The false positive rate implied by base rate, PPV and FNR

Chouldechova's identity: \(fpr = \frac{p}{1-p}\,\frac{1-ppv}{ppv}\,(1-fnr)\) (Research.P5.Table.chouldechova). Because it is an identity, two groups that share ppv and fnr but differ in base rate cannot share fpr (Research.P5.impossibility): no risk score, however built, escapes it.

Usage

morie_fairness_implied_fpr(p, ppv, fnr)

Arguments

p

Base rate in (0, 1).

ppv

Positive predictive value in (0, 1].

fnr

False negative rate in [0, 1).

Value

The false positive rate the three imply.

Examples

r <- morie_fairness_rates(120, 60, 40, 280)
morie_fairness_implied_fpr(r$p, r$ppv, r$fnr)   # equals r$fpr exactly
#> [1] 0.1764706
# same ppv and fnr, different base rates: the fpr must differ
morie_fairness_implied_fpr(0.30, 0.6, 0.25)
#> [1] 0.2142857
morie_fairness_implied_fpr(0.50, 0.6, 0.25)
#> [1] 0.5