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Decision analysis

Decision analysis
Literature review current through: Jan 2024.
This topic last updated: Oct 20, 2022.

INTRODUCTION — Decision analysis is a quantitative evaluation of the outcomes that result from a set of choices in a specific clinical situation. It is similar in many ways to the qualitative assessments clinicians make every day in the clinical decision-making process. When faced with a particular problem, clinicians develop an array of possible actions ranging from doing nothing, to obtaining more information by performing diagnostic tests, to recommending various therapeutic interventions. This process is often implicit and occurs in the context of internal algorithms and heuristics (mental shortcuts) that the clinician has developed and acquired over time.

Decision analysis, by requiring a specific model structure and quantitative assessment of the various likelihoods and values of the outcomes, makes the decision process explicit and much more amenable to examination, discussion, and intellectual challenge.

Decision models are often used as an analytic tool to conduct cost-effectiveness analyses since decision analysis methodology can be used to find the expected value of most any outcome. Cost-effectiveness analysis is discussed separately. (See "A short primer on cost-effectiveness analysis".)

TYPES OF QUESTIONS APPROPRIATE FOR DECISION ANALYSIS — The range of clinical questions appropriate for decision analysis is vast. The two major requirements for its use include:

The question focuses upon a specific decision that must be made

There is a tradeoff involved in the decision

"Tradeoff" means that one of the choices considered should not be unambiguously superior. As an example, a diagnostic test might carry some risk, but the tradeoff is more appropriate therapy when treatment is directed by the results of that test.

The scope of the clinical question should be sufficiently narrow. For example, consider the clinical decision of prescribing statin therapy in patients with elevated cholesterol based upon estimated 10-year risk of developing atherosclerotic cardiovascular disease (ASCVD). Asking "Should patients with elevated cholesterol levels be treated with statins?" poses a question so broad and complex that it is unanswerable. In contrast, a question such as, "What is the benefit of statin therapy at different 10-year risk levels?" is sufficiently specific to be amenable to decision analysis.

Another key characteristic of questions that are appropriate for decision analysis is that there should be debate or uncertainty regarding the best choice. It is unlikely that decision analysis would be useful if it addresses the exact question already answered definitively by randomized controlled trials.

Clinicians frequently encounter clinical questions that are not directly answered by the available medical literature. One may be faced with a patient who is significantly older or has more comorbidities than the study population in a published trial or who has a set of unique attributes that make the direct application of results from a published study problematic. In general, decision analyses have been developed to:

Assist in clinical decision-making for a specific individual patient

Estimate optimal strategies for classes of patients with specific clinical characteristics in given situations

Link estimates of both clinical and economic outcomes (cost-effectiveness analysis) to help inform health policy questions

Provide estimates of expected outcomes in situations where classic methods such as randomized trials are either impossible or impractical

There are several advantages of using decision analysis to investigate options involving a single patient. Placing the problem in an explicit, analytic context forces clinicians to make their assumptions clear, and the presence of a structured model rapidly focuses clinical disagreements. Decision analyses can directly incorporate issues regarding quality of life and how the particular patient values various outcomes. As an example, if possible death in the near-term is the trade-off for a potential cure, then maximizing life expectancy may not be the most important outcome for a terminally ill patient who wants to live to witness a grandchild's graduation from college several months hence. Such individual patient preferences can be incorporated directly into decision analyses by altering the value of the various outcomes.

Decision analyses are performed more commonly to evaluate the appropriate strategy for a class of patients identified by a set of clinical characteristics. Often this will involve combining data from a variety of different sources to provide a comprehensive analysis of the clinical question. An example is a decision analysis weighing different approaches to managing patients with small renal masses (active surveillance versus immediate intervention) [1]. The model combined several kinds of data, including baseline incidence of renal cell carcinoma, the risks of the various procedures, and the estimated risk of metastatic progression with and without intervention. The analysis demonstrated that expected 10-year survival for patients managed with active surveillance was similar to those managed with immediate intervention, but total costs were lower for active surveillance. This example also illustrates how a decision analysis of a clinical problem can be linked to economic data to produce a cost-effectiveness analysis. (See "A short primer on cost-effectiveness analysis".)

Decision analysis can also be used to provide estimates of risks and benefits for groups of patients with characteristics somewhat different from patients studied in previous randomized controlled trials, as demonstrated in the example below. (See 'Example' below.)

