OASIS: An interpretable, finite-sample valid alternative to Pearson's X² for scientific discovery

Area of Science:

• Statistics
• Genomics
• Bioinformatics

Background:

• Contingency tables are crucial in quantitative research but existing statistical tests lack computational efficiency and statistical validity for finite samples.
• Reference-free genomic inference presents challenges requiring robust statistical methods for analyzing count data.

Purpose of the Study:

• To develop a novel family of statistical tests, Optimized Adaptive Statistic for Inferring Structure (OASIS), for contingency tables.
• To provide computationally efficient and statistically valid tests suitable for finite observations, particularly in genomic applications.

Main Methods:

• OASIS constructs a test statistic linear in the normalized data matrix, utilizing concentration inequalities for closed-form P-value bounds.
• Derivation of the asymptotic distribution of the OASIS test statistic to validate finite-sample bounds.
• Application of OASIS to genomic sequencing data for strain detection and analysis of overdispersed data.

Main Results:

• OASIS provides interpretable decomposition of contingency tables, aiding in the understanding of null hypothesis rejection.
• Experiments demonstrate OASIS's power and interpretability in genomic data, enabling de novo detection of SARS-CoV-2 and Mycobacterium tuberculosis strains.
• Simulations show OASIS is robust to overdispersion, controls false discovery rate effectively, and outperforms Pearson's chi-squared test in certain scenarios.

Conclusions:

• OASIS represents a significant advancement in statistical testing for contingency tables, offering improved efficiency and validity.
• The method facilitates novel applications in genomics, such as identifying microbial strains, which were previously unachievable.
• OASIS demonstrates superior performance and robustness compared to traditional methods like Pearson's chi-squared test, especially for complex biological data.