Statistical Tests for Proportion Difference in One-to-Two Matched Binary Diagnostic Data: Application to Environmental Testing of Salmonella in the United States
Abstract
1. Introduction
2. Basic Concepts, Terminologies, and Notations
2.1. Joint Counting Table for Two Diagnostic Testing Strategies
2.2. Miettinen’s Exact Test
- The n vectors are independently and identically distributed;
- are mutually independent conditionally on . Miettinen [9] proposed an exact test based on the multinomial formulation. Conditioning on and , and have independent binomial distributions. Under ,The computation of the p-value for hypothesis testing is , i.e.,
3. Randomized Exact Test
3.1. Test Statistic
- Randomly sample .
- Calculate , , and .
- Calculate the p-value as or with .
3.2. Power of Randomized Exact Test
4. Asymptotic Test
5. Simulation
5.1. The Simulation Setting
5.2. Simulation Results
6. Application Examples
6.1. Dual Sample Pooling Test
6.2. Pen-Based Oral Fluid Specimens for Influenza a Virus Detection
7. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Diagnostic Testing Strategy 2 | |||||
---|---|---|---|---|---|
2 | 1 | 0 | Total | ||
Strategy 1 | 1 | ||||
0 | |||||
Total | n |
Test 2 | |||||
---|---|---|---|---|---|
2 | 1 | 0 | Total | ||
Test 1 | 1 | 0 | 7 | 0 | 7 |
0 | 0 | 0 | 97 | 97 | |
Total | 0 | 7 | 97 | 104 |
NS | |||||
---|---|---|---|---|---|
2 | 1 | 0 | Total | ||
OF | 1 | 114 | 28 | 29 | 171 |
0 | 2 | 7 | 42 | 51 | |
Total | 116 | 35 | 81 | 222 |
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Lin, H.; Zhu, A.; Wang, C. Statistical Tests for Proportion Difference in One-to-Two Matched Binary Diagnostic Data: Application to Environmental Testing of Salmonella in the United States. Mathematics 2024, 12, 741. https://doi.org/10.3390/math12050741
Lin H, Zhu A, Wang C. Statistical Tests for Proportion Difference in One-to-Two Matched Binary Diagnostic Data: Application to Environmental Testing of Salmonella in the United States. Mathematics. 2024; 12(5):741. https://doi.org/10.3390/math12050741
Chicago/Turabian StyleLin, Hui, Adam Zhu, and Chong Wang. 2024. "Statistical Tests for Proportion Difference in One-to-Two Matched Binary Diagnostic Data: Application to Environmental Testing of Salmonella in the United States" Mathematics 12, no. 5: 741. https://doi.org/10.3390/math12050741
APA StyleLin, H., Zhu, A., & Wang, C. (2024). Statistical Tests for Proportion Difference in One-to-Two Matched Binary Diagnostic Data: Application to Environmental Testing of Salmonella in the United States. Mathematics, 12(5), 741. https://doi.org/10.3390/math12050741