CONDUCTING A DECISION ANALYSIS OF A SPECIFIC PROBLEM — Developing and constructing a decision analysis follows a logical series of steps. Problems or errors in any step can alter the eventual results; thus, proper adherence to each of these steps is important both from the view of a researcher conducting an analysis and a clinician interpreting the results of a published study.

Throughout the remainder of this topic review, the basic techniques of decision analysis are described in a primer-based style, with no assumption of prior knowledge or experience. In addition, we have annotated and explained the decision analysis process using an example to illustrate how these methods were applied in a published study [2]. (See 'Example' below.)

Step 1: Frame the question

Population, condition, interventions, and outcomes – The process of defining the scope and boundaries of the particular clinical situation to be analyzed is similar to developing selection criteria for a randomized controlled trial. The purpose is to define the particular population of patients, conditions, and intervention strategies that are appropriate to the analysis. (See "Evidence-based medicine", section on 'Formulating a clinical question'.)

Perspective – One of the most important decisions to be made in a decision analysis is the perspective from which the analysis is to be conducted. A decision analysis conducted from the point of view of an individual patient may look different when analyzed from society's point of view, where secondary effects on others in the population (eg, from transmission of an infectious disease) would need to be included.

Time frame – The time horizon of the analysis needs to be specified and be consistent with the clinical reality of the condition. A time horizon of one month, for example, would be inappropriate for a decision analysis of a cholesterol lowering medication since gains in survival may not be realized for years. On the other hand, a decision analysis of different treatments for urinary tract infection might not need to consider outcomes beyond one or two months after treatment. In general, the time frame should match the natural history of the disease process.

Step 2: Structure the clinical problem — Structuring the problem simply means constructing a decision model that represents the relevant components of the problem. The mathematical representation of a decision model is called a decision tree and is composed of several discrete elements. Elements combined into trees contain an arbitrary amount of detail. Virtually any decision can be modeled, but it is important that the choices considered are realistic. As an example, a decision analysis examining bypass surgery versus medical therapy but ignoring percutaneous coronary intervention might be inappropriate.

There is constant tension between increasing the level of detail to be as clinically realistic as possible versus the feasibility of model construction, validation, and presentation [3]. The more detail desired, the more difficult the model is to construct, validate, and present. However, the less detailed the analysis and the greater the number of simplifying assumptions, the more vulnerable is the analysis to attack for lacking clinically meaningful elements.

All decision trees begin with a decision node, which represents the decision to be made (figure 1A-B).

Figure 1A illustrates a decision with two options, Choice 1 and Choice 2, representing a generic clinical decision. Such a decision could represent the choice between medical and surgical therapy for a particular condition; empiric treatment for a disease versus diagnostic testing; or different follow-up intervals after resection of a cancer.

Following a decision node is one or more chance nodes. In this example, Outcome 1 and Outcome 2 are possible consequences of Choice 1, and Outcome 3 and Outcome 4 are possible consequences of Choice 2. Each branch of a chance node is characterized by a probability between 0.0 and 1.0 (p1 through p4), which represents the likelihood that the particular event will occur. The sum of all probabilities at a chance node must equal 1.0 (100 percent).

At the end of each branch is a terminal node, which represents a state of health or outcome that results from traversing a particular path through the tree. As an example, if Choice 1 represents a surgical intervention, Outcome 1 might be operative mortality, and therefore Value 1 (or V1, which might represent life expectancy) would be the value assigned to immediate death, which is by convention 0.0.

See below for a more detailed example. (See 'Example' below.)

Step 3: Estimate the relevant probabilities — Once a decision tree has been structured, the numeric values of the various probabilities need to be determined. There are many sources of data that can be used to make these determinations. Although there is a generally accepted hierarchy of evidence for primary studies (figure 2), this schema is not always useful for decision analysis, since the particular study type may not be conducive to estimating a given parameter. As an example, a randomized controlled trial is an excellent source for comparing one therapy versus another, but it is a poor source of data regarding the incidence of a particular disease. Thus, it is important to tailor the data source to the type of data required (table 1).

It is rarely the case that all of the data needed to parameterize a decision model can be found in a single study. If that were true, it would be likely that the question being asked had already been answered.

The sources used to estimate probabilities need to take into consideration potential differences in characteristics of populations between published trials and the population of interest to the decision analyst. As an example, carotid endarterectomy was found to be beneficial in patients with asymptomatic carotid stenosis in a trial in which the operative mortality was 3 percent [4]. The local rate should be used in the analysis if it is different from the published rate.

