Performing a Cost-Benefit Analysis Using Markov Modeling
Assignment: Performing a Cost-Benefit Analysis Using Markov Modeling Directions · Rascati, Chapter 10, questions 1-5, pg. 221-223 Please be sure to complete the table and show both the non-discounted AND discounted costs in each cycle so you may receive full credit for this problem. Hint: You shouldn't have fractions of a patient in your Markov model, so round the number of patients to the nearest whole number: 10.5 would be 11 patients, and 10.4 would be 10 patients. Second hint: So that you can be sure you are making your calculations correctly, I'm providing the answer to question #1: Total cost of the Prevention Coaching Program is $70,000 with no discounting; $61,756 with 5% discount rate. Question #3: In a CBA, a benefit-to-cost ratio is calculated for a single intervention, which is different from a CEA or CUA where one ICER is calculated for two competing alternatives. In this problem, the intervention for which you are being asked to calculate a benefit-to-cost ratio is the coaching program. The cost, or "input," is the cost of the coaching program. The benefit, or "output," is the cost savings produced by coaching program, which is the savings (reduction) in medication cost when the coaching program is implemented (vs. not using the coaching program). You are being asked to calculate the benefit-to-cost ratio of the coaching program two times: once without discounting and once with discounting. So for question #3, you need to give two answers to this question. Error in homework question in e-book rental: It's been brought to my attention that there is a typo in a rental e-book. (The e-books available free through our library do NOT have this typo). Chapter 10, Question 2, the medication and total cost in cycle 3 without coaching program should be $18,000, not $18,500. Grading · Questions 1 - 3 are worth two points each · Questions 4 & 5 are worth one point each Rubric Chapter 10: Markov Modeling Chapter 10: Markov Modeling Criteria Ratings Pts This criterion is linked to a Learning OutcomeQuestion 1 Complete the table and provide the following: (a) Total costs (with units labeled) for patients in coaching group when no discounting is performed, and (b) Total costs (with units labeled) for patients in coaching group when 5% discounting is performed (beginning in cycle 2). 2.0 pts This criterion is linked to a Learning OutcomeQuestion 2 Complete the table and provide the following: (a) Total costs (with units labeled) for patients in the control group when no discounting is performed, and (b) Total costs (with units labeled) for patients in the control group when 5% discounting is performed (beginning in cycle 2). 2.0 pts This criterion is linked to a Learning OutcomeQuestion 3 Calculate the benefit-to-cost ratio of the program with AND without discounting with units labeled (partial credit available if work shown). 2.0 pts This criterion is linked to a Learning OutcomeQuestion 4 Explain in complete sentences if using a half-cycle correction is appropriate in this example. 1.0 pts This criterion is linked to a Learning OutcomeQuestion 5 Describe in complete sentences what other costs and outcomes would be included in a more clinically relevant (and more complex) model. 1.0 pts This criterion is linked to a Learning OutcomeTimeliness 10% point deduction for each day late. 0.0 pts Total Points: 8.0 193 ✦ Overview In Chapter 9, relatively simple models and short-term health consequences were presented. For many diseases and conditions, more complex outcomes and longer follow-up periods need to be modeled. For these analyses, patients may move back and forth, or transition, between health states over periods of time.1–4 For exam- ple, a patient who has a blood clot (embolism) may be given a blood thinner (anti- coagulant) to reduce the risk of further embolisms. Three possible health states are the patient dies from the embolism, the patient has blood-related problems from the medications (e.g., internal bleeding), or the patient lives with no complications or side effects. Outcomes past this initial health state can be followed further to see whether patients develop future embolisms or future internal bleeding. Each follow-up interval is called a cycle, the time period that is determined to be clini- cally relevant to the specific disease or condition. Markov analysis allows for a more accurate presentation of these complex scenarios that occur over a number of cycles, or intervals. ✦ StepS in MarkOv MOdeling There are five steps for Markov modeling: (1) choose the health states that repre- sent the possible outcomes from each intervention; (2) determine possible transi- tions between health states; (3) choose how long each cycle should be and how many cycles will be analyzed; (4) estimate the probabilities associated with moving Markov Modeling Objectives Upon completing this chapter, the reader will be able to: 1. Explain when Markov modeling may be useful. 