Stochastic-Tree Models in Medical Decision Making

Abstract

Abstract:The stochastic tree is a recently introduced generalization of the decision tree which allows the explicit depiction of temporal uncertainty, while still employing the familiar rollback procedure for decision trees. We offer in this paper an introduction to stochastic tree modeling and techniques involved in their application to medical treatment decisions. We also describe an application of these tools to the analysis of the decision to undergo a total hip replacement from the perspectives of an individual patient (via utility analysis) and of society (via cost-effectiveness analysis). For medical analyses, the most commonly used method for the formulation and display of discrete-time Markov chains is the Markov cycle tree developed by Hollenberg [1984]. Hazen [1992] introduced a continuous-time analog of the Markov-cycle tree, the stochastic tree, which combines features of decision trees [Raiffa 1968] and stochasticprocess transition diagrams. Stochastic tree diagrams not only can depict continuously distributed temporal uncertainties, but, like decision trees, can be rolled back to determine optimal decisions. This rollback procedure is an instance of the method of successive approximations from stochastic dynamic programming (Denardo [1982], Ross [1970]). It can be applied not only for risk-neutral objective functions, such as mean quality adjusted lifetime [Hazen 1992], but also for the calculation of expected utility .One of the first applications of stochastic tree modeling in medical decision making was an investigation of total hip replacement surgery for patients with severe osteoarthritis 4 (OA) of the hip. An estimated 120,000 hip replacements are performed per year in North America [Harris and Sledge 1990]. This decision is interesting from a number of points of view. Although total hip replacement surgery (total hip arthroplasty, THA) is the most successful procedure for patients with advanced arthritis of the hip, the treatment decision for an individual patient with this condition can be difficult. While the surgery offers the potential of increased quality of life, it carries additional risk of mortality and morbidity.From a societal perspective, given the increasing incidence of severe osteoarthritis of the hip, the growing demand for THA, and the high costs associated with the procedure, there is concern that a larger share of health care resources will be spent on THA in the future.Rising costs and attempts to improve the efficiency of health care delivery have stimulated the need for analyses that objectively examine the trade-offs between therapeutic benefits and expenditures. If the economic consequences of surgical interventions are included, procedures such as THA are particularly vulnerable to scrutiny for several reasons. First, it is an elective procedure. Second, its target population is largely geriatric. Third, it is an expensive, high-technology procedure. Finally, in terms of short-term costs alone, medical management would appear to represent a less expensive treatment...

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