Step 4: Estimate the values of the outcomes — The structure of the problem defines the specific outcome measure to be used. As noted above, life expectancy is not likely to be a relevant outcome for an analysis of different treatment strategies for urinary tract infection. In contrast, if death is a possible outcome of one or more strategies, life expectancy would be an appropriate outcome measure. The most important aspect in assigning outcomes is that they be measured in the same units across all branches.

A useful feature of decision analysis is that a given model can be evaluated using different outcome measures. As an example, in addition to survival, the investigator may want to track the effect of different therapies upon the rate of stroke, myocardial infarction, pulmonary embolization, etc, across various treatment options. The decision model can be analyzed using any of those outcomes.

It is intuitively obvious that a year of life in full health is not the same as a year with severe angina or a year of life following a stroke or an amputation. Patients place different values on those health states and are willing to accept risks (undergo operations, take medications with side effects) to avoid them. In decision analyses, one can consider quality of life (QOL) and length of life simultaneously.

The important attribute of QOL measures for decision models is that they allow quantitative comparisons among different health states. In other words, QOL adjustments for decision models must be able to make comparisons of the form: "One year of life with a stroke is worth X percent of a year of life in full health." When measured in this manner, decision analyses produce estimates of quality-adjusted life years (QALYs). Multiple methods to incorporate quality of life are available [5,6].

Step 5: Analyze the tree: The mechanics of the analysis — The "answer" to a decision analysis problem is the strategy that maximizes the expected value of the outcome. As an example, if the outcome of interest were life expectancy, the result of a decision analysis would be of the form: "the average life expectancy with strategy A is 10.2 years versus 9.8 years with strategy B; therefore strategy A is the optimal strategy."

These "expected values" or "expected utilities" are determined by recursive evaluation of the tree (known as averaging out and folding back) from right to left, replacing each chance node with the expected value of the combination of branches that arise from that chance node. The value of each branch at a decision node is the arithmetic average of the branches that follow. For the simple tree in the figure (figure 1A):

Expected value of Choice 1 = (p1*V1) + (p2*V2)

Expected value of Choice 2 = (p3*V3) + (p4*V4)

More concretely, the figure illustrates the calculation for hypothetical probabilities and life expectancies (figure 3). Such a tree might represent the choice between two therapies, one with little difference between its possible outcomes (Choice 1) and the other offering a chance of longer life at the risk of a shorter life (Choice 2). In this example, Choice 2 is the preferred strategy in terms of life expectancy.

Step 6: Test the model's assumptions: Sensitivity analysis — The results obtained from a decision analysis depend upon the accuracy of the data used to estimate the probabilities and outcomes. It is rarely the case that estimates are known with complete certainty; even in data from very large population-based studies, estimates of mortality and effectiveness are couched in confidence limits.

One of the major advantages of decision analysis models is their ability to rapidly test their assumptions and input data. As an example, in referring to the hypothetical example in Figure 2, suppose the life expectancy estimate of 10 years for patients who experienced Outcome 1 came from a relatively small study, and the confidence limits on life expectancy ranged from 8 to 12 years. That range could be used to recalculate the model several times in order to examine whether such differences would change which strategy was optimal (table 2).

The table represents a one-way sensitivity analysis since it varies the value of only a single variable (table 2). More than one parameter can be varied, producing two-, three-, and multiway sensitivity analyses that relate the expected value of the choices to simultaneous variations in the values of several variables.

Sensitivity analysis is also a helpful tool in constructing and validating decision models. The model's answer can be compared with the "true" answer to validate the model structure by evaluating a tree using parameters for which the result is known a priori. As an example, in a choice between a more effective (but riskier) surgical therapy and a less effective (but safer) medical therapy, a sensitivity analysis that postulated a zero mortality rate for the surgical intervention should advocate the surgical arm since there would be no downside risk. If the model did not indicate that the surgical arm was preferred, an error or "bug" in the model would likely be present.

Step 7: Interpret the results — Interpreting the results of a decision analysis is often the most complicated task. Unlike other experimental designs or study types, it is often not the explicit result from a decision analysis that becomes its most important contribution to decision-making. Rather, the ability of a decision analysis to explore how the optimal strategy in a particular clinical situation changes with variation in assumptions (and therefore to identify areas for further data needs) is often one of the most powerful attributes of this type of analysis.

