions (CDFs) using a chi-squared approximation.
- Averaged CDFs from multiple imputations to create a combined CDF for determining confidence limits.
- Compared CLIP's performance against Rubin's Rules and Bayesian sampling methods (Markov Chain Monte Carlo) using simulated and real-world Alzheimer's disease data.
Main Results:
- CLIP demonstrated superior performance compared to Rubin's Rules in analyzing both simulated and real Alzheimer's disease data.
- CLIP provides a reliable method for calculating confidence intervals when traditional assumptions are violated.
- The study confirmed CLIP's utility as a confirmatory tool for validating simpler methods like RR.
Conclusions:
- The Combination of Likelihood Profiles (CLIP) method is a robust and reliable approach for handling missing data in logistic regression analyses, particularly for small or challenging datasets.
- CLIP offers an effective alternative to existing methods, providing more accurate confidence intervals.
- The CLIP method is accessible through the R package logistf, facilitating its use in research.
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