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Med Decis Making. 2013 Nov;33(8):1039-50. doi: 10.1177/0272989X13491462. Epub 2013 Jun 19.

Applying the payoff time framework to carotid artery disease management.

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  • 1Division of Vascular Surgery, Pittsburgh, PA (THY).





Asymptomatic stenosis of the carotid arteries is associated with stroke. Carotid revascularization can reduce the future risk of stroke but can also trigger an immediate stroke. The objective was to model the generic relationship between immediate risk, long-term benefit, and life expectancy for any one-time prophylactic treatment and then apply the model to the use of revascularization in the management of asymptomatic carotid disease.


In the "payoff time" framework, the possibility of losing quality-adjusted life-years (QALYs) because of revascularization failure is conceptualized as an "investment" that is eventually recouped over time, on average. Using this framework, we developed simple mathematical forms that define relationships between the following: perioperative probability of stroke (P); annual stroke rate without revascularization (r0); annual stroke rate after revascularization, conditional on not having suffered perioperative stroke (r1); utility levels assigned to the asymptomatic state (ua) and stroke state (us); and mortality rates (λ).


In patients whose life expectancy is below a critical life expectancy (CLE = P/(1-P)r0-r1, the "investment" will never pay off, and revascularization will lead to loss of QALYs, on average. CLE is independent of utilities assigned to the health states if a rank ordering exists in which ua > us. For clinically relevant values (P = 3%, r0 = 1%, r1 = 0.5%), the CLE is approximately 6.4 years, which is longer than published guidelines regarding patient selection for revascularization.


In managing asymptomatic carotid disease, the payoff time framework specifies a CLE beneath which patients, on average, will not benefit from revascularization. This formula is suitable for clinical use at the patient's bedside and can account for patient variability, the ability of clinicians who perform revascularization, and the particular revascularization technology that is chosen.


carotid revascularization; decision analysis; model; shared decision making

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