APPLYING THE PAYOFF TIME FRAMEWORK TO CAROTID DISEASE MANAGEMENT

Purpose: Asymptomatic carotid artery stenosis is associated with stroke, and while surgery to correct stenosis can reduce stroke risk, surgery can sometimes cause stroke immediately, leading to a net loss of benefit, especially in patient populations with a high baseline mortality rate. We model the relationship between immediate risk, long term benefit, and life expectancy in order to generate a simple, clinically relevant formula that can aid decisions about carotid surgery.

Method: We use the recently articulated concept of the “payoff time” to compare initial risks of surgery with subsequent benefits. Quality-adjusted life-years (QALYs) lost initially due to surgery are an “investment” that is recouped over time. If the patient cohort has a short life expectancy, this investment is not recovered. We sought simple closed-forms that defined the relationship between perioperative stroke risk (P), annual rate of stroke without surgery (r₀), annual rate of stroke after surgery conditional on not having had a perioperative stroke (r₁), utility levels assigned to the baseline state (u_b) and the stroked state (u_s), and life expectancy (1/λ), assuming the declining exponential approximation of life expectancy (DEALE). Numeric models, using parameters from the published literature, were constructed to verify mathematical solutions. 

Result: In order for there to be a finite payoff time for carotid surgery to correct an asymptomatic stenosis, there is a minimum critical life expectancy (MCLE=1/λ*), given by the following equation: 1/λ* = P/(r₀–r₁). This relationship is independent of the utilities assigned to the health states, if a simple rank ordering exists where u_b>u_s. For clinically relevant values in asymptomatic patients (P=3%, r₀=1%, r₁=0.5%), the MCLE is 6 years, which is longer than published guidelines regarding patient selection for this intervention. Figure 1 demonstrates that for a representative 1/λ>MCLE, total cumulative QALYs associated with surgery, as compared to non-operative management, are greater than zero, but for a representative 1/λ<MCLE, total cumulative QALYs are negative.

\s Figure 1

Conclusion: For patients with asymptomatic carotid disease, the payoff time framework specifies a MCLE=1/λ*=P/(r₀-r₁) as the life expectancy threshold that determines if there is any benefit from surgery. The MCLE is approximately 6 years, suggesting that many clinically relevant populations with asymptomatic carotid disease and short life expectancy do not benefit from surgery because they suffer too much perioperative harm compared to the benefit they receive.