OASIS: An interpretable, finite-sample valid alternative to Pearson’sX²for scientific discovery

Abstract

Contingency tables, data represented as counts matrices, are ubiquitous across quantitative research and data-science applications. Existing statistical tests are insufficient however, as none are simultaneously computationally efficient and statistically valid for a finite number of observations. In this work, motivated by a recent application in reference-genome-free inference (Chaung et al., 2022), we develop OASIS (Optimized Adaptive Statistic for Inferring Structure), a family of statistical tests for contingency tables. OASIS constructs a test-statistic which is linear in the normalized data matrix, providing closed form p-value bounds through classical concentration inequalities. In the process, OASIS provides a decomposition of the table, lending interpretability to its rejection of the null. We derive the asymptotic distribution of the OASIS test statistic, showing that these finite-sample bounds correctly characterize the p-value bound derived up to a variance term. Experiments on genomic sequencing data highlight the power and interpretability of OASIS. The same method based on OASIS significance calls detects SARS-CoV-2 and Mycobacterium Tuberculosis strains de novo, which cannot be achieved with current approaches. We demonstrate in simulations that OASIS is robust to overdispersion, a common feature in genomic data like single cell RNA-sequencing, where under accepted noise models OASIS still provides good control of the false discovery rate, while Pearson's X2 test consistently rejects the null. Additionally, we show on synthetic data that OASIS is more powerful than Pearson's X2 test in certain regimes, including for some important two group alternatives, which we corroborate with approximate power calculations.

Unsupervised reference-free inference reveals unrecognized regulated transcriptomic complexity in human single cells

“…Classical and parametric tests struggle to prioritize biologically important variation because they are overpowered in the context of noise generated from biochemical sampling, and may report inaccurate p-values. SPLASH’s test provides finite-sample valid p-value bounds, unlike Pearson’s chi-squared test, better controls false positive calls under commonly used models such as negative binomial for scRNA-seq (Buen Abad Najar, Yosef, and Lareau 2020; Baharav, Tse, and Salzman 2023), and performs inference independent of any cell metadata such as cell type.…”

SPLASH2 provides ultra-efficient, scalable, and unsupervised discovery on raw sequencing reads

“…Additional outputs such as an asymptotically-valid p-value are also available. Additional statistical details regarding SPLASH are available in (Baharav, Tse, and Salzman 2024). For each anchor, SPLASH computes an "effect size", which falls within the range of 0 to 1.…”

“…Step 2 involves merging the target sequences and their counts found for each anchor across all samples to build a contingency table of target counts for each unique anchor. The contingency table is then used to compute a statistically valid p-value through an unsupervised optimization (Baharav, Tse, and Salzman 2024;Chaung et al 2023) (Methods). This step is memory-frugal as the contingency table is represented by a sparse matrix and each contingency table is loaded into memory individually.…”