Compute sucess probabilities (tau_j's)

Compute joint probabilities of P(W = j, Y = k) for j, k = 0, 1.

Usage

get_prob(theta, pi0, alpha, beta, alpha0)

Arguments

theta

A numeric that provides the true prevalence of a given disease.

pi0

A numeric that provides the prevalence or proportion of people (in the whole population) who are positive, as measured through a non-random, but systematic sampling (e.g. based on medical selection).

alpha

A numeric that provides the False Negative (FN) rate for the sample R.

beta

A numeric that provides the False Positive (FP) rate for the sample R.

alpha0

A numeric that corresponds to the probability that a random participant has been incorrectly declared positive through the nontransparent procedure. In most applications, this probability is likely very close to zero.

Value

A vector containing tau1, tau2, tau3 and tau4.

Author

Stephane Guerrier

Examples

prob1 = get_prob(theta = 0.02, pi0 = 0.01, alpha = 0, beta = 0, alpha0 = 0)
prob1
#> [1] 0.01 0.00 0.01 0.98
sum(prob1)
#> [1] 1

prob2 = get_prob(theta = 0.02, pi0 = 0.01, alpha = 0.001, beta = 0, alpha0 = 0.001)
prob2
#> [1] 0.00902098 0.00097902 0.01195902 0.97804098
sum(prob2)
#> [1] 1