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World J. Surg. 23, 1227–1231, 1999 WORLD Journal of

SURGERY © 1999 by the Société

Internationale de Chirurgie

Decision Analysis for the Surgeon

Daryl S. Kucey, M.D., M.Sc.

Department of Surgery, University of Toronto, The Banting Institute, 100 College Street, Toronto, Ontario M5G 1L5, Canada

Abstract. Surgical practice, by nature, is full of important decision mak- ing scenarios. Surgeons have begun to utilize the decision sciences as a methodology of approaching clinically relevant surgical problems. This article provides a brief overview of some of the important concepts of the decision sciences as they apply to practicing surgeons. Concepts discussed include the basic principles behind decision trees, valuing outcomes, and Markov modeling as well as the pros and cons of the decision analytic approach. Decision analysis is a valuable aid in determining answers to clinical scenarios, and understanding the principles behind this method- ology is an important addition to the armamentarium of all practicing surgeons.

Decision making is a crucial component of the daily practice of surgery. Uncertainty arises from many sources, and in most cir- cumstances surgeons formulate answers to clinical problems by utilizing the store of knowledge and clinical experience they have accumulated over time. If uncertainty regarding the decision problem remains, a surgeon may the seek the experience of senior colleagues or the published experience of peers at other centers. Occasionally, one is able to find a randomized controlled clinical trial that offers a definitive answer to the clinical question. Despite this standard approach to clinical uncertainties, there remain innumerable situations in clinical surgery that are fraught with doubt and quandary.

In recent years, surgeons have begun to turn to statistical methodologies to assist in this decision-making process. The de- cision sciences have evolved from techniques largely limited to business applications and have become a popular methodology to assess a large variety of clinical scenarios. The recent emphasis on cost-effective medical care has served to increase the interest in decision analysis. Although decision analysis does not provide definitive answers for all clinical scenarios, it is an important addition to the surgeon’s armamentarium and one about which all surgeons should have basic knowledge. In addition, an under- standing of the benefits and limitations of this technique aid the surgeon in deciphering the current medical literature. This article provides an overview of the decision sciences from the perspective of a practicing surgeon.

What Is Decision Analysis?

Decision analysis is a mathematic tool that attempts to emulate the human decision-making process. Although we may not be aware of it, each decision we make is based on an evaluation of the options at hand followed by a choice based on the perceived outcomes derived from that choice. Decision analysis seeks to provide a systematic approach to decision making under condi- tions of uncertainty by providing an intuitive framework through which complex problems can be studied. The technique can be summarized as four basic steps [1].

Step 1: Identification, definition, and bounding of the decision problem. The first and most important consideration is to identify and define exactly what the decision problem is. To do this one must have a disease state and an outcome goal in mind. Once this is done in as concise a manner as possible, the problem must then be looked at objectively and critically from many viewpoints to identify all of the possible alternative options available to solve the problem or treat the clinical situation. One must also consider the consequences of each treatment option and what ramifications they have to the outcome of the patient. For example, if one chooses to treat a patient surgically, the operation may go as planned or there may be expected or unexpected complications of this treatment path. Therefore it is essential to realize that each decision action has many possible predictable reactions. One must also consider what possible clinical information could be obtained from the physical examination and biochemical or imaging testing and how the results of these tests or examinations would affect the decision-making process and the outcome of the patient. Lastly, one must consider the possible clinical states a patient may pass through over time and how these differing levels of health would affect the decision-making and patient outcome.

Step 2: Structuring the decision problem. The decision tree is the fundamental analytic tool for decision analysis. It is a tech- nique that displays the proper temporal and logical sequence of events in a clinical decision problem. Commonly, a problem we might think to be simple or straightforward becomes complex when all the possible options and consequences are explored. Independent of its size, each decision tree has four basic structural components: (1) the clinical starting point (the trunk of the tree); (2) the alternative actions that are available to the decision maker (the major branches of the tree); (3) the events that follow from

Correspondence to: D.S. Kucey, M.D., Sunnybrook Health Science Cen- tre, 2075 Bayview Avenue, H-185, Toronto, Ontario M4N 3M5, Canada.

and affect these actions, such as clinical information obtained or the clinical consequences revealed (subbranches of the tree); and (4) the outcomes for the patient that are associated with each possible scenario of actions and consequences (the foliage of the tree).

