In a one-way sensitivity analysis, we only vary the value for one variable. In a two-way analysis…you guessed it, we vary two values simultaneously. Consider the issue of how we value overtreatment (giving an antibiotic to someone who doesn’t need one) versus undertreatment (not giving an antibiotic to someone who has strep). First, we have to create two variables, UtilityUnderTreatment and UtilityOverTreatment:
The diagram has replaced the static values of 0.6 for the utility of undertreatment and 0.8 for the utility of overtreatment with the variable names. If we do the two-way sensitivity analysis for overtreatment and undertreatment, we get the following diagram:
Don’t you love it? Another confusing diagram! Actually this one is a little easier to interpret in some ways that the one-way sensitivity analysis. Below, we’ve assumed that undertreatment and overtreatment have the same utility, so we’ve plotted UtilityOverTreatment = 0.7 and UtilityUnderTreatment = 0.7:
Look at the color of the background at the point at which the red lines cross. It is green, indicating that the preferred strategy for this combination of UtilityOverTreatment and UtilityUnderTreatment. Of course, this all assumes that we the probability of strep is back to 20%. What if it is only 5%, which is typical of adult outpatient populations? Changing the baseline probability of strep to 5%, rerunning the two-way sensitivity analysis, and redrawing our plot yields the following graph:
What do you know! Now the best strategy is no treatment or testing. On the other hand, if we think that undertreatment is worse than overtreatment (UtilityUnderTreatment = 0.5, UtilityOverTreatment = 0.8) then the best strategy is ordering a rapid antigen test.
All of this begs the question – what about a 3-way analysis? That’s possible, but it is really just a series of two-way analyses placed side by side.