Total screening size with probability guarantee (Zhou Eq 6.3)

Given a required number of cases n and a disease prevalence, compute the total enrollment needed so that, with probability 1-beta, at least n cases are captured: N satisfies P(Binomial(N, prev) >= n) >= 1-beta.

Usage

screen_required(n, prevalence, beta = 0.1)

Arguments

n

Required number of cases; positive integer (e.g. the target_state_cases_needed from a diagnostic accuracy calculation).

prevalence

Disease prevalence in the screening population; scalar in (0, 1) (e.g. 0.20 for a 20 percent clinic prevalence).

beta

Acceptable probability of falling short; scalar in (0, 1). Default 0.10, i.e. a 90 percent guarantee of capturing at least n cases.

Value

Integer total enrollment N (screening list size).

Examples

# A colon-cancer screening validation needs 196 confirmed cases;
# clinic prevalence is 20%. Enroll enough patients to capture
# 196 cases with 90% probability:
screen_required(n = 196, prevalence = 0.20, beta = 0.10)
#> [1] 1061

# More stringent 95% guarantee:
screen_required(n = 196, prevalence = 0.20, beta = 0.05)
#> [1] 1085