Several conditions must be met before the results can be incorporated into day-to-day practice [7,8]:

Relevant competing strategies must be included

All clinically relevant outcomes given those strategies must be described

The data used for calibration (both probabilities and outcomes) must be acquired and summarized in a clear and reasonable manner

Appropriate sensitivity analyses must be performed.

Furthermore, the consumer of a decision analysis should examine several details of an analysis prior to using the results to change practice or policy.

The patient population should closely match the patients seen by the clinician. A decision analysis exploring coronary artery bypass graft versus percutaneous coronary intervention in young male patients with chronic stable angina probably will not inform the same decision as in older adult women with crescendo angina.

The reader needs to assess the strength of the result. Decision analyses do not contain statistical indicators such as p-values. Thus, one relies on the sensitivity analysis to indicate whether outcomes change over appropriate ranges of relevant variables. If sensitivity analyses indicate that the optimal choice is strongly dependent upon a given parameter, one should try to develop accurate measures of the parameter estimate.

EXAMPLE — The issue of thrombolytic therapy in older adult patients with myocardial infarction (MI) provides a good example of how decision analysis can be used in clinical practice.

Step 1: Frame the question — Clinical trials of thrombolytic agents in acute MI have demonstrated benefit in the patient populations studied, but the evidence of their benefit in older adults has been mixed. Noting that no trial had directly addressed this issue, one group performed a decision analysis to address the problem [2]. Their approach represents a common use of decision analysis: extending tried and true therapies into populations somewhat dissimilar from those initially studied.

The thrombolysis issue has several characteristics that make it appropriate for decision analysis:

There is a specific choice (to give thrombolytic therapy or not)

There are accurate data on the characteristics and outcomes of MIs in older adults

There is strong evidence of efficacy in certain study populations

The following sections describe a decision analysis published in 1992 [2]. The published version of this analysis did not include a figure of the decision model, but we present the model so that the reader may follow and replicate the analysis.

Step 2: Structure the clinical problem — The decision tree models two mutually exclusive strategies: whether to give thrombolytic therapy to an older adult patient with acute MI or provide only supportive care (figure 4).

If thrombolysis is chosen, the patient may experience a complication of therapy (eg, cerebral hemorrhage). In this analysis, complications of thrombolysis are assumed to be equivalent to death. However, because a cerebral hemorrhage may not always be tantamount to death, their assumption biases the analysis against thrombolysis by making the complications worse than they might actually be.

The diagnostic criteria for MI are not perfect. Thus, some patients given thrombolytics have actually not had an MI (false positives). For this reason, a chance node representing actual MI versus no MI follows the complication/no complication node. Although this assumption about MI diagnostic criteria is probably no longer explicitly correct, most diagnostic tests have errors, and this analysis demonstrates how to incorporate them into a decision tree.

The patient may die or survive whether or not she has an MI, although the likelihood of death will be much higher with MI.

The no thrombolysis strategy looks the same structurally except for the absence of the complication/no complication branch, since no drug is administered.

Step 3: Estimate the relevant probabilities — The structure of the tree and the number of branches at chance nodes define the probabilities required to "parameterize" the tree. In this model, estimates of the probability of MI, the mortality rates with and without infarction, and the efficacy and risks of thrombolytic therapy are required (table 3). Most of the data for this analysis came from published trials including the Groupo Italiano per lo Studio della Streptochinasi nell'Infarcto Miocardio (GISSI [9]) and the Second International Study of Infarct Survival (ISIS-2 [10]) trials. Other data were collected from the literature. The estimated probabilities used in their analysis are growing older, but this represents one of the benefits of developing a model: The parameters can be updated with more current information as it becomes available.

Step 4: Estimate the values of the outcomes — The values at the end of each terminal node for the basic analysis are simply the value of surviving (set to 1) or dying (0) in the hospital. The expected value of each branch will be the average probability of in-hospital survival for a cohort of patients treated under that strategy (thrombolysis or no thrombolysis).

The authors also needed to estimate the number of years of life saved and the costs of the interventions for the purposes of also conducting a cost-effectiveness analysis (beyond the scope of this topic review) (see "A short primer on cost-effectiveness analysis"). They obtained these values from a cardiovascular risk prediction model, the Coronary Heart Disease Policy Model [11]. As an example, they estimated that a 70-year-old patient would have a life expectancy of 5.5 years after MI. For calculating average life expectancy (rather than probability of survival) under each strategy, the specific life expectancies for each outcome would be inserted in their appropriate terminal nodes, with the value of death remaining at zero.

