Decision Analysis. John M. Inadomi. Decision trees. Background. Key points Decision analysis is used to compare competing

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1 5 Decision Analysis John M. Inadomi Key points Decision analysis is used to compare competing strategies of management under conditions of uncertainty. Various methods may be employed to construct a decision model (decision tree, Markov model) and analyze the results (mean outcomes, Monte Carlo simulation, discrete event simulation). The results of decision analysis may assist policymakers to prioritize competing healthcare interventions, in addition to providing a framework to generate hypotheses for further research. Background Decision analysis is a research method designed to synthesize data in order to derive a summary conclusion [1]. The origins of decision analysis lie in game theory, historically associated with economics and business administration and subsequently extended to medical research [2,3]. In biomedical research, decision analysis is often used quantitatively to compare competing strategies of clinical management under conditions of uncertainty. The analysis generally consists of mathematical equations constructed to model idealized subjects or cohorts with various disease states, then superimposing different decision options. The results of these analyses may then be applied to individual patients or groups of patients to guide clinical decision-making and health policy [4 7]. This chapter will provide an overview of decision analysis and construct a framework by which one may intelligently critique studies that appear in published literature (Table 5.1). The intention is to allow the reader to become more familiar with the terminology, use, and limitations inherent with this form of research. Decision trees The most basic form of decision analysis is a decision tree. As with all good research, a relevant question must be formulated that identifies the specific problem to be solved. A hypothesis should then be generated in a form that can be tested by the analysis. It is important to format the question in a manner that provides the opportunity to retrieve reliable data with which one may populate the variables of the model. If the question is too broad, insufficient data sources will be available and the model will suffer from inadequate information. However, a question that is too limited in scope may not be generalizable to relevant populations. GI Epidemiology: Diseases and Clinical Methodology, Second Edition. Edited by Nicholas J. Talley et al. C 2014 John Wiley & Sons, Ltd, with the exception of original artwork which is C Mayo Foundation for Medical Education and Research. Published 2014 by John Wiley & Sons, Ltd. Companion website: 33

2 CHAPTER 5 Table 5.1 Description of various types of decision analysis methods Method Format Description Decision tree Linear model Model that initiates at a decision node then flows in a unidirectional fashion to chance nodes and terminal (outcome) nodes Markov model Recursive model Model that involves transitions between various health states in a time-dependent fashion, allowing repetitive movement between nodes Monte Carlo simulation Static, stochastic Form of analysis in which values for multiple variables are simultaneously varied. Inputs/outputs do not vary with time (static), but include random variation (stochastic) Discrete event simulation (beyond scope of chapter discussion) Dynamic, stochastic Form of analysis in which variables are simultaneously varied. Inputs vary over time (dynamic), with accounting for random variation After the clinical problem and hypothesis are defined, a clinical scenario is developed at the point where a decision to pursue one of several strategies must be made. From this point, defined as the decision node, two or more arms of the tree are drawn, each depicting a different strategy In the example shown in Fig. 5.1, the clinical decision to be made is: What is the best colorectal screening test? and four diagnostic testing strategies are presented. As it is likely that each strategy may result in numerous outcomes, this is depicted by the use of branching arms of each strategy. At each branch point, or chance node, the possibility of following an individual arm is set by the probability of achieving that outcome. Conventionally, the sequence is drawn from left to right, representing the progression of events in chronological order leading to the ultimate outcome of the analysis. Additionally, decision nodes are represented by squares, while chance nodes are designated by circles. Outcomes of the tree are the terminal events of the model, and can be years of life, death and morbidity, but also any other state of health or disease. Because the goal of therapy may not necessarily be solely to increase life expectancy, but rather to improve quality of life, decision analysis has incorporated the concept of utilities, or patient preferences, to adjust benefit to reflect the fact that some health states are preferred over others [8 12]. For example, a year of life in perfect health may be valued more highly than a similar amount of time undergoing chemotherapy, or time spent after sustaining a complication of an intervention that sustains life. Quality-adjusted life years (QALYs) use utilities to adjust the absolute gain or loss in life in an effort to reflect morbidities associated with various diseases and interventions [12]. As decision trees are generally designed to compare competing strategies of management, the difference in strategies in terms of life years or QALYs saved or lost may be calculated. Outcomes may also include monetary gains or losses. In this manner, the difference in costs between strategies may be compared, either alone or simultaneously with comparison of benefit, thus providing the basis for cost-effectiveness analysis, which will be covered in another chapter. Outcomes are generally denoted by boxes or triangles in a decision tree. After a clinical problem is identified and appropriately constructed in a model, such as a decision tree, information must be gathered to populate the variables in the tree. Specifically, values must be provided to indicate the probability of following each arm that emanates from a chance node in the model [13]. As it is desirable to use the best evidence to support the choice of value for each variable, a systematic review of the literature or meta-analysis should be performed for all variables [14]. Data retrieved through literature review should be examined for validity through evidence-based methods [14 21]. If multiple data sources are not available to provide sufficient information, expert opinion may be used although this method is less rigorous than the former. In all cases, the range of reasonable values for 34

