md2sens: Compute Sensitivity and Specificty based on MD.

In MKinfer: Inferential Statistics

Compute Sensitivity and Specificty based on MD.

Description

The function calculates the sensitivity and specificity for a given mean difference (MD) and specified standard deviations of the two groups. This is achieved by using the optimal cut-off poin based on Youden's J statistic.

Usage

md2sens(delta, sd1 = 1, sd2 = 1)

Arguments

delta	(absolute) mean difference of the two groups.
sd1	standard deviation of first group.
sd2	standard deviation of second group.

Details

This function can be used to demonstrate how (standardized) effect sizes translate into sensitivity and specifity, based on two normal distributions.

The two standard diviations are assumed to be equal if their difference is smaller than 1e-08.

Value

Numeric vector with sensitivity and specificity.

Author(s)

Matthias Kohl [e-mail]

References

B\"ohning D, B\"ohning W, Holling H (2008). Revisiting Youden's index as a useful measure of the misclassification error in meta-analysis of diagnostic studies. Stat Methods Med Res. 17(6), 543-54.

J.H. Zhang, T.D.Y. Chung and K.R. Oldenburg (1999). A simple statistical parameter for use in evaluation and validation of high throughput screening assays. Journal of Biomolecular Screening 4 (2): 67-73.

Examples

## (standardized) mean difference to sensitivity/specificity
## equal variances
library(ggplot2)
delta <- seq(from = 0.0, to = 6, by = 0.05)
res <- sapply(delta, md2sens)
DF <- data.frame(SMD = delta, sensitivity = res[1,], 
                 specificity = res[2,])
ggplot(DF, aes(x = SMD, y = sensitivity)) +
  geom_line() + ylim(0.5, 1.0) + xlab("(standardized) mean difference") +
  ylab("sensitivity = specificity") + ggtitle("SD1 = SD2 = 1")

## unequal variances
delta <- seq(from = 0.0, to = 6, by = 0.05)
res <- sapply(delta, md2sens, sd1 = 1, sd2 = 2)
DF <- data.frame(MD = delta, performance = c(res[1,], res[2,]),
                 measure = c(rep("sensitivity", length(delta)),
                             rep("specificity", length(delta))))
ggplot(DF, aes(x = MD, y = performance, color = measure)) +
  geom_line() + ylim(0, 1.0) + xlab("mean difference") +
  scale_color_manual(values = c("darkblue", "darkred")) +
  ggtitle("SD1 = 1, SD2 = 2")

MKinfer documentation built on Dec. 15, 2025, 9:06 a.m.