The harmonic mean p-value for combining dependent tests
A python implementation of harmonicmeanp
The harmonic mean p-value (hmp) is a useful test for combining the p-values from multiple dependent tests, however, I could not find any python implementations so I wrote my own.
Included is
- Basic hmp test (hmp.stat(..))
- Worst-case upper bound (hmp.upper_bound(..))
- Asymptotically exact hmp test (hmp.hmp(..))
hmp.hmp should be preferred wherever possible
Example usage
import hmp
L = 50 # Number of tests
# Something that should definetly be accepted, if all tests < alpha
p_values = [0.049] * L
print(hmp.stat(p_values)) # Basic (0.049)
print(hmp.upper_bound(p_values)) # Overly conservative worst-case (0.521)
print(hmp.hmp(p_values)) # Exact (0.0468)
# Now lets try something that should definetly be rejected, all tests >> alpha
p_values = [0.5] * L
print(hmp.stat(p_values)) # Basic (0.5)
print(hmp.upper_bound(p_values)) # Over Conservative (>1)
print(hmp.hmp(p_values)) # Exact (0.654)If you want to pass weights in, they can be passed to any of the methods. Weights must be non-negative and sum to 1.
hmp.hmp(p_values, weights=[1/L] * L) # Uniform weightsThe original reference can be viewed here and the r-implementation is here
Any citations should go to the original author, but feel free to use and reference this implementation as you see fit.
@article{wilson2019harmonic,
title={The harmonic mean p-value for combining dependent tests},
author={Wilson, Daniel J},
journal={Proceedings of the National Academy of Sciences},
volume={116},
number={4},
pages={1195--1200},
year={2019},
publisher={National Acad Sciences}
}