3 DECISION ANALYSIS Colorectal screening test No screening FOBT Virtual colonoscopy Colonoscopy Figure 5.1 Decision tree comparing strategies to reduce mortality from colorectal. Examined strategies include: no screening, fecal occult blood testing (FOBT), colonoscopy, and virtual colonoscopy (VC). The tree begins with a decision node (square) and branches to the four competing strategies after which the potential outcomes of each strategy, including development, cure, or death from are modeled. In this idealized model, mortality from competing causes is not considered, nor are complications from diagnostic or therapeutic interventions. Each strategy leads to chance nodes (circles) at which point the probability of achieving each outcome is based on the value of the variables emanating from the node. The example assumes that in the absence of screening there is a 6% lifetime risk of developing colorectal, and 50% survive 0.50 survive survive survive of patients are assumed to die from their disease. FOBT is assumed to have an identical rate of development but a 25% relative risk reduction in mortality (50% [50% 25% = 12.5%] = 37.5% absolute mortality risk). Virtual (VC) and conventional colonoscopy (colonoscopy) are assumed to decrease incidence by 75% and 90%, respectively (1.5% and 0.6% incidence), and have similar benefit on detected mortality as FOBT. To simplify the example it is assumed that all patients who develop do so at age 65 years, and either die within one year or achieve normal life expectancy if cured of. In the absence of colorectal mortality, patients are assumed to live to age 80 years ( years of additional life expectancy). each variable must be entertained. A sensitivity analysis should be performed (see below) to determine whether variations in the initial assumptions of the model cause the conclusions of the analysis to change. After constructing the decision tree, defining outcomes and specifying values for the variables in the tree, the analysis may be performed. This is accomplished through folding back and averaging [1]. This process starts on the right side of the tree, with the outcomes boxes, and folds back to the left, finishing at the decision node. The value of each outcome is multiplied by the probability of achieving the outcome; these weighted values are then summed at the chance node that led to the outcomes. The process repeats from right to left, with each successive value at a chance node being multiplied by the probability 35

4 CHAPTER 5 Colorectal screening test No screening FOBT Colonoscopy: Virtual colonoscopy Colonoscopy Figure 5.2 The decision tree is analyzed by folding back and averaging. Starting from the right side of the tree, the value of each outcome is multiplied by the probability of achieving that outcome. This value is summed with the other weighted outcomes at the chance node leading to those outcomes. In turn, these values are weighted by the probability of following that branch of the tree and summed with other weighted outcomes at the next more survive survive survive survive.00; P = ; P = ; P = proximal (to the left in the tree) chance node. At the most proximal branch of each strategy there will be a single value representing the weighted sum of outcomes associated with that strategy. This value may be compared to the competing strategies at the decision node in order to determine the optimal strategy. In this case screening colonoscopy is modeled to produce the greatest number of life years. of getting to that node, and again summed with the other weighted values at the next more proximal chance node in the tree. At the most proximal chance nodes, just before (to the right) of the decision node, there will be a single value representing each arm or strategy modeled in the tree (Fig. 5.2). The optimal strategy is identified by comparison of the values associated with each strategy. Thus, in the analysis shown in Fig. 5.2, the optimal colorectal screening test is colonoscopy because this strategy yields the greatest number of life years (29.97) compared with strategies using virtual colonoscopy (29.92), fecal occult blood testing (FOBT) (29.68), or no screening (29.58). This comparisonrepresentsthebase-case scenario in which the initial assumptions of the model are utilized to calculate the outcome. Although the base-case scenario is usually presented first in a study, the most important step in the analysis is performance of a sensitivity analysis. By varying the values of each variable in the model, one may test the stability of the conclusions of the analysis and determine which variables contribute most heavily to the results. Sensitivity analyses may be performed by varying one or more variables simultaneously, using the range of reasonable values for each variable that was determined from the literature, or from expert opinion. If small changes in a variable cause the conclusion of the analysis to change, the model is said 36