Step 3: Characterizing the information needed to solve the problem. The type of information that must be sought includes probabilistic chances of certain choices and outcomes occurring. For example, one might need to know the chance that a female patient with right lower quadrant pain, nausea, an elevated white blood cell count, and signs of peritonitis has acute appendicitis, in contrast to other right lower quadrant pathology. Another exam- ple is determining the probability of death, stroke, or myocardial infarction after carotid endarterectomy in a certain clinical situa- tion. The chance of these events occurring can be established using information that has been previously published in the liter- ature, new primary data from observational or experimental stud- ies, or consensus polling of experts in the area. Some probabilities may have to be calculated using the probabilistic theory (Baye’s theorem) [2]. Once the probability of all of the branch points in the tree is established, the outcome of interest must be quantified. The outcome may vary from life versus death to number of days of disease-free survival to quality-adjusted life expectancy to length of stay to number of dollars spent. The value assigned to this outcome again must be established using existing data or by objectively valuing the outcome states.

Step 4: Choosing a preferred course of action. Decision analysis maximizes quantities as a means to an end. Therefore the treat- ment strategy that maximizes life expectancy or minimizes death or cost is the preferred strategy for solving the problem. Because this type of analysis relies on a number of probabilities and outcome values that could change depending on the individual patient, a sensitivity analysis of the conclusions should be per- formed. A sensitivity analysis is merely a method of varying one or a number of variables at once to determine the threshold values for choosing one decision pathway preferentially over another. A practical example of significant threshold values is illustrated by the large carotid endarterectomy trials [3–9]. If the operating surgeon’s perioperative morbidity and mortality rates are less than 3%, patients with both symptomatic and asymptomatic carotid lesions might benefit from endarterectomy. However, if the rate is 6%, asymptomatic patients no longer benefit but symptomatic patients still do. If the rate is greater than 10%, no patients benefit from this type of procedure. Changes in the value of key proba- bilities in a decision tree therefore may have a profound influence on the outcome of the decision analysis.

Figure 1 illustrates a simple decision tree with hypothetic prob- abilities of certain events happening. There are two possible strategies to answer the clinical question. In this case, treatment A maximizes the chance of a good outcome (in terms of quality- adjusted life years) and therefore would be termed the dominant or preferred treatment plan.

Valuing Outcomes

To determine what value to place on nonmonetary outcomes, decision analysts rely on a variety of tools to help define objective value for often subjective clinical states. For example, if we rank quality of life on a scale of 0 to 1, with 0 being death and 1 being

perfect health, where does claudication at two blocks walking distance fit? To value intermediate health states, the surgeon should be familiar with two methodologies: the standard gamble and multiattribute utility models.

Standard Gamble

The standard gamble is one of the most basic tools utilized for valuing outcomes. Figure 2 illustrates a simple lottery where the candidate is faced with making a choice. On one hand is a decision pathway that offers a certain result (probability 5 1) with no risk involved; but we do not know the value associated with this sure-fire outcome, and indeed it is not a perfect health state (perfect health or death). Therefore the value of this state is between 0 and 1. On the other hand the best possible outcome is offered (perfect health: probability of this happening is 1 2 p). Unfortunately, to achieve this outcome some risk is involved (death; probability of death 5 p). The patient therefore faces a decision choice: At what point would I be willing to take the risk of achieving a perfect outcome? If the patient would never gamble at a chance of perfect health he or she is considered “risk ad- verse,” which suggests that this patient considers any quality-of- life highly (close to 1). On the other hand, some patients are “risk takers,” which suggests that the intermediate state, in their per- ception, is valued lowly (close to 0). The point at which equilib- rium is reached between the two decision arms (neither is more desirous) is considered the value of the intermediate health state. For example, if patients are faced with a choice between certain chronic pain and a lottery that offered a chance at perfect health but was associated with a risk of death, the risk of death (p) they would accept to achieve that state of perfect health would be related to the value they associate with the health state of chronic pain (1 2 p).

Fig. 1. Basic decision tree. The utilities for the health states have been empirically designated as cure 5 1.0, improved 5 0.75, no benefit 5 0.50, worse 5 0.25, death 5 0.00. Treatment A (TxA) is the dominant pathway and would be deemed the preferred decision pathway. TxB: treatment B.

