When a surgeon is deciding whether to operate for a herniated disc (HNP), he has two choices (operate or not) and he will be either right or wrong with each choice. If he operates, he will either find a herniated disc (treat, disease; t,d) or not find one (treat, no disease; t,nd); If he decides not to operate, his patient may have a HNP (not treat, disease; nt,d) or not nave a HNP (not treat, no disease; nt,nd). Decision analysis is a way to assign a value to each of those possible outcomes, then work back to see how probable the diagnosis of herniated disc needs to be to justify an operation. For a herniated lumbar disc, this threshold is above about a 70-75% chance of having a herniated disc.
The value, called the utility (U) of each of the four possible outcomes is a judgment made by the patient (or society) of the desirability of that outcome. The U of an outcome will vary, depending on the person’s health status, work requirements, obesity, duration of symptoms, etc.
In my estimates of U, valuation of outcomes were derived from medical literature. Of patients having surgery and no herniated disc found, 37% nevertheless had a satisfactory result. I assigned this outcome of treating with surgery and finding no disease, Ut,nd a value of .37. If a HNP was treated at surgery, relief was found in 85%; Ut,d = .85. With non-operative management about two-thirds of people with HNP are improved after one year, so Unt,d = .66. As for those without a HNP, non-operative measures, such as physical therapy, chiropractic, etc. improved 90%; Unt,nd = .90
If we use p as the proportion of disease (HNP) actually present, which is the PV% expressed as a decimal, (and the non-HNP proportion is thus 1-p) then:
The Expected Value of Treatment (EVt) = p x Ut,d + (1-p) x Ut,nd
If the chance of having a HNP = 50%, then p = .5 and
EVtreat = .5 x .85 + .5 x ..37 = .61
Expected Value of No Treatment (EVnt) = (1-p) x Unt,nd + p x Unt,d
In our example of having a 50% chance of HNP, p=.5
EVnt = .5 x .9 + .5 x .66 = .78
Thus, with a chance of having an HNP only being 50%, the value of not having surgery is greater.
What are the odds of having a HNP that is the borderline between recommending surgery or not? That so-called threshold can be found by putting the above two equations equal and solving for p. That p-value is .74. Therefore a PVpos of around 75% or more (or a PVneg of 25% or less) is the threshold for recommending an operation for HNP used in the LOBAK app (ref 10).