pooled_testing.py

"""
Evaluation of Group Testing for SARS-Cov-2 RNA.pdf
"""

from __future__ import division
import itertools, random

def runs(n, R, C, npositive):
    return [run(R, C, npositive) for _ in range(n)]

# R, C: Dimensions (rows/columns) of the well plate.
# prevalence: Rate of positive samples.
def run(R, C, prevalence):
    all_rows = set(range(R))
    all_cols = set(range(C))

    # All of the well coordinates, and a set of positive ones
    # sprinkled at random.
    wells = list(itertools.product(all_rows, all_cols))
    positive_wells = [coords for coords in wells
                      if random.random() < prevalence]

    # Test pooled samples for rows and columns;
    # exclude the negative rows and columns.
    pos_rows = {r for (r,c) in positive_wells}
    pos_cols = {c for (r,c) in positive_wells}
    remaining_samples = [(r,c) for (r,c) in wells
                         if r in pos_rows
                         and c in pos_cols]

    def show_well_plate():
        for r in range(R):
            for c in range(C):
                if (r,c) in positive_wells: print '*',
                elif (r,c) in remaining_samples: print '.',
                else: print ' ',
            print

    total_test_count = R + C + len(remaining_samples)
    return total_test_count

def average(xs): return sum(xs) / len(xs)

trials = 10000
prevalence = 0.01

def experiment(R, C):
    better_by = R*C / average(runs(trials, R, C, prevalence))
    return better_by

## experiment(8, 12)
#. 4.448171847705716
## experiment(10, 10)
#. 4.5975954575756885

## experiment(16, 24)
#. 6.991300928168024
## experiment(20, 20)
#. 7.145434603196153