Comparing two treatments by decision theory

Area of Science:

• Biostatistics
• Experimental Design
• Decision Theory

Background:

• Comparing treatments in randomized experiments is crucial for evidence-based medicine.
• Existing methods may not adequately account for the magnitude of treatment effects or the consequences of incorrect conclusions.

Purpose of the Study:

• To apply decision theory to the comparison of two treatments in randomized experiments.
• To provide a framework for assessing treatment superiority, non-inferiority, and average bioequivalence.
• To highlight the necessity of defining treatment effect magnitudes and loss functions.

Main Methods:

• Utilized decision theory principles for experimental analysis.
• Incorporated definitions for 'small' and 'large' treatment effects.
• Specified loss functions to quantify consequences of erroneous conclusions.

Main Results:

• Demonstrated a decision-theoretic approach for treatment comparison.
• Argued that analyses omitting effect magnitude and loss functions are deficient.
• Discussed sample size calculations pertinent to this decision-theoretic framework.

Conclusions:

• A robust experimental analysis necessitates defining the magnitude of treatment effects and associated losses.
• The proposed decision-theoretic framework offers a more comprehensive approach to treatment comparison.
• This methodology supports informed decision-making in clinical trials and experimental studies.