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Multiattribute Utility Models

Health states are complex entities and usually cannot be ad- dressed with a single standard gamble. There are many factors that contribute to a patient’s holistic well-being, including not only physical pain and suffering but mental health, social skills, and perception of self-worth.

To address the value of health states from a more comprehen- sive point of view, a number of general and disease-specific utility models have been designed. Examples of multiattribute utility models [10, 11] are the short form 36 (SF-36), the Health Utilities Index, and the injury severity score (ISS). The commonality of all of these models is that the patient is assessed by a number of viewpoints or domains, and a value is then placed on their overall well-being. These scales and guidelines have been based on re- petitive studies of large groups of individuals using basic tech- niques such as the standard gamble in each of the domains of the model. All of these domain values are then combined to give the overall health score.

Although they provide a more holistic measurement of overall health, the difficulty with multiattribute scoring mechanisms is that they may dilute disease-specific functional outcomes. For example, details of the impact of an amputation in a patient with occlusive vascular disease from a functional point of view is not closely assessed. On the other hand, if one merely uses a disease- specific score, the impact of an amputation on the patient’s life in general is underassessed. Therefore analyses using these scoring mechanisms often utilize a general measurement tool (e.g., SF-36) combined with a disease-specific score.

From a practitioner’s point-of-view, the generalizability of util- ity models to an individual patient in an actual medical practice can be difficult: Is my patient the same as the average person? The answer to this dilemma is that utility values must always be interpreted with caution and in the presence of sensitivity analysis calculations before important decisions are made regarding indi- vidual patients. Therefore despite the use of advanced math- ematic tools, the interpretation still requires what would termed “the art of medicine.”

Markov Modeling

Another technique that is useful to understand is Markov mod- eling [12]. This mathematic tool is helpful when one applies

decision analysis to help calculate life expectancy or quality- adjusted life years (QALYs) following treatment interventions in the management of a chronic disease. A simple Markov model is illustrated in Figure 3. In uncomplicated terms, a Markov model consists of a number of health states that may range from perfect health to death. These health states are all related to the disease process in question and serve to model the natural history of the disease. For example, if the disease we are studying is lower limb occlusive vascular disease, the health states a patient might pass through would include an asymptomatic phase, intermittent clau- dication, night pain, rest pain, ulceration, gangrene, limb loss, and death. For each time period t (typically 1 year but could be any measure of time) the patient has disease x there is a chance that the patient may die, a chance he or she may be cured, and chances that the patient may improve or worsen slightly or stay the same. A Markov cycle is a mechanism that allows the patient to reenter the same probability tree over and over again as time progresses and allows chronic diseases to evolve as they would in a real life scenario. The Markov process continues to cycle over and over until the chance of death is equal to 1 and the probability of the patient existing in the other health states is zero. Death is called “an absorbing state” because you cannot leave this state. Once death is achieved, you can then add up the time spent in each of the nonabsorbing states to calculate overall life expectancy, or you can quality-adjust the value you assign to each of the nonabsorb- ing states (possibly via the standard gamble) to determine QALYs.

Pros and Cons of Decision Analysis

Understanding the basic concepts involved in the decision sci- ences offers advantages to every practicing surgeon. The most compelling benefit is an enhanced ability to structure decision problems in a logical, stepwise fashion. Many surgeons already ponder problems decision-analytically even though they do not

Fig. 2. Standard gamble. The utility of the intermediate state is estimated when indifference exists between selecting the pathway leading to chronic pain and the lottery between cure and death. For example, if indifference exists at p 5 0.50, chronic pain would be given a utility of 0.50.

Fig. 3. Basic Markov model. t: interval of time; pdeath: probability of death occurring during one turn of the time cycle; pbetter: probability of getting better; pworse: probability of getting worse; psame: chance of staying the same; pcure: probability of being cured during the time inter- val. Death is an absorbing state.

Kucey: Decision Analysis for the Surgeon 1229

realize it. Formal introduction to analytic techniques makes prac- titioners more aware of the consequences and outcomes related to different treatment strategies and hopefully helps make the deci- sion process easier for the surgeon. Introduction to the terminol- ogy used for decision analysis may make communication between physicians easier by applying a more objective value to subjective circumstances. For example, the use of quantities such as proba- bilities may help avoid ambiguous terms such as rarely, some- times, or often.

