Pharmacoeconomics & Health OutcomesPharmacoeconomics & Health Outcomes

Decision Analysis Part 1

Leon E. Cosler, R.Ph., Ph.D.Associate Professor of Pharmacoeconomics

Albany College of Pharmacy

Road Map: Decision Analysis Road Map: Decision Analysis

1. Describe the steps involved

2. Construct a decision tree analysis

3. Use and interpret the results

Where’s he getting this?

• Text chapter 8

Decision Analysis Decision Analysis

• A quantitative approach to decision making

• Uses a diagram for choices and outcomes

• Quantifies uncertain events

• Imposes logical thinking

• Method used “inside” CEA, CUA, etc.

• Emphasis on ‘expected values’

Decision Analysis: History Decision Analysis: History

• WW II military applications• allocation of scarce resources

• 1970’s + in medical / health literature

• 1987: >200 published medical studies

• 1995: 81 articles for Rx products

• 2008: 21,840 PubMed hits in the last 5 years

““Expected” ValuesExpected” Values

• In probability theory the expected value of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value").

• It represents the average amount one "expects" as the outcome of the random trial when identical odds are repeated many times.

• The expected value itself may be unlikely or even impossible (ex. Dice)

• These strategies are used in gambling, attempts at

medical therapies, or other problem solving situations.

Expected Value of rolling 1 die:Expected Value of rolling 1 die:Expected Value:

Face ValueChances or

probability (as ratio)

Chances or probability (as

decimal)

"Expected Values"

1 x 1/6 0.167 = 0.1672 x 1/6 0.167 = 0.3333 x 1/6 0.167 = 0.5004 x 1/6 0.167 = 0.6675 x 1/6 0.167 = 0.8336 x 1/6 0.167 = 1.000

Expected Value (Σ): 3.500

Expected Value of rolling 2 dice:Expected Value of rolling 2 dice:

Expected Value:

Sum of 2 dice:

Chances or probability (as ratio)

Chances or probability

(as decimal)

"Expected Values"

2 x 1 / 36 0.028 = 0.056 1+13 x 2 / 36 0.056 = 0.167 1+2 2+14 x 3 / 36 0.083 = 0.333 1+3 3+1 2+25 x 4 / 36 0.111 = 0.556 1+4 4+1 2+3 3+26 x 5 / 36 0.139 = 0.833 1+5 5+1 2+4 4+2 3+37 x 6 / 36 0.167 = 1.167 1+6 6+1 2+5 5+2 3+4 4+38 x 5 / 36 0.139 = 1.111 2+6 6+2 3+5 5+3 4+49 x 4 / 36 0.111 = 1.000 3+6 6+3 4+5 5+4

10 x 3 / 36 0.083 = 0.833 4+6 6+4 5+511 x 2 / 36 0.056 = 0.611 6+5 5+612 x 1 / 36 0.028 = 0.333 6+6

Expected Value (Σ): 7.000

Possible Combinations of 2 dice:

Expected ValuesExpected Values

Expected ValuesExpected ValuesValue ("Payoff") Probability

0.01$ X 0.0385 ( 1 / 26) = 0.0004$ 1.00$ X 0.0385 = 0.0385$ 5.00$ X 0.0385 = 0.1923$

10.00$ X 0.0385 = 0.3846$ 25.00$ X 0.0385 = 0.9615$ 50.00$ X 0.0385 = 1.9231$ 75.00$ X 0.0385 = 2.8846$

100.00$ X 0.0385 = 3.8462$ 200.00$ X 0.0385 = 7.6923$ 300.00$ X 0.0385 = 11.5385$ 400.00$ X 0.0385 = 15.3846$ 500.00$ X 0.0385 = 19.2308$ 750.00$ X 0.0385 = 28.8462$

1,000.00$ X 0.0385 = 38.4615$ 5,000.00$ X 0.0385 = 192.3077$

10,000.00$ X 0.0385 = 384.6154$ 25,000.00$ X 0.0385 = 961.5385$ 50,000.00$ X 0.0385 = 1,923.0769$ 75,000.00$ X 0.0385 = 2,884.6154$

100,000.00$ X 0.0385 = 3,846.1538$ 200,000.00$ X 0.0385 = 7,692.3077$ 300,000.00$ X 0.0385 = 11,538.4615$ 400,000.00$ X 0.0385 = 15,384.6154$ 500,000.00$ X 0.0385 = 19,230.7692$ 750,000.00$ X 0.0385 = 28,846.1538$

1,000,000.00$ X 0.0385 = 38,461.5385$

∑ = 131,477.54$

Value ("Payoff") Probability0.01$ X 0.0400 ( 1 / 25) = 0.0004$ 1.00$ X 0.0400 = 0.0400$ 5.00$ X 0.0400 = 0.2000$

