First, we have to create a variable called “ProbStrep”, and replace the fixed value of 0.2 with that variable wherever it appears in the tree:
Then, we do the sensitivity analysis. Doing so creates this initially confusing diagram:
Whew! Let’s take it slowly… The graph plots the expected value (or overall utility for a particular management option) on the y-axis. The probability of strep is on the x-axis. The three possible management strategies (no treatment or testing, order rapid antigen test, or treat empirically) are indicated by the green, blue, and red plots respectively.
Got it so far? Now, pick a probability of strep, like 0.2 (20%). Begin at the x-axis, and move upward in a perpendicular line. We’ve drawn the line below in red:
As you move up the line, you first cross the red triangles of the “Treat empirically” management strategy. At the point where you cross that strategy, look to the left to find the expected utility for that strategy at that probability of strep: about 0.84. Keep going up, and you next cross the green circles of the “No treatment or testing” strategy; the corresponding expected utility is about 0.92. Finally, you cross the blue diamonds of the “Order rapid antigen test” strategy, which has a corresponding expected utility of 0.98.
If you’ve been paying attention, those numbers should look familiar. They are exactly the expected utilities that you found for the “baseline” model. Why? The baseline model assumed a 20% probability of strep, of course.
Let’s draw a line at a much higher probability of strep of 90%:
In this case, the topmost strategy is “Treat empirically”, with an expected utility of 0.98 at this probability of strep pharyngitis. Note that the graph has two dotted lines, and that they are labeled “Threshold values”. A threshold value is the point at which there is a transition from one strategy to another having the highest expected utility. In this model: