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Appendix H Definitions and Examples of Operational Systems Engineering Tools and Concepts Agent-based models: See definition of simulation models below. Bayesian networks are probabilistic graphical models that describe v ­ ariables of interest and possible relationships (e.g., a patient’s true medical status, field experience, test results, pre-existing status) and their probabilistic interdependencies. Bayesian networks encode probabilistic relationships among variables and account for circumstances in which data are missing and can be used to discover causal relationships (e.g., the relationship between symptoms and diseases). They are a good method for combining prior knowledge and newly collected data. Bayesian decision trees: See definition of decision trees below. Cellular automata (CA) models: See definition of simulation models below. Cognitive task analysis is a method of identifying the cognitive de- mands on a user’s cognitive resources (e.g., memory, attention, and deci- sion making) from various aspects of system designs. This type of analy- sis is a way of looking at a system from the point of view of users and determining the thought processes that users follow to perform specific tasks. The information gained from such an analysis can help designers 169

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170 Systems Engineering to Improve Traumatic Brain Injury CARE and users to focus on system features that users find hard to learn and to identify the points at which cognitive challenges might arise. Decision-tree analysis is a tool that enumerates all possible outcomes of different choices in a given situation and computes the most likely result(s) of each. The purpose is to help a decision maker choose among decision options and to identify the strategy most likely to reach a particular goal. A decision tree takes the form of a graph with tree-like branches that shows all of the possible consequences of each decision option—including the probability, resource cost, and utility. In short, decision trees are visual and analytical decision-support tools for calcu- lating the expected values (or utility) of competing alternatives. Bayesian decision trees are a more advanced method that incor- porates Bayesian networks into decision trees in order to account for uncertainties in the values and outcomes of decisions. Decision trees are also closely related to influence diagrams (see below). Discrete-event models: See definition of simulation models below. Fuzzy logic models are predictive or control models developed from fuzzy set theory that deal with reasoning and relationships that are ap- proximate, approximately known, or estimated (rather than precise). Similar conceptually to probability theory (but different mathemati- cally), fuzzy set theory is based on a graduated valuation of the degree of “membership” in various elements in a set (e.g., as a patient’s screening test score increases, his or her degree of membership for a particular level of traumatic brain injury [TBI] severity rises or falls). The extent to which each element is true is described with a membership function valued on the (0, 1) interval. In fuzzy logic, the degree of truth of a state- ment ranges from 0 to 1 and is not constrained to the two truth values (e.g., does or does not have mild TBI [mTBI]). For example, fuzzy logic predictive models can assimilate “degrees of truth,” or membership v ­ alues, based on the results of screening tests to determine the most likely “state” (or status) of a patient. Influence diagrams (also called decision networks) are compact graphi- cal and mathematical representations of a decision situation (in a sense, they are generalizations of Bayesian networks) in probabilistic inference problems and decision-making problems. Influence diagrams are a

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appendix H 171 tool for identifying and displaying the essential elements of a decision problem (e.g., decisions, uncertainties, and objectives) and how they influence each other. Judgment models are a qualitative approach to making estimates based on consultation with one or more experts who have experience in the problem domain. For example, an expert-consensus mechanism, such as the Delphi technique, might be used to estimate the likelihood that a patient with a certain combination of presenting conditions does in fact have mTBI. Markov chain models are stochastic processes in which a system (e.g., a patient or facility) transitions among a series of states (e.g., a patient being healthy, mildly sick, extremely sick, or dead; or a facility being empty, at half capacity, or full) and the Markovian (or “memoryless”) property exists. The memoryless property means that the conditional probability of the system being in any given state in the future depends only upon its present state and is independent of any past states. (More advanced types of Markov chains can include several past states in the transition probabilities, but are memoryless beyond that amount of history.) Future states are reached by transitioning from one state to another with certain probabilities, rather than deterministically or with certainty. For example, given today’s weather (state i at time t), tomor- row (time t + 1) it will be raining, cloudy, or clear j (j = 1, 2, 3) with defined transition probabilities pi,j. At each step, the system may change from its current state to another state or remain in the same state, ac- cording to these transition probabilities. Changes between states are called transitions, and the probabilities associated with these changes are called transition probabilities. Markov decision processes (MDPs) and Markov decision theory are extensions of Markov chains that provide a mathematical framework for modeling sequential decision making in situations in which outcomes are partly random (depending on actions or decisions by the decision maker). These models are often used to determine the optimal schedule of decisions, taking into account probabilistic events, demands, out- comes, and resource constraints. An MDP is a discrete-time stochastic control process characterized by a set of states (e.g., a patient’s condition or the number of patients in a facility) and random (stochastic) future

