TeachingDemos (version 1.2)

fagan.plot: Create a Fagan plot to demonstrate Bayes Theorem and screening tests

Description

These functions create a plot showing the relationship between the prior probability, the LR (combination of sensitivity and specificity), and the posterior probability.

Usage

fagan.plot(probs.pre.test, LR, test.result="+")
plotFagan()
plotFagan2()

Arguments

probs.pre.test

The prior probability

LR

the likelihood ratio (sensitivity/(1-specificity))

test.result

either '+' or '-' indicating whether you want the probability of the event or of not seeing the event

Value

• These functions are run for their side effects and do not return a meaningful value

Details

When Bayes theorem is expressed in terms of log-odds it turns out that the posterior log-odds are a linear function of the prior log-odds and the log likelihood ratio. These functions plot an axis on the left with the prior log-odds, an axis in the middle representing the log likelihood ratio and an axis on the right representing the posterior log-odds. A line is then drawn from the prior probability on the left through the LR in the center and extended to the posterior probability on the right. The fagan.plot creates the plot based on input to the function. The plotFagan and plotFagan2 functions set up Tk windows with sliders representing the possible inputs and show how the plot and the posterior probability changes when you adjust the inputs. The plotFagan function creates sliders for the prior probability and the LR, while the plotFagan2 function replaces the LR slider with 2 sliders for the sensitivity and specificity. More detail on the plots and the math behind them can be found at the websites below.

References

Fagan TJ. Nomogram for Bayes theorem. N Engl J Med 1975;293(5):257-61. http://www.cmh.edu/stats/definitions/fagan.htm http://ebm.bmjjournals.com/cgi/content/full/6/6/164

See Also

slider

Examples

fagan.plot(0.8, 2)

 fagan.plot(0.8, 0.95/(1-0.90) )

 plotFagan()

 plotFagan2()