Type I Error Probability Spending for Post-Market Drug and Vaccine Safety Surveillance With Poisson Data.

Area of Science:

• Statistics
• Statistical Hypothesis Testing
• Sequential Analysis

Background:

• Statistical sequential hypothesis testing analyzes cumulative data over time.
• Key methods include group sequential and continuous sequential approaches.
• The comparative performance of these approaches requires further investigation.

Purpose of the Study:

• To determine if continuous sequential analysis is superior to group sequential analysis for Poisson processes.
• To identify optimal statistical hypothesis testing designs.
• To compare Type I error spending functions for expected number of events to signal.

Main Methods:

• Mathematical proofs for Poisson stochastic processes.
• Comparison of continuous and group sequential analyses across various performance measures.
• Evaluation of classical Type I error spending functions under different tuning parameter scenarios.

Main Results:

• Continuous sequential analysis is proven to be uniformly better than group sequential analysis for Poisson processes.
• Optimal statistical hypothesis testing solutions are found within continuous designs.
• A log-exp shape for the Type I error spending function is identified as the best choice in most evaluated scenarios.

Conclusions:

• Continuous sequential designs are optimal for statistical hypothesis testing with cumulative data from Poisson processes.
• The findings provide guidance on selecting effective Type I error spending functions for improved statistical performance.