hwetests 0.8.9

A python package containing two statistical tests for HWE testing: Gibbs Sampling tests and a modified Chi Squared tests that handles ambiguity

The Hardy-Weinberg Equilibrium (HWE) assumption is essential to many population genetics models, which assumes that allele pairs from a given population are random. An HWE test needs to test whether the pairing are random or not.

Our python package contains three statistical tests for HWE testing:

• ASTA
• UMAT
• UMAT with uncertainty

Both ASTA and UMAT with sampling assume ambiguity in the observations while UMAT does not.

Table of Contents

• Installation
• Examples
• Quick tour

Installation

Use the package manager pip to install hwetests.

pip install hwetests

Examples

Here we show how to use our package with simulated data given in our package.

ASTA test

from hwetests import asta
from hwetests.tests import dataloader

if __name__ == '__main__':
    # getting the absolute path to the 'ambiguous_data.csv' file
    ambiguous_data_path = dataloader.get_path(is_ambiguous=True)
    # Perform ASTA
    p_value, statistic, dof = asta.full_algorithm(file_path=ambiguous_data_path,
                                                  cutoff_value=4.0)
    print(f'p-value: {p_value}')
    print(f'statistic: {statistic}')
    print(f'degrees of freedom: {dof}')

UMAT test

from hwetests import umat
from hwetests.tests import dataloader
import numpy as np

if __name__ == '__main__':
    # getting the absolute path to the 'unambiguous_data.csv' file
    unambiguous_data_path = dataloader.get_path(is_ambiguous=False)
    # import data from csv file as a numpy array
    data = np.genfromtxt(unambiguous_data_path, delimiter=',')
    # Perform UMAT
    p_value = umat.full_algorithm(data)
    print(f'p-value: {p_value}')

UMAT with uncertainty test

from hwetests import umat_with_uncertainty
from hwetests.tests import dataloader

if __name__ == '__main__':
    # getting the absolute path to the 'ambiguous_data.csv' file
    ambiguous_data_path = dataloader.get_path(is_ambiguous=True)
    # Perform UMAT with sampling
    p_value = umat_with_uncertainty.full_algorithm(file_path='../data/ambiguous_data.csv')
    print(f'p-value: {p_value}')

You can find the scripts and the simulated data in:

├───src
│   ├───hwetests
    │   ├───tests
    │   │   ├───data
    │   │   │   └───unambiguous_data.csv # for ASTA and UMAT with sampling (contains 50k population, 20 alleles, 0.2 uncertainty, in HWE)
    │   │   │   └───ambiguous_data.csv # for UMAT (contains 100k population, in HWE)
    │   │   ├───scripts
    │   │   │   └───asta_test.py
    │   │   │   └───umat_test.py
    │   │   │   └───umat_with_sampling_test.py
    │   │   └───dataloader.py

Quick tour

To immediately use our package, you only need to run a single function.
First you have to prepare a csv file which have a different format for the ambiguous and the unambiguous case.

Ambiguous case

The csv should look like this:

ID,Allele1,Allele2,Probability
0,2,12,0.1
0,6,7,0.9
1,0,17,1.0

• ID: the ID of the individual
• Allele1: the first allele
• Allele2: the second allele
• Probability: the probability of the pair (Allele1, Allele2) to be the true pair for the given ID.

A few notes:

• The csv file is not required to have the column names in the first row.
• The probabilities are not required to sum to 1 for each ID (they are normalized in the code).
• A row that contains the pair (Allele1, Allele2) and another row that contains the pair (Allele2, Allele1) are treated as the same pair.

You can then run ASTA or UMAT with uncertainty using one function:

ASTA

def full_algorithm(file_path,
                   is_first_row_contains_columns_names=False,
                   cutoff_value=0.0,
                   should_save_csv=False,
                   should_save_plot=False,
                   title=''):

Where:

• file_path: A path to a csv file with columns: 1) index or id of a donor (integer or string). Assuming columns are separated with , or + and no whitespaces in the csv file. 2) first allele (integer or string). 3) second allele (integer or string). 4) probability (float).
• is_first_row_contains_columns_names: True if the first row in the csv file contains the columns names, False otherwise.
• cutoff_value: (optional, default value is 0.0) A float value that decides to not account (O-E)^2 / E in the summation of the Chi-Squared statistic if E < cutoff.
• should_save_csv: (optional, default value is False) Either boolean or string, if it's True then a csv with the columns: [first allele, second allele, observed, expected, variance] is saved (named 'alleles_data.csv') and if it's a string then a csv with the given string name is saved.
• should_save_plot: (optional, default value is False) Either boolean or string, if it's True then an image containing 2 bar plots is saved (named 'alleles_barplot.png') for each allele showing its chi squared statistic over degrees of freedom (summing over the observations only associated with this allele) and -log_10(p_value). If it's a string and ends with '.pdf' then the plot is saved in pdf format. Otherwise, it's saved in png format. If it's a string then a png with the given string name is saved.
• title: (optional, default value is '') A string that will be the title of the plot.

Returns: p-value (float), Chi-Squared statistic (float), degrees of freedom (integer)

UMAT with uncertainty

def full_algorithm(file_path,
                   start_from=30000,
                   iterations=100000,
                   is_first_row_contains_columns_names=False):

Where:

• file_path: A path to a csv file with columns: 1) index or id of a donor (integer or string). 2) first allele (integer or string). 3) second allele (integer or string). 4) probability (float). Assuming columns are separated with , or + and no whitespaces in the csv file.
• start_from: The index to start from when calculating the p-value.
• iterations: The amount of iterations to perform.
• is_first_row_contains_columns_names: If True then it is assumed that the first row contains the columns names: i.e. 'column1,column2,...'.

Returns: A p-value under the null Hypothesis that observations are distributed around HWE.

Unambiguous case

The csv should look like this:

0,2,12
3,6,7
1,0,17

Which represents a square matrix where each element a_ij is the number of times the pair (i, j) or (j, i) was observed.
You can then run UMAT with one function:

UMAT

def full_algorithm(observations,
                   start_from=30000,
                   iterations=100000,
                   should_save_plot=False):

Where:

• observations: A numpy square matrix where a_ij is the amount of donors observed alleles i,j.
• should_save_plot: Either boolean or string, if it's True then plot of the perturbations is saved (named 'umat_plot.png') and if it's a string then a plot with the given string name is saved.
• start_from: The index to start from when calculating the p-value.
• iterations: The amount of iterations to perform.

Returns: A p-value under the null Hypothesis that observations are distributed around HWE.