If medical controversies are structured in a decision-analysis framework, the disagreements contributing to the controversy may be understood more clearly. Medical problems are typically complex, with a number of contributing small controversies. If the problem is structured logically, the small issues that contribute to the overall problem can then be recognized. If these small dis- agreements are then studied and resolved in a logical fashion, the larger controversy may then be closer to resolution. Another incentive to familiarize oneself with decision analysis is the grow- ing concern over health care expenditures. The physician, who is the primary advocate for patient care and the gatekeeper for access to health services, must be familiar with the methodologies used for the assessment of health care resource utilization, such as cost-effectiveness analysis and cost-benefit analysis, both of which are products of the decision sciences [13]. An understanding of the methodologies utilized in the management side of health care delivery continues to ensure an influential position for surgeons in health care policy development and administration.

Unfortunately, one of the biggest disadvantages of the decision sciences stems from the fact that clinical decision problems are complex. As a result of this complexity it is may be difficult to model the problem realistically: There are just too many potential branches and subbranches of the decision tree. Therefore to simplify the technical aspects of decision analysis, often assump- tions regarding the treatment protocol, the patient, or the disease process may have to be made. Assumptions might be looked on as concessions made in the model to simplify the issue. Unfortu- nately, the more concessions that are made, the less realistic and generalizable the model becomes. For example, to assess the utility of infrainguinal revascularization in someone with intermit- tent claudication, one might make the assumption that the prob- lem is unilateral only at a single point in time. This is clearly not realistic in most patients, but to simplify the decision model it may be necessary to model the problem in this fashion.

Another drawback is the difficulty of determining the utility of specific patients and the fact that the value of utility may change over time and depend on the circumstance in which the patient finds himself or herself. For example, prior to amputation, a patient may say that the utility of the amputated state is zero; but after it has occurred and the patient has dealt with the situation emotionally, the utility of the amputated state in the patient’s mind increases. This enigma underlines the basic human instinct that life of any sort is precious. Lastly, thinking probabilistically from the physician’s point of view may be a difficult concept to accept. Many physicians prefer generally applicable clinical max- ims and clear-cut choices, rather than dealing with chance or probability.

Decision analysis is merely an aid for clinical reasoning, not a substitution for sound clinical judgment, and it must always be used and interpreted with this in mind. Despite the obvious shortcomings of the decision sciences, familiarity with these meth-

odologies provides surgeons with tools that can serve to improve their approach to the unique challenges present in the practice of clinical medicine.

Résumé

Le propre de la pratique chirurgicale est de devoir prendre des décisions importantes dans un certain nombre de scénarios. Depuis peu, les chirurgiens ont commencé à utiliser une méthodologie décisionnelle pour résoudre les problèmes de clinique chirurgicale. Dans cet article, on revoit brièvement les concepts importants de la démarche décisionnelle tels qu’ils s’appliquent aux chirurgiens dans la pratique. Les concepts discutés ici comprennent les principes de base des arbres de décision, l’évaluation des résultats et le modèle de Markov, ainsi que les pour et les contres de l’approche analytique de la démarche décisionnelle. L’analyse décisionnelle est une aide importante dans la détermination des réponses aux scénarios cliniques. Comprendre les principes derrière cette méthodologie est un plus pour tous les chirurgiens dans leur pratique.

Resumen

La práctica quirúrgica, por naturaleza, está plena de importantes escenarios para la toma de decisiones. Recientemente los cirujanos han comenzado a utilizar las ciencias de la decisión como metodologı́a para enfrentar problemas quirúrgicos de relevancia clı́nica. El presente artı́culo revisa la aplicación de los conceptos importantes provenientes de las ciencias de la decisión a la práctica quirúrgica. Se discuten los principios básicos en que se fundamentan los árboles de decisión, la valoración de resultados finales, y la modelación markoviana, ası́ como los pros y los contras del enfoque analı́tico de decisión. El análisis de decisión es un instrumento de valor para determinar escenarios clı́nicos y comprender los principios que sustentan esta metodologı́a y, como tal, representa una importante adición al armamentario de la práctica quirúrgica.

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