2. List the steps in Markov modeling. 3. Interpret a pictorial representation of a Markov model. 4. Explain the advantages and disadvantages of Markov modeling. Chapter 10 194 Part II • AdvAnced Topics (i.e., transitioning) in and out of health states; and (5) estimate the costs and out- comes associated with each option.1 Each step is discussed in this chapter using a general example (Fig. 10.1) and a more specific diabetes mellitus (DM) example (Fig. 10.2). The DM analysis will model the cost-effectiveness of using a speci- fied diet and exercise plan to increase the length of time that prediabetic patients (impaired glucose tolerance [IGT] is plasma glucose >140 to <200 mg/dl="" 2="" hours="" after="" glucose="" challenge)="" avoid="" the="" transition="" to="" dm="" (plasma="" glucose="">200 mg/dL 2 hours after glucose challenge). For the DM example, patients are followed up for Cycle 1 1.00 0 0 1.00 1.00 1.00 1.00 0.70 0.20 0.10 0.90 1.90 0.80 1.80 0.49 0.26 0.25 0.75 2.65 0.62 2.42 0.34 0.26 0.40 0.60 3.25 0.47 2.89 0.00 0.00 1.00 0 4.99 0 4.16 Well Sick Dead Percent Well Percent Sick Percent Dead Life Years Per Cycle Total Life Years QALY Per Cycle Total QALY Cycle 2 Well Sick Dead Cycle 3 Well Sick Dead Cycle 4 Well Sick Dead Cycle 20 Well Sick Dead Example Calculations: Cycle 1 to Cycle 2 70% of 100% stay well = 70% well 20% of 100% get sick = 20% sick 10% of 100% die = 10% dead Cycle 2 to Cycle 3 70% of 70% stay well = 49% well 20% of 70% (14%) get sick plus 60% of 20% stay sick (12%) = 26% sick 10% of 70% (7%) die plus 40% of 20% (8%) die + 100% of 10% (10%) stay dead = 25% dead Cycle 3 to Cycle 4 70% of 49% stay well = 34% well 20% of 49% (10%) get sick plus 60% of 26% (16%) stay sick = 26% sick 10% of 49% (5%) die plus 40% of 26% (10%) die + 100% of 25% stay dead (25%) = 40% dead QALY Calculations Cycle 1 = 100% * 1.0 QALY = 1.00 QALY Cycle 2 = (70% * 1.0 QALY) + 20% (0.5 QALY) + 10% (0 QALY) = 0.80 QALY Cycle 3 = (49% * 1.0 QALY) + 26% (0.5 QALY) + 25% (0 QALY) = 0.62 QALY Cycle 4 = (34% * 1.0 QALY) + 26% (0.5 QALY) + 40% (0 QALY) = 0.47 QALY FIGURE 10.1. Bubble diagram for a general Markov model. chapter 10 • MArkov Modeling 195 Cycle 1 Without Diet and Exercise Program 1.00 0.00 1.00 1.00 0.90 0.10 0.90 1.90 0.81 0.19 0.81 2.71 0.73 0.27 0.73 3.44 0.66 0.34 0.66 4.10 IGT DM IGT DM IGT DM IGT DM IGT DM Years IGT per Cycle Total Years IGT Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 1 With Diet and Exercise Program 1.00 0.00 1.00 1.00 0.95 0.05 0.95 1.95 0.90 0.10 0.90 2.85 0.86 0.14 0.86 3.71 0.81 0.19 0.81 4.52 IGT DM IGT DM IGT DM IGT DM IGT DM Years IGT per Cycle Total Years IGT Cycle 2 Cycle 3 Cycle 4 Cycle 5 FIGURE 10.2. Bubble diagram for the diabetes example. IGT 5 Impared Glucose Tolerance DM 5 Diabetes Mellitis. 196 Part II • AdvAnced Topics 5 years, and it is assumed that none of the patients die during this time frame. The cost of the diet and exercise program is $300 per year. (Estimates and probabilities for this example are used for illustrative purposes only. Published research articles should indicate how these estimates were derived.) Step 1: Choose Health States First, a delineation of mutually exclusive health states should be determined by listing different scenarios a patient might reasonably experience. These are referred to as Markov states. Patients cannot be in more than one health state during each cycle. A simple general example is “well, sick, or dead.” Graphically, by convention, each health state is placed in an oval or circle in a bubble diagram (Fig. 10.1). Time cycles are depicted on the left of the graph. For the DM example, we are concerned with two health states: IGT and DM (Fig. 10.2). A more complex Markov model is illustrated in Example 10.1. Step 2: determine transitions Next, possible transitions between states are determined based on clinical infor- mation. Can patients move (i.e., transition) from one health state to another? For example, if the patient dies, this is called an absorbing state. An absorb- ing state indicates that patients cannot move to another health state in a later cycle. Graphically, arrows are used to indicate which transitions are allowed. In the general example given in Figure 10.1, we assume that everyone starts out in the well state. For cycle 1, each patient can stay well, or can move to the sick or dead states. For the next cycle, patients in the well state can again stay well or move to the sick or dead states. Those in the dead state cannot move back to the other two states. Depending on the disease of interest, patients may or may not be able to move back to the well state after being in the sick state. For example, if a patient gets sick from an infection, it is likely that he or she can recover