Introduction

In previous chapters we have seen several applications of decision trees to solve clinical problems under conditions of uncertainty. Decision trees work well in analyzing chance events with limited recursion and a limited time horizon. The limited number of sequential decisions or chance nodes allows one to capture all the necessary information to maximize expected utility. However, when events can occur repeatedly over an extended time period, the decision-tree framework can become unmanageable. Many decision situations involve events occurring over the lifetime of the patient, thus extending far into the future. Life spans vary, but conventional trees require us to specify a fixed time horizon. The probabilities and utilities of these events may change over time and must be accounted for. This is the case for most chronic conditions. Examples include heart disease, Alzheimer’s disease, various cancers, diabetes, asthma, osteoporosis, human immunodeficiency virus (HIV), inflammatory bowel disease, multiple sclerosis and more. This chapter offers a methodology for dealing with recurring events and extended (variable) time horizons.

EXAMPLE

Consider a patient with peripheral arterial disease (PAD: obstruction of the arteries to the legs) for whom a decision has to be made for either bypass surgery or percutaneous intervention (PI). We assume that conservative treatment through an exercise regimen has not provided sufficient relief. A very simplified decision tree is presented in Figure 10.1. Following the choice of treatment, the patient may die as a result of the procedure (captured in the ‘mortality’ branches) or survive the procedure. If the patient survives, treatment may fail and the patient returns to the pre-procedure prognosis, or treatment may be successful and the patient is relieved of symptoms. If we consider some fixed time horizon like a year or five years, we can assign utilities to the three possible outcomes (success, failure, death) and calculate expected utilities to choose a preferred treatment. In the current structure, there is no explicit allowance for the time horizon we are considering, nor for the timing of the various events. Even if we consider a fixed time horizon of, say, five years, there surely is a different implication for prognosis if failure occurs in the first year versus the fifth year.