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172 Systems Engineering to Improve Traumatic Brain Injury CARE events. In each state, at discrete points in time, a decision maker can choose among several “control” actions (e.g., level of treatment, ­capacity expansion). For a current state, s, and an action, a, a state transition function, Pa(s), determines the transition probabilities to each of the next possible states. The decision maker often earns a reward or penalty for each state that actually occurs. The state transitions of an MDP have the memoryless property described above (given that the state of the MDP at time t is known, transition probabilities to a new state at time t + 1 are independent of all previous states or actions). Note that the differ- ence between Markov chains and MDPs is that MDPs include actions (allowing choice) and rewards (motivation). Mixed-integer programming (MIP) models are mathematical opti- mization models that minimize or maximize a specified objective func- tion, subject to a set of constraints (either linear or nonlinear); in MIP models, some of the decision variables are integers (e.g., the optimal number of facilities or medical personnel to locate in a given region). MIPs are heavily used in practice for solving problems in transportation and manufacturing, but they are also useful for some aspects of TBI care. For example, in a resource-location-allocation study, an MIP model was used to locate TBI treatment units in the Department of Veterans Affairs. The objective was to simultaneously determine optimal facility locations and the optimal assignment of patients to those facilities. Monte Carlo models: See definition of simulation models below. Partially observable Markov decision processes (POMDPs) are a variation of MDPs in which the current true state may not be known with certainty (e.g., a patient’s true TBI status); instead, decisions (e.g., treatment, removal from field) are made based on current knowledge about the current state. Sensitivity analysis is a general term for studying the impact on results of uncertainties in a model’s logic or data, such as how different values of an independent variable or different processing steps will impact results. Typically, sensitivity analyses are conducted on uncertain values to explore how much the impact of a decision or policy will (or will not) change under different assumptions. Sensitivity analyses can be conducted on an ad hoc basis or more scientifically, such as by using the

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appendix H 173 theory of experimental design. Sensitivity analyses can also be helpful for identifying the model assumptions that have the least (or most) impact on the results, which can be helpful when there are uncertainties in data. In particular, sensitivity analyses can help identify those data elements for which better estimates would be the most helpful and those that do not have to be specified very accurately in order to make a good decision. In this way, one can make better decisions about how to invest research time and money in the development, collection, and researching of data for a model. Signal-detection theory (SDT) is used to analyze and optimize situ- ations in which a decision is made that classifies ambiguous informa- tion (e.g., test results) into one of two categories (e.g., patient is sick or not) by trying to distinguish whether the observed result was created by the category of interest (called the signal in the SDT framework) or by random chance (called the noise). A common medical example is a blood test for a disease for which positive patients present with a range of numeric values and negative patients with a different range of values, but the ranges overlap—thus complicating the task of deciding whether a high result is a true “signal” or noise. SDT provides a mathematical framework for assessing such decisions—for quantifying the test’s ability to discriminate and for determining the optimal threshold for calling a patient positive or negative. Simulation models are computer models that emulate the logic of a process and use randomly generated data whenever a chance or ran- dom event (e.g., develops TBI, passes test, time durations) occurs in the model. Simulation models are very useful for studying the range of outcomes and most likely results of possible alternative process designs and courses of action. Such models often are used to analyze “what if ” situations (e.g., what if we did something this way instead of that), or they can be used as part of an optimization computer program to find an overall optimal solution. Because of the flexibility and utility of com- puter simulations, they are widely used in operations research. Several types of simulation models might be helpful in modeling TBI: • Discrete-event models are used to model the sequential/ran- dom flow of “things” (e.g., patients, personnel) through pro- cesses (e.g., the military field or the health care process), typically

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174 Systems Engineering to Improve Traumatic Brain Injury CARE with the patient requiring various services that require various r ­ esources for various amounts of time. A discrete-event model is often used to assess system design and optimize flow, capacity, resource requirements, policies, and so on. • Monte Carlo models are often used to analyze statistical prob- lems that are otherwise “difficult” to solve. An example might be a series of integrated screening tests in which decisions are made after each screening (e.g., to conduct the next test, remove the individual from the field, or redeploy the individual); the analyst might be interested in determining the overall cost and accuracy (sensitivity, specificity) of a given process or protocol. For example, Monte Carlo models have been used to analyze and optimize cancer screening decision processes. • Agent-based models are based on the idea of “agents” that r ­ epresent each autonomous or semi-autonomous decision maker who chooses his or her next action based on the current status of the surrounding environment. This type of model is often used to model wartime theaters and other engagement activities, but for TBI it might be used to model medical decision making. • Cellular automata (CA) models are used to model geographic movements in situations where the probability that a number of “things” (e.g., soldiers, patients) will move from their current grid locations to adjoining cells is dictated by the activities and state of affairs around them. CA models are widely used to model the spread of disease, species migration, forest fires, and other such events. For TBI, a CA model might be used to model the general geographic dispersal and flow of patients through different medi- cal states or physical locations. Value-stream analysis (VSA) is a tool used to evaluate all of the specific actions involved in a process, determine the relative value added of each action, and identify waste. VSA is often used to eliminate wasteful steps and create efficient processes comprising only value-added activities that maximize performance. With this type of analysis, one can separate a ­ ctivities that contribute to value creation from activities that create waste and then identify opportunities for improvement.