10.00$ X 0.0400 = 0.4000$ 25.00$ X 0.0400 = 1.0000$ 50.00$ X 0.0400 = 2.0000$ 75.00$ X 0.0400 = 3.0000$

100.00$ X 0.0400 = 4.0000$ 200.00$ X 0.0400 = 8.0000$ 300.00$ X 0.0400 = 12.0000$ 400.00$ X 0.0400 = 16.0000$ 500.00$ X 0.0400 = 20.0000$ 750.00$ X 0.0400 = 30.0000$

1,000.00$ X 0.0400 = 40.0000$ 5,000.00$ X 0.0400 = 200.0000$

10,000.00$ X 0.0400 = 400.0000$ 25,000.00$ X 0.0400 = 1,000.0000$ 50,000.00$ X 0.0400 = 2,000.0000$ 75,000.00$ X 0.0400 = 3,000.0000$

100,000.00$ X 0.0400 = 4,000.0000$ 200,000.00$ X 0.0400 = 8,000.0000$ 300,000.00$ X 0.0400 = 12,000.0000$ 400,000.00$ X 0.0400 = 16,000.0000$ 500,000.00$ X 0.0000 = -$ 750,000.00$ X 0.0400 = 30,000.0000$

1,000,000.00$ X 0.0400 = 40,000.0000$

∑ = 116,736.64$

Important symbols:Important symbols:

A “choice” node: what follows is result of a decision

A “chance” node:

what follows is uncertain &

requires probabilities

STARTHERE TIME

Decision Analysis StepsDecision Analysis Steps

1: Identify a decision which needs to be made

2: Diagram the decision & all plausible results

- diagram consequences over time

- include probabilities for each result

- calculate “expected values” for each decision

- identify the preferred alternative

MATH ...MATH ...

Example 1Example 1

Patients with medical condition ‘X’ have two choices for initial treatment:

a.) surgery or b.) Rx therapy.

If, after 3 months of Rx therapy, there is no improvement; patients will then get surgery.

Assumptions:

a. the surgery is 100% effective in all cases

b. the Rx treatment has no adverse effects; but is only 90% effective

c. the following cost data apply to each treatment

Treatment Effectiveness Direct Costs

Surgery 100% $100,000

Drug 90% $250 per month

Example 1Example 1

Goal:• What is the ‘average’ or ‘expected’ treatment cost per patient

for patients treated with:

• a.) Rx therapy or b.) Surgery

Decision Analysis Decision Analysis (“Cosler method”)(“Cosler method”)

1

2

3

$ ???,???

$ ???,???

$ ???,???

?? %

?? %

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$ ???

$ ???

$ ???

Decision Analysis Decision Analysis (“Cosler method”)(“Cosler method”)

1

2

3

$ 100,750

$ 750

$ 100000

10 %

90 %

100 %

$ 10075

$ 675

$ 100000

RXIneffective P=0.1 Surgery

P=1.0

Effective P=0.9

surgery P=1.0

Total: 100%

Total: 100%

10,750

100,000

Decision Analysis Worksheet #1Decision Analysis Worksheet #11

2

3

Example 1 Decision AnalysisExample 1 Decision Analysis

?

?

Decision Analysis: Example 2Decision Analysis: Example 2

Consider whether or not to give Ab prophylaxis after c-sect to reduce post-partum infection (endometritis). A normal c-section results in a 3 day stay. If infection occurs, it results in an additional 4 days in the hospital. There are no other significant implications for using the antibiotic (no allergic reactions, etc.)

- What is the expected cost per patientfor pts with Ab Tx and without Ab Tx?

Decision Analysis: Example 2Decision Analysis: Example 2

Utilization Data Cost Length of Stay

Antibiotic Prophylaxis: 300$ Normal C-section 7,000$ 3 daysEndometritis 8,000$ 4 days

Probabilities:Endometritis with no Ab: 25%Endometritis with Ab: 8%

- What is the expected cost per patientfor pts with Ab Tx and without Ab Tx?

Example 2: Decision AnalysisExample 2: Decision Analysis

prophylax

No prophylax

Decision AnalysisDecision Analysis

Prophylaxis

NoProphylaxis

Decision AnalysisDecision Analysis

Prophylaxis

NoProphylaxis

92%

8 %

75 %

25 %

15,300

7000

15000

$ 6716

1224

7942

5250

3750

9000

Infection will not occur

Infection will occur

Infection will occur

Infection will not occur

P=0.08

P=0.02

P=0.25

P=0.75

7300

That’s all for today… !That’s all for today… !

Decision Analysis Decision Analysis (“Cosler method”)(“Cosler method”)

1

2

3

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