5 DECISION ANALYSIS to be sensitive to that variable. An important goal of decision analysis is hypothesis generation if a model exhibits sensitivity to a particular variable, research should be pursued in an effort to define more precisely the value associated with that variable so as to establish more firmly the certainty of the conclusions of the analysis. If changing the values of other variables does not change the conclusions of the analysis, further research in these areas may be deemed less critical towards defining the optimal management. No Procedural complication Cancer Dead Markov models Note that in the example provided for decision trees, the age of diagnosis was assumed to be constant because age was not included as a variable in the model. Although it is possible to construct a tree in which the age of diagnosis varies, this requires addition of multiple additional branches to the tree increasing its complexity. In this situation, a more elegant solution is construction of a Markov model. This model may be used to answer research questions that examine transitions between various stages of health [22]. A Markov model is a recursive model, allowing movement back and forth between points in a model, unlike decision trees, which constrain movement to occur in one direction. Markov models may be preferred to decision trees when it is important to incorporate the impact of time in the simulation, thus identifying when events occur. In addition, Markov models provide a means by which to introduce more complex interactions between health states. Construction of a Markov model begins with identification of the health states that define a clinical scenario [1]. These include healthy, dead, and various states of disease. Second, allowable transitions from one state to another are drawn as arrows (Fig. 5.3). Some arrows may be bidirectional to illustrate the ability to move from one state to another and back again. Other arrows are unidirectional such as those leading to sink states, states that cannot be left once entered (i.e. death). Arrows may also indicate the ability to remain within a state. Third, a cycle length must be chosen to represent the amount of time that elapses during transitions between states. The cycle should be chosen to reflect the clinical scenario modeled and is generally equal to the minimum amount of time required when moving from one state of health to Figure 5.3 Markov model. The ovals represent the modeled health states, the arrows illustrate the possible transitions between health states that occur during each cycle of the model. In this example, patients who do not have may develop, may sustain a complication from an intervention to decrease mortality (e.g. a perforation during a screening colonoscopy) or die from non- causes. Similarly, patients in whom has developed may be cured of, sustain complications related to treatment or die of. The looped arrows indicate the possibility that patients may remain in a particular health state during subsequent cycles. another. Fourth, the values for variables representing the transitions are derived, usually from existing literature, as was described for the development of decision trees. Fifth, outcomes are defined for the analysis such as costs, life years or QALYs. Unlike decision trees where outcomes are calculated only at the conclusion of the analysis, outcomes for a Markov model may be accumulated over the duration of the model by assignment of incremental rewards to each health state. As a result, several advantages are acquired including the ability to allow clinical events to occur multiple times during the simulation, and application of discounting, which is used to reflect patients time preferences for receiving various outcomes. Markov models can be analyzed in several different ways. The standard method in medical research involves calculation of the mean outcomes of a hypothetical cohort of patients. Alternative methods include stochastic simulations such as Monte Carlo analysis, which will be briefly discussed, discrete event simulation, and matrix algebra, which is dealt with by more detailed papers on the subject [22,23]. Analysis of a hypothetical cohort is generally performed with 37

6 CHAPTER 5 assistance from computer programs, although the mathematical functions required are generally limited to multiplication and addition. The general scheme for analysis involves distribution of a hypothetical group of patients into the initial health states, according to the proportions appropriate for the question that is being asked. For every cycle, the hypothetical cohort is redistributed among various health states in a manner regulated by the transition rates specified in the model. Simply stated, a proportion of the cohort in a given state will exit that state and enter another state based on the rate established for that transition. Once all transitions into and out of each health state have been performed, outcomes for each cycle are reassigned. Outcomes may be costs, clinical events (gastrointestinal bleeds, s, surgeries, etc.) or life years proportioned to the cycle length, which may be further adjusted by utilities to derive QALYs. This process is repeated for each cycle specified by the investigator and the various outcomes are summed to calculate the results. For the base-case analysis, the results would be expressed as the mean or average expected outcomes such as the costs, number of s, or life years associated with each strategy. Additionally, comparison between strategies should be provided to estimate outcomes such as the mean number of s averted, life years gained or difference in costs between competing strategies. Markov models may also be analyzed using a specialized form of stochastic analysis known as a Monte Carlo simulation [24]. This is a multiple-way sensitivity analysis in which any or all of the variables in the model are varied simultaneously. Furthermore, the values for each variable may be randomly picked from a predefined distribution of possibilities that may be in the form of a normal, exponential, bimodal, or other distribution (second-order simulation). The model is run multiple times, each run using a different set of values for each variable. The use of distributions allows certain values to be chosen more frequently than others to represent a particular variable. The results of a Monte Carlo simulation include expected values and the range of outcomes in the form of a density function (such as the mean and 95% confidence intervals in the case of normal distributions), and thus give a more complete picture of the range of probable results of the analysis. Monte Carlo simulation uses variable inputs that do not vary over time, thus it is generally considered a static analysis. Discrete event simulation, in contrast, allows the model inputs to vary over the duration of the simulation period, and thus it is considered a dynamic analysis. Limitations of decision analysis It is important to understand the inherent limitations of decision analytic studies. Greatest among these is the reliance of models on the assumptions upon which they are constructed. Although assumptions are generally limited to the values assigned to variables in the model, they should also pertain to the structure of the model or the manner in which the various elements interact with each other. To examine the impact of base-case assumptions, rigorous sensitivity analysis is performed to test whether the model conclusions are robust to changes in the parameter estimates (values of variables in the model) or changes in the model structure. If clinically plausible changes in the value assigned to a variable result in differing conclusions, the model is stated to be sensitive to that variable. Sensitive variables are logical targets for further research, because they are identified to be important parameters required to define optimal management. Variables that are not associated with changes in outcome in sensitivity analysis are either well defined through previous research, or are less important in defining disease management. In this manner decision analysis fulfills one of its primary functions, which is hypothesis generation, or the identification of relevant research questions. Structural assumptions are necessary in order to simplify complex medical events but are more difficult to identify and test. The challenge of model construction is to include key variables relevant to the clinical question being raised while excluding less important ones. Simplification of real world events is essential and requires input from investigators who are experts in the field in question. Full disclosure of the model including parameter and structural assumptions is essential for validation of its conclusions. Despite its limitations, decision analysis remains an essential tool for health services and outcomes research. These techniques allow comparison of competing management strategies in a quantitative fashion, summarize existing literature into a single metric, and generate hypotheses based on the important factors governing clinical management. 38

