MKinfer (version 1.3)

md2sens: 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)

Value

Numeric vector with sensitivity and specificity.

Arguments

delta

(absolute) mean difference of the two groups.

sd1

standard deviation of first group.

sd2

standard deviation of second group.

Author

Matthias Kohl

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.

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")