cellink.at.compute_acat

cellink.at.compute_acat(pvs, tolerance=1e-16, weights=None)

Aggregate p-values using the Cauchy combination method (ACAT).

This function performs p-value aggregation using the ACAT (Aggregated Cauchy Association Test) method, which is particularly powerful and robust for combining dependent and sparse p-values. It supports missing values (NaNs) and optional weighting.

Parameters:

• pvs (np.ndarray) – A 2D array of shape (n_different_tests, n_tests_to_integrate), where each row contains the p-values to be aggregated into a single meta p-value. Values must be in the range [0, 1]. NaNs are allowed and will be ignored during aggregation.

• tolerance (float, optional) – A small threshold to avoid issues with extremely small p-values. Values below tolerance are capped at tolerance to maintain numerical stability. Default is 1e-16.

• weights (np.ndarray, optional) – A 1D array of non-negative weights with shape (n_tests_to_integrate,). If provided, it should sum to 1 or will be internally normalized. If None, equal weights are used.

Return type:

ndarray

Returns:

np.ndarray A 1D array of aggregated p-values, one for each row of the input pvs.

Notes

The ACAT method transforms each p-value p using the tangent function:

T = sum_i w_i * tan[(0.5 - p_i) * pi]

Then the aggregated p-value is computed using the Cauchy distribution:

p_combined = 0.5 - arctan(T) / pi

References

Liu, et al (2019). ACAT: A Fast and Powerful p Value Combination Method for Rare-Variant Analysis in Sequencing Studies The American Journal of Human Genetics, 104(3), 410–421. https://doi.org/10.1016/j.ajhg.2019.01.002