7 DECISION ANALYSIS Conclusions Decision analysis is conducted to compare outcomes between competing strategies of management under conditions of uncertainty. A variety of tools, including decision trees and Markov models, have been adapted to biomedical research in order to calculate a quantitative summary of existing data concerning a research topic that may guide clinical decision-making and even health policy. Of potentially greater impact is the ability of these studies to generate hypotheses that inform future research efforts to optimize health benefits. References 1 Petitti DB. Meta-analysis, Decision analysis and Costeffectiveness Analysis. New York: Oxford University Press, Von Neumann J, Morgenstern O. Theory of Games and Economic Theory. New York: John Wiley & Sons, Henschke UK, Flehinger BJ. Decision theory in therapy. Cancer 1967;20: Pauker SG, Kassirer JP. Decision analysis. New Engl J Med 1987;3: Weinstein M, Fineberg H. Clinical Decision Analysis. Philadelphia: Saunders, SoxHC,etal.Medical Decision Making. Stoneham, MA: Butterworth, Kassirer JP. The principles of clinical decision making: an introduction to decision analysis. Yale J Biol Med 1976;49: Froberg DG, Kane RL. Methodology for measuring health-state preferences II: Scaling methods. J Clin Epidemiol 1989;42: Froberg DG, Kane RL. Methodology for measuring health-state preferences I: Measurement strategies. J Clin Epidemiol 1989;42: Froberg DG, Kane RL. Methodology for measuring health-state preferences IV: Progress and a research agenda. J Clin Epidemiol 1989;42: Froberg DG, Kane RL. Methodology for measuring health-state preferences III: Population and context effects. J Clin Epidemiol 1989;42: La Puma J, Lawlor EF. Quality-adjusted life-years. Ethical implications for physicians and policymakers. JAMA 1990;263: Richardson WS, Detsky AS. Users guides to the medical literature. VII. How to use a clinical decision analysis. A. Are the results of the study valid? Evidence-Based Medicine Working Group. JAMA 1995;273: Oxman AD, et al. Users guides to the medical literature. VI. How to use an overview. Evidence-Based Medicine Working Group. JAMA 1994;272: Guyatt GH, et al. Users guides to the medical literature. II. How to use an article about therapy or prevention. B. What were the results and will they help me in caring for my patients? Evidence-Based Medicine Working Group. JAMA 1994;271:59. Jaeschke R, et al. Users guides to the medical literature. III. How to use an article about a diagnostic test. B. What are the results and will they help me in caring for my patients? The Evidence-Based Medicine Working Group. JAMA 1994;271: Jaeschke R, et al. Users guides to the medical literature. III. How to use an article about a diagnostic test. A. Are the results of the study valid? Evidence-Based Medicine Working Group. JAMA 1994;271: Guyatt GH, et al. Users guides to the medical literature. II. How to use an article about therapy or prevention. A. Are the results of the study valid? Evidence-Based Medicine Working Group. JAMA 1993;270: Oxman AD, et al. Users guides to the medical literature. I. How to get started. The Evidence-Based Medicine Working Group. JAMA 1993;270: Laupacis A, et al. Users guides to the medical literature. V. How to use an article about prognosis. Evidence-Based Medicine Working Group. JAMA 1994;272: Levine M, et al. Users guides to the medical literature. IV. How to use an article about harm. Evidence-Based Medicine Working Group. JAMA 1994;271: Beck JR, Pauker SG. The Markov process in medical prognosis. Med Decis Making 1983;3: Platell CF, et al. Flexible sigmoidoscopy screening for colorectal neoplasia in average-risk people: evaluation of a five-year rescreening interval. Med J Aust 2002;176: Doubilet P, et al. Probabilistic sensitivity analysis using Monte Carlo simulation. A practical approach. Med Decis Making 1985;5: