gaste-test 0.1.0

Gamma approximation of stratified truncated exact test

Gaste Package

Welcome to the Gaste package! This package provides a set of tools and utilities for analyzing stratified 2x2 contingency table. Gives the exact or approximate p-value of the overall association between features and outcomes under 2x2 stratified contingency table.

Installation

To install the Gaste package, simply run the following command:

pip install gaste-test

Basic import

Once installed, you can import the Gaste package or the main function in your Python code using the following line:

import gaste-test
from gaste-test import get_pval_comb, StratifiedTable2x2

Features

The Gaste package offers the following features:

• Exact calcul of p-value combination of one tail Fisher's exact test
• Approximation of the law of combination by Gamma approximation distribution
• Incorporating truncation into the p-value combination enhances statistical power in scenarios featuring few effects or contradictory effects between strata
• Visualization: Forest plot for data analysis.

Example of use

Example of Berkeley's admission in 1973 by departement and gender :

>>> admission = pd.read_csv("admission.csv")

Department	Male-Admitted	Female-Admitted	Male-Rejected	Female-Rejected
A	512	89	313	19
B	353	17	207	8
C	120	202	205	391
D	138	131	279	244
E	53	94	138	299
F	22	24	351	317

    # Data preparation
>>> nb_strata = admission.shape[0]
>>> rows = ("Admitted", "Rejected")
>>> columns = ("Men", "Women")
>>> contingency_table = np.array(
        admission.loc[:, admission.columns != "Department"]
    ).reshape((nb_strata, 2, 2))
>>> strat_label = ["Department " + dep for dep in admission["Department"]]
    # Create object
>>> stratified_table = StratifiedTable2x2(
        contingency_table, labels=strat_label, name_rows=rows, name_columns=columns
    )
>>> stratified_table.resume()

Studies	Men Admitted	Women Admitted	Men Rejected	Women Rejected	$p_s^-$	$p_s^+$	OR	log(OR)	CI	log(CI)	%W(fixed)
Department A	512	89	313	19	1.15063e-05	0.999996	0.349	-1.052	[0.209, 0.584]	[-1.567, -0.537]	18.5
Department B	353	17	207	8	0.391761	0.759839	0.803	-0.22	[0.340, 1.892]	[-1.078, 0.638]	3.7
Department C	120	202	205	391	0.826548	0.212876	1.133	0.125	[0.855, 1.502]	[-0.157, 0.407]	28
Department D	138	131	279	244	0.318816	0.73277	0.921	-0.082	[0.686, 1.237]	[-0.376, 0.212]	28.6
Department E	53	94	138	299	0.864569	0.184058	1.222	0.2	[0.825, 1.809]	[-0.192, 0.593]	13.8
Department F	22	24	351	317	0.319845	0.780128	0.828	-0.189	[0.455, 1.506]	[-0.787, 0.409]	7.3

Pooled odd ratio with MH method : 0.9047
Confident interval at 95.0% of pooled odd ratio : (0.7719, 1.0603)

>>> stratified_table.nb_combination
1719197241840
>>> stratified_table.gaste(alternative='less')
The support of the combined p-value is 1.72e+12, over the compute explicite threshold of 1.00e+07 , the moment matching estimator is used.
statistic: 29.8576, p-value: 0.0012
>>> stratified_table.gaste(alternative='greater')
The support of the combined p-value is 1.72e+12, over the compute explicite threshold of 1.00e+07 , the moment matching estimator is used.
statistic: 8.1468, p-value: 0.6862
>>> stratified_table.plot(thresh_adjust=0.03, save="analysis_admission.png")

Example: Razzack AA, Hassan SA, Pasya SKR, et al. A Meta-Analysis of Association between Remdesivir and Mortality among Critically-Ill COVID-19 Patients. Infect Chemother. 2021;53(3):512-518. doi:10.3947/ic.2021.0060

>>> contingency_table = [
        [[59, 77], [482, 444]],
        [[301, 303], [2442, 2405]],
        [[3, 4], [190, 196]],
        [[22, 10], [128, 67]],
    ]
>>> strat_label = ["ACTT-1 2020", "SOLIDARITY 2020", "Spinner 2020", "Wang 2020"]
>>> rows = ("Remdesivir", "Placebo")
>>> columns = ("Event", "No event")
>>> stratified_table = StratifiedTable2x2(
        contingency_table, labels=strat_label, name_rows=rows, name_columns=columns
    )
>>> stratified_table.nb_combination
21881640
>>> stratified_table.gaste(alternative='less')
The support of the combined p-value is 2.19e+07, over the compute explicite threshold of 1.00e+07 , the moment matching estimator is used.
statistic: 29.8576, p-value: 0.1527
>>> stratified_table.gaste(alternative='greater')
The support of the combined p-value is 2.19e+07, over the compute explicite threshold of 1.00e+07 , the moment matching estimator is used.
statistic: 8.1468, p-value: 0.8658
    # Force exact calculation by increasing the limit threshold of exact computation
>>> stratified_table.gaste(alternative='less', limit_computation_exact=3*10**7)
The support of the combined p-value is 2.19e+07, under the compute explicite threshold of 3.00e+07 , the explicite calculation is used.
[137, 605, 8, 33] size 21881640
100%|██████████████████████████████████████████████████████| 21881640/21881640 [00:41<00:00, 524130.92it/s]
statistic: 29.8576, p-value: 0.1529
>>> stratified_table.plot(thresh_adjust=0.03, save="analysis_admission.png")

