Posterior After Two Positive Tests

Problem

Posterior probability of disease after two conditionally independent positive tests, given prevalence, sensitivities and specificities:

posterior odds = prior odds * LR1 * LR2 with LR = sensitivity / (1 - specificity).

Return 1.0 when a specificity equals 1, and handle prevalences of 0 and 1 gracefully.

Hint

Multiplying likelihood ratios is the same as applying Bayes' rule twice.

case 1

in: [0.01,0.9,0.9,0.9,0.9]

expected: 0.4500000000000001

case 2

in: [0.001,0.99,0.95,0.99,0.95]

expected: 0.28183229813664556

case 3

in: [0.5,0.9,0.9,0.9,0.9]

expected: 0.9878048780487805

case 4

in: [0.01,0.9,1,0.9,0.9]

expected: 1

Starter codePython

def two_test_posterior(prevalence, sens1, spec1, sens2, spec2):
    # Your code here
    pass

4 test cases · run your code against them in the editor