https://github.com/limix/chiscore
Test statistics derived from linear combination of chi-squared distributions.
https://github.com/limix/chiscore
Last synced: 6 months ago
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Test statistics derived from linear combination of chi-squared distributions.
- Host: GitHub
- URL: https://github.com/limix/chiscore
- Owner: limix
- License: mit
- Created: 2018-09-20T04:39:05.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2021-03-01T16:28:18.000Z (about 4 years ago)
- Last Synced: 2024-10-12T21:45:10.423Z (7 months ago)
- Language: Python
- Homepage:
- Size: 97.7 KB
- Stars: 4
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
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README
# chiscore
Estimate the joint significance of test statistics derived from linear combination
of chi-squared distributions.
## Install
We recommend installing it via
[conda](http://conda.pydata.org/docs/index.html):
```bash
conda install -c conda-forge chiscore
```
Alternatively, chiscore can also be installed using
[pip](https://pypi.python.org/pypi/pip):
```bash
pip install chiscore
```
## Running the tests
After installation, you can test it
```bash
python -c "import chiscore; chiscore.test()"
```
as long as you have [pytest](https://docs.pytest.org/en/latest/).
## Usage
### Davies
```python
>>> from chiscore import davies_pvalue
>>> q = 1.5
>>> w = [[0.3, 5.0], [5.0, 1.5]]
>>> davies_pvalue(q, w)
{'p_value': 0.6151796819770086, 'param': {'liu_pval': 0.6151796819770086, 'Is_Converged': 1.0}, 'p_value_resampling': None, 'pval_zero_msg': None}
```
### Liu
Let us approximate
π = 0.5β
ΟΒ²(1, 1) + 0.4β
ΟΒ²(2, 0.6) + 0.1β
ΟΒ²(1, 0.8),
and evaluate Pr(π > 2).
```python
>>> from chiscore import liu_sf
>>>
>>> w = [0.5, 0.4, 0.1]
>>> dofs = [1, 2, 1]
>>> deltas = [1, 0.6, 0.8]
>>> (q, dof, delta, _) = liu_sf(2, w, dofs, deltas)
>>> q
0.4577529852208846
>>> dof
3.5556138890755395
>>> delta
0.7491921870025307
```
Therefore, we have
Pr(π > 2) β Pr(ΟΒ²(3.56, 0.75) > π‘βΊπβ + πβ) = 0.458.
### P-value
```python
>>> from chiscore import optimal_davies_pvalue
>>> q = [1.5, 3.0]
>>> mu = -0.5
>>> var = 1.0
>>> kur = 3.0
>>> w = [10.0, 0.2, 0.1, 0.3]
>>> remain_var = 0.5
>>> df = 3.4
>>> trho = [5.1, 0.2]
>>> grid = [0., 0.01]
>>> optimal_davies_pvalue(q, mu, var, kur, w, remain_var, df, trho, grid)
0.966039962464624
```
## Authors
* [Danilo Horta](https://github.com/horta)
## References
* Lee, Seunggeun, Michael C. Wu, and Xihong Lin. "Optimal tests for rare variant
effects in sequencing association studies." Biostatistics 13.4 (2012): 762-775.
* Liu, H., Tang, Y., & Zhang, H. H. (2009). A new chi-square approximation to the
distribution of non-negative definite quadratic forms in non-central normal
variables. Computational Statistics & Data Analysis, 53(4), 853-856.
## License
This project is licensed under the [MIT License](https://raw.githubusercontent.com/limix/chiscore/master/LICENSE.md).