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Assignment
Decision Analysis and
Markov Modeling
Pharmacoeconomics
Fatma Adel Soliman
20142995;Fatma Adel
Soliman
Fall 2017
Course Coordinator: Dr. Hany Aboutabl
Faculty of Pharmaceutical Sciences & Pharmaceutical Industries
Level 4_Group C

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What is decision analysis?
Decision analysis is the application of an analytical
method for systematically comparing different decision
options.
Decision analysis graphically displays choices and
facilitates the calculation of values needed to compare
these options.
It assists with selecting the best or most cost-effective
alternative.
Decision analysis is a tool that has been used for years
in many fields. This method of analysis assists in
making decisions when the decision is complex and
there is uncertainty about some of the information.
Steps in decision analysis
The steps in the decision process are relatively
straightforward, especially with the availability of
computer programs that greatly simplify the
calculations.
Articles reporting a decision analysis should include a
graphical depiction (decision tree) of the choices and
outcomes of interest.

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Step 1: Identify the Specific Decision
The specific decision to be evaluated should be clearly
defined by answering the questions: What is the
objective of the study? Over what period of time will
the analysis be conducted (e.g., the episode of care, a
year)? Will the perspective be that of the patient, the
medical care plan, an institution or organization, or
society? For the example problem, the decision is
whether to add a new antibiotic to an institutional
formulary to treat infections.
The perspective is that of the institution, and the time
period of interest is the episode of care (about 2
weeks).
Step 2: Specify Alternatives
Ideally, the most effective treatments or alternatives
should be compared. In pharmacotherapy evaluations,
makers of innovative new products may compare or
measure themselves against a standard (i.e., older,
more well-established) therapy.
This is most often the case with new chemical entities.
Decision analysis could compare more than two
treatment options (e.g., it could compare the five most

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common strains) or an intervention versus no
intervention (e.g., a diabetes clinic versus no clinic).
For the example problem, the use of the new
medication (antibiotic A) will be compared with that of
the current standard (antibiotic B).
Step 3: Draw the Decision Analysis Structure
Lines are drawn to joint decision points (branches or
arms of a decision tree), represented as choice nodes,
chance nodes, or terminal (final outcome) nodes.
Nodes are places in the decision tree where different
options occur; branching becomes possible at this
point. There are three types of nodes:
1. In a choice node, a choice is allowed (e.g.,
treatment A versus treatment B);
2. In a chance node, chance comes into the equation
(e.g., the chance or probability of cure or adverse
events for different treatment options); and
3. In a terminal node, the final outcome of interest
for each option in the decision is presented. The
units used to measure final outcomes (e.g., dollars
or quality-adjusted life years [QALYs] must be the
same for each option being considered. By
convention, software programs use a square box

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to represent a choice node, a circle to represent a
chance node, and a triangle for a terminal branch
or final outcome.
Decision tree structure for the antibiotic example
Terminal
Node
Chance
Node
Choice
Node

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Step 4: Specify Possible Costs, Outcomes, and
Probabilities
For each option, information should be obtained for
the probability of occurrence and the consequences of
the occurrence. Probabilities are assigned for each
branch of the chance nodes, and the sum of the
probabilities for each branch must add up to 1.00.
Consequences are reported as monetary outcomes,
health-related outcomes, or both. Decision analysis
articles should provide a listing of the probability, cost,
and outcome estimates used in the analysis, including
where or how the estimates were obtained (e.g.,
literature review, clinical trial, expert panel).
Estimates for the antibiotic example

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Step 5: Perform Calculations
At each terminal node, the probability of a patient
having that outcome is calculated by multiplying the
probability of each arm from the choice node to the
terminal node. The total costs for each terminal node
are calculated by adding up the costs over all of the
branches from the choice node to the terminal node.
The product of the costs multiplied by the probability
(C * P) is calculated for each node and then summed
for each option.
Average cost per treatment choice for the antibiotic example

