Youden's J statistic

Calculate the optimal probability classification threshold using Youden's J statistic.

Usage

calc_youden(estimates, truth)

Arguments

estimates

A vector of classification probabilities. Values should represent the probability of 1 in the truth argument.

truth

An integer vector of 0 and 1 representing the true classifications.

Value

A numeric scalar representing the optimal probability threshold.

Details

Youden's J statistic (Youden, 1950) is defined as sensitivty + specificity - 1. As such, the value of the J-index ranges from [0, 1], and is 1 when there are no false positive and no false negatives (i.e., sensitivity and specificity). The J-index is calculated for each possible threshold defined by the ROC curve (e.g., create_roc()). The optimality criterion is then defined as:

$$\text{max}(sensitivity + specificity - 1)$$

References

Youden, W. J. (1950). Index for rating diagnostic tests. Cancer, 3(1), 32-35. doi:10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3

See also

Other optimal threshold methods: calc_cz(), calc_gmean(), calc_topleft()

Examples

calc_youden(estimates = dcm_probs$att1$estimate,
            truth = dcm_probs$att1$truth)
#> [1] 0.3170266

calc_youden(estimates = dcm_probs$att2$estimate,
            truth = dcm_probs$att2$truth)
#> [1] 0.6789389

calc_youden(estimates = dcm_probs$att3$estimate,
            truth = dcm_probs$att3$truth)
#> [1] 0.3722605