BIAS IN LINEAR MODEL POWER AND SAMPLE SIZE CALCULATION DUE TO ESTIMATING NONCENTRALITY

Area of Science:

• Statistics
• Biostatistics
• Quantitative Research Methods

Background:

• Power and sample size calculations are crucial for study design, often relying on estimates from initial trials.
• These calculations can be highly inaccurate within the General Linear Univariate Model (GLUM) due to biased estimators and data censoring.
• Censoring, where calculations are conditional on specific initial trial outcomes (e.g., significance), introduces significant bias.

Purpose of the Study:

• To identify and address inaccuracies in power and sample size calculations within the GLUM framework.
• To develop methods for accurate estimation of noncentrality, power, and sample size, particularly when censoring is present.
• To demonstrate the impact of these inaccuracies using a real-world example.

Main Methods:

• Investigated biased noncentrality estimators and censored power calculations in GLUM.
• Utilized truncated noncentral F distributions for accurate estimation in censored scenarios.
• Applied power analysis to human carbon monoxide exposure data.

Main Results:

• Found that power and sample size calculations in GLUM can be substantially inaccurate.
• Demonstrated that censoring significantly impacts sample size requirements.
• Highlighted potential biases in standard power calculation methods.

Conclusions:

• Accurate power and sample size calculations are essential for robust study planning and interpretation.
• Confidence bounds are recommended for estimating GLUM noncentrality, power, and sample size, regardless of censoring.
• The findings underscore the need for careful consideration of estimation methods in study design, particularly in biostatistical applications.