Step 5: Analyze the tree (average out/fold back) — The tree is analyzed using the standard averaging-out and folding back approach described above. The tree is folded back from right to left, and the average value at each chance node is calculated (figure 5). Given the baseline assumptions provided in Figure 4, the expected value of complication-free survival is 0.7864 for the thrombolytic arm versus 0.7559 for the standard therapy strategy.

The results can also be presented in two other forms:

The number needed to treat to save one additional life

Life expectancy

In order to calculate life expectancies, one would need to know the life expectancy after MI for a patient of a given age, estimated in this study to be 5.5 years for a 70-year-old male [2]. Using standard life expectancy tables for survival without MI, the relevant life expectancies could be entered as the values of the terminal node, and the analysis repeated to find the expected life expectancy for each strategy.

Step 6: Test assumptions (sensitivity analysis) — We have provided a simple one-way sensitivity analysis as an introduction, changing only the probability of a fatal complication of thrombolytic therapy over a reasonable range of values (0 to 6 percent). This can be seen in a figure (figure 6). As expected, the probability of surviving under the thrombolysis strategy decreases as the risk of fatal complication rises. At a probability of fatal complication greater than 0.042 (the so-called "threshold"), the thrombolytic strategy becomes inferior to the no-thrombolytic strategy.

The published paper presents several examples of two-way sensitivity analyses, where two variables (eg, probability of MI and effectiveness of thrombolytic therapy) are varied simultaneously to determine when thrombolytic therapy is beneficial [2]. All of the analyses demonstrated that for reasonable ranges of values surrounding their baseline estimates, thrombolysis remained the preferred strategy.

Step 7: Interpret the results — This analysis has most of the features of a sound decision analysis. For patients presenting with suspected MI, the model presents two options: thrombolysis versus no thrombolysis. One could question why primary percutaneous coronary intervention was not considered, as this option has been included in many of the MI interventional studies. The data used to calibrate the model come from several large trials and the outcomes modeled were reasonable, although one could have modeled minor complications as well. Several sensitivity analyses were performed, all indicating that the results were quite robust.

EXTENSIONS

More complex modeling (Markov models) — Simple node and branch decision trees can be used to develop models of arbitrary complexity, but the methodology is not particularly well suited to modeling events that occur repetitively over time, or to analyzing interventions that alter the risk of future events. Such problems are more appropriately structured using methods that explicitly include the element of time. One such technique is the Markov process. Markov models are an extremely powerful complement to decision analysis for expanding the types and complexity of clinical situations that can be effectively analyzed [12]. Complex models of underlying physiologic processes have been incorporated into decision models, allowing a clinically realistic representation of the disease process [13].

Linking decision analysis with cost analysis — Decision models are often used as the analytic "engine" to conduct cost-effectiveness analyses since decision analysis methodology can be used to find the expected value of most any outcome. Cost-effectiveness analysis is a methodology that examines the simultaneous effect of different strategies upon clinical and economic outcomes. (See "A short primer on cost-effectiveness analysis".)

By including both costs and clinical effects in one model, analyses can provide estimates of the cost per year of life saved, the cost per quality-adjusted life year saved, etc.

RESOURCES — Two professional societies, the Society for Medical Decision Making and the Professional Society for Health Economics and Outcomes Research, developed a series of position papers outlining good research practices for using decision models to address problems in health care. Although not a primer, they are an excellent resource for the appropriate use of modeling methodologies. These resources provide an overview of the following aspects of decision analysis:

Decision modeling [14]

Conceptualizing a decision problem and a model [15]

Constructing state transition models [16]

Discrete event simulation models [17]

Dynamic transmission models [18]

Estimating the values of model parameters and including uncertainty [19]

Validating models [20]

SUMMARY

What is decision analysis? – Decision analysis is a quantitative evaluation of the outcomes that result from a set of choices in a specific clinical situation. It is similar in many ways to the qualitative assessments clinicians make every day in the clinical decision-making process. (See 'Introduction' above.)

What types of questions does decision analysis address? – The range of clinical questions appropriate for decision analysis is vast. The two major requirements for its use include (see 'Types of questions appropriate for decision analysis' above):

The question focuses upon a specific decision that must be made

There is a tradeoff involved in the decision

How is decision analysis conducted? – Decision analysis is performed using estimates of probabilities of events and values placed on outcomes. These outcomes may include patient values such as quality-adjusted life years or rates of events such as death. (See 'Conducting a decision analysis of a specific problem' above.)

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Topic 2758 Version 19.0

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