Example without object StratifiedTable2x2, only get_pval_comb function

    # Data from Rothman, K.J. (1982). "Spermicide use and Down's syndrome," American Journal of Public Health, 72(4), pp. 399-401. doi 10.2105/AJPH.72.4.399.
>>> contingency_table = [[[3, 9], [104, 1059]], [[1, 3], [5, 89]]]
    # Format data to get (sample size, marginal A, marginal B)
>>> params = np.vstack((np.sum(contingency_table, axis=(1,2)), np.sum(contingency_table, axis=2).T[0], np.sum(contingency_table, axis=1).T[0])).T
>>> params
array([[1175,   12,  107],
       [  98,    4,    6]])
>>> # Same as : params = [[3+9+104+1059, 3+9, 3+104], [1+3+5+89, 1+3, 1+5]]
    # computation of p-value
>>> from scipy.stats import hypergeom
>>> pval_under = [hypergeom(*param).cdf(k) for param, k in zip(params, np.array(contingency_table)[:,0,0])]
>>> pval_under
[0.9818678457734665, 0.9821041004573289]
>>> pval_over = [hypergeom(*param).sf(k-1) for param, k in zip(params, np.array(contingency_table)[:,0,0])]
>>> pval_over
[0.08808167695347509, 0.2264843810557321]
>>> from gaste_test import get_pval_comb
>>> get_pval_comb(params, pval_under, "under")
0.9946415406410173
>>> get_pval_comb(params, pval_over, "over")
0.05029422728685044

Example of R wrapper with reticulate

As input to the StratifiedTable2x2 object, we have presented a contingency table in the form of an array of shape (nb_strat, 2,2) as. But we can also give as input a list of tuples 4 integers representing ($N_s$, $n_s$, $K_s$, $a_s$) where $N_s$ is the total count of events and non-events, $n_s is the count of events in both categories, $K_s$ is the total count in the first category, and $a_s$ is the count of events in the first category. This is illustrated below when using the package in R through reticulate

> library(reticulate)
> py_install("gaste-test")
> gaste <- import("gaste_test", delay_load = TRUE, convert = TRUE)
> params <- list(c(300, 80, 60, 15),
+                c(300, 70, 50, 5), 
+                c(250, 130, 40, 20), 
+                c(300, 80, 60, 18))
> params_ <- r_to_py(params)
> stb <- gaste$StratifiedTable2x2(params_)
> stb$resume()
           $k_s$  $K_s-k_s$  ...           log(CI)  %W(fixed)
Studies                      ...                             
Stratum 0     15         45  ...   [-0.758, 0.542]       26.4
Stratum 1      5         45  ...  [-2.117, -0.185]       26.4
Stratum 2     20         20  ...   [-0.772, 0.581]       23.8
Stratum 3     18         42  ...   [-0.416, 0.831]       23.5

[4 rows x 11 columns]

Pooled odd ratio with MH method :  0.8251
Confident interval at 95.0% of pooled odd ratio : (0.586, 1.1618)
> stb$gaste('less')
The support of the combined p-value is 7.78e+06, under the compute explicite threshold of 1.00e+07 , the explicite calculation is used.
[61, 51, 41, 61] size 7780611 max supp 61
100%|██████████| 7780611/7780611 [00:12<00:00, 640481.60it/s]
statistic: 13.1942, p-value: 0.0586
> stb$gaste('greater')
The support of the combined p-value is 7.78e+06, under the compute explicite threshold of 1.00e+07 , the explicite calculation is used.
[61, 51, 41, 61] size 7780611 max supp 61
100%|██████████| 7780611/7780611 [00:12<00:00, 621091.29it/s]
statistic: 3.9103, p-value: 0.7847
> stb$plot(save='test.png')

Documentation

For detailed information on how to use the Gaste package, please refer to the sphinx documentation

Contributing

We welcome contributions from the community! If you would like to contribute to the Gaste package, feel free to contact the autor by mail.

License

The Gaste package is licensed under the MIT License.