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Calculations for the antibiotic example
These calculations show that antibiotic B is less
expensive even when including the costs of treating
adverse events. But because antibiotic A is a better
clinical option (higher probability of success and lower
probability of adverse events), decision makers could
use either the incremental cost-effectiveness ratio
(ICER) to determine whether to add antibiotic A to the
formulary.
outcome Cost
($)
Probability Cost * Probability
($)
Antibiotic A
Success ith no ad erse
e ents
$600 0.81 $486
Success ith ad erse e ents $1,600 . $
Failure ith no ad erse e ents $ . $
Failure ith ad erse e ents $ , . $
Total for antibiotic A $
Antibiotic B
Success ith no ad erse
e ents
$ . $
Success ith ad erse e ents $ , . $
Failure ith no ad erse e ents $ . $
Failure ith ad erse e ents $ , . $
Total for antibiotic B 1 $

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Sensitivity analysis for the antibiotic example
Step 6: Conduct a Sensitivity Analysis
Sensitivity analysis involves recalculating the cost
estimate with different quantitative values for selected
input values, or parameters, in order to compare the
results with the original estimate. If a small change in
the value of a cost element’s parameter or assumption
yields a large change in the overall cost estimate, the
results are considered sensitive to that parameter or
assumption.

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Markov Modeling
A Markov Model is a stochastic model which models
temporal or sequential data, i.e., data that are ordered.
It provides a way to model the dependencies of current
information (e.g. weather) with previous information.
It is composed of states, transition scheme between
states, and emission of outputs (discrete or
continuous).
• Several goals can be accomplished by using
Markov models:
1. Learn statistics of sequential data.
2. Do prediction or estimation.
3. Recognize patterns.
When Markov Modeling may be Useful
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.
Markov analysis allows for a more accurate
presentation of these complex scenarios that occurs
over a number of cycles, or intervals.

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Bubble diagram for the diabetes example
Steps in Markov Modeling
There are five steps for Markov Modeling:
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.
IGT=Impared Glucose Tolerance DM = Diabetes Mellitis

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Dead
Absorbing
state
Step 2: Determine Transitions
Next, possible transitions between states are
determined based on clinical information. Can patients
move (i.e., transition) from one health state to another?
For example, if the patient dies, this called an
absorbing state.
An absorbing state indicates that the patient cannot
move to another health state in later cycle.
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.
Well
Sick
0.10
0.70
0.20
0.60
0.40

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Step 3: Choose Length and Number of Cycles
The cycle length depends on the disease being
modeled. For the diabetes example, five 1-year cycles
were used to determine the impact of the diet and
exercise program on progression to diabetes.
Step 4: Estimate Transition Probabilities
Transition probabilities are used to estimate the
percent of patients who are likely to move from one
health state to another during each cycle. These
probability values come from previous research or
expert panel estimates.
For diabetes example;
For patients who did not receive the
specific diet and exercise program,
there was 10% probability per year
(cycle) that they would transition
from IGT to DM (90% would stay in the IGT
state).
IGT
DM
Absorbing
state
0.10
0.90

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For patients who received the
program, the probability of DM was
reduced to 5% per year (95% would
stay in the IGT state).
Step 5: Calculate Costs and Outcomes
Outcomes for each health state should be estimated
and given a value. If the outcome of interest is years of
life gained or saved and each cycle is for 1 year, then
each person who is alive during a cycle gets a value of
1.0 as his or her outcome for that cycle.
IGT
DM
Absorbing
state
0.95
0.05

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The Advantages and Disadvantages of Markov
Modeling
Advantages
1. Its great flexibility in expressing dynamic system
behavior.
2. Can Model most kinds of system behavior that can be
modeled by combinatorial models (i.e. Reliability block
diagrams, fault trees, etc).
Disadvantages
1. Can be more complex than simple decision trees and
therefore less transparent to decision makers.
2. It is "memoryless" because the markovian assumption is
that the probability of moving from state to state is not
based on the previous experiences from former cycles.
3. In practice, a patient's medical history is an important
determinant in the probability of his or her future health.
4. More advanced and complex computations, such as using
tunnel states, allow for integration of health experiences
from previous cycles.
5. The data needed to estimate probabilities and costs,
especially in the long term, are often unavailable. Most
clinical studies measure outcomes for a short time, and
extrapolation into the future may compound errors in
estimates.