Combined P-Value Functions for Compatible Effect Estimation and Hypothesis Testing in Drug Regulation.

Area of Science:

• Biostatistics
• Pharmacometrics
• Regulatory Science

Background:

• The two-trials rule in drug efficacy requires two significant trials.
• Combining effect estimates from multiple trials is complex.
• Fixed-effect meta-analysis may produce misleading confidence intervals.

Purpose of the Study:

• To unify the two-trials rule and meta-analysis within a combined p-value framework.
• To derive compatible p-values, effect estimates, and confidence intervals.
• To evaluate different p-value combination methods for two trials.

Main Methods:

• Recasting the two-trials rule and meta-analysis using combined p-value functions.
• Deriving closed-form solutions for p-values, effect estimates, and confidence intervals.
• Analyzing Wilkinson's, Stouffer's, Edgington's, Fisher's, Pearson's, and Tippett's methods.

Main Results:

• All methods consistently estimate the true effect when trials have identical effects, though bias varies.
• Methods differ in their convergence when true effects diverge: conservative (Pearson's), anti-conservative (Fisher's, Tippett's), and balanced (Edgington's, meta-analysis).
• Edgington's confidence intervals encompass individual trial effects, unlike meta-analytic intervals.

Conclusions:

• The choice of method depends on the specific estimand of interest.
• All analyzed methods can be appropriate for combining results from two trials.
• The R package 'twotrials' facilitates compatible hypothesis testing and effect estimation.