Inferences about a linear combination of proportions

Area of Science:

• Biostatistics
• Statistical Inference
• Applied Mathematics

Background:

• Asymptotic inferences for one or two binomial proportions are common.
• Inferences for linear combinations of K independent proportions (L = Σβ(i)p(i)) are less explored, primarily using the Wald method.

Purpose of the Study:

• To present the score method as a superior approach for asymptotic inferences on linear combinations of independent binomial proportions.
• To provide practical tools and theoretical justification for the score method.

Main Methods:

• Utilizing the score method for statistical inferences.
• Developing approximate, easily calculable formulas.
• Providing a general proof for Agresti's heuristic method.

Main Results:

• The score method offers a more efficient and robust approach compared to the Wald method.
• The study provides a free program for implementing the score method.
• Agresti's heuristic method is generally proven.

Conclusions:

• The score method is the recommended approach for asymptotic inferences on linear combinations of independent binomial proportions due to its desirable spatial and parametric convexity properties.
• The findings offer practical solutions and theoretical validation for improved statistical analysis.