The Bubilic Plague problem

What should you – as director of health for your city of 10 million people - to

manage this illness.

The problem:-

• A new disease – Bubilic Plague - has begun to inflict the people in your town. If untreated, the disease will kill. The illness shows no symptoms at an early stage so once people realize they are ill they need emergency treatment.

• There is a treatment available to cure the illness at an early stage (before symptoms show), but this costs.

• There is a very effective emergency treatment available to cure those who show symptoms and do not get treated at an early stage, but this costs a lot more!

• Fisser drugs have developed a test to see if people have the plague – it is very reasonably priced and they claim it is very reliable.

Your decision

• What should you do to manage this illness in your community– Provide early treatment to everyone?– Provide emergency treatment to those who get ill?– Test everyone and only treat those that the test

shows are ill?

• It’s your decision – and – as the illness can be treated with confidence, your decision criteria is minimum cost.

The facts

• 1% of the population will get the disease.• Fisser’s test is 99% accurate, and costs $1 per person

tested.• Early treatment costs $5 per person• Emergency treatment costs $100 per person who falls

ill.• You can provide early treatment to your family so the

fear of them falling ill doesn’t influence your decision.• The city auditor will expect you to provide a

thorough justification for your decision, whatever it is.

So – your decision is?

Sick?

Y0.01

N0.99

100 1.0000

Decide not to test – but treat thosewho fall ill .

0 0.0000

Average (Expected) Cost per person = 1.0000

Decide to provide early treatment to everybody

Average (Expected) Costper person = 5.0000

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.01

N0.99

+ve0.99

-ve0.01

-ve0.99

+ve0.01

6

101

6

1

0.0099

0.0594

0.0001

0.0101

0.0099

0.0594

0.9801

0.9801

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 1.1090

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.01

N0.99

+ve0.99

-ve0.01

-ve0.99

+ve0.01

6

101

6

1

0.0099

0.0594

0.0001

0.0101

0.0099

0.0594

0.9801

0.9801

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 1.1090

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.01

N0.99

+ve0.99

-ve0.01

-ve0.99

+ve0.01

6

1

0.0099

0.0001

0.0099

0.0594

0.9801

0.9801

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 1.1090

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.01

N0.99

+ve0.99

-ve0.01

-ve0.99

+ve0.01

6

101

6

1

0.0099

0.0001

0.0099

0.0594

0.9801

0.9801

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 1.1090

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.01

N0.99

+ve0.99

-ve0.01

-ve0.99

+ve0.01

6

101

6

1

0.0099

0.0594

0.0001

0.0101

0.0099

0.0594

0.9801

0.9801

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 1.1090

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.01

N0.99

+ve0.99

-ve0.01

-ve0.99

+ve0.01

6

101

6

1

0.0099

0.0594

0.0001

0.0101

0.0099

0.0594

0.9801

0.9801

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 1.1090

What if the test cost was $0.80?

• Would this change your decision?

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.01

N0.99

+ve0.99

-ve0.01

-ve0.99

+ve0.01

5.8

100.8

5.8

0.8

0.0099

.0574

0.0001

0.0101

0.0099

0.0574

0.9801

0.7841

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 0.9090

The new facts

• The disease is more common than first thought; 3% of the population will get the disease.

• Fisser’s test has been improved and is now 99.3% accurate, and costs have come down to $0 .75 per person tested.

• Early treatment still costs $5 per person• Emergency treatment has proven to be more difficult and

is now expected to cost $500 per person who falls ill.• You can vaccinate your family so you don’t need the fear

of them falling ill influence your decision.• The city auditor will still expect you to provide a

thorough justification for your decision, whatever it is.

Sick?

Y0.03

N0.97

500 15.0000

Decide not to test – but treat thosewho fall ill .

0 0.0000

Average (Expected) Cost per person = 15.0000

Decide to provide early treatment to everybody

Average (Expected) Costper person = 5.0000

Test

Sick?

Test

Test +ve

Test +ve

Test -ve

Test -ve

Y0.03

N0.97

+ve0.993

-ve0.007

-ve0.993

+ve0.007

5.75

500.75

5.75

0.75

0.02979

0.1713

0.00021

0.1052

0.00679

0.0390

0.96321

0.7224

Decide to test everybody and treat those the test says are ill.

Average (Expected) Cost per person = 1.0379

So – Has your decision changed?

How expensive does emergency treatment have to be before it

would be better to provide early treatment to everybody?

Exploration Well Example

• Cost of Exploration Well = $5mm (after tax)• Probability of finding oil (Ps) = 10%• If successful:

– Low case reserves = 0.1mm BO Probability = 0.25– Mid case reserves = 1.0mm BO Probability = 0.50– High case reserves = 10.0 mm BO Probability = 0.25

• Reserves determined by analysis of prospect by team of Geologists, Geophysicists, Petroleum Engineers and Facilities Engineers.

– Low case Oil Value = $5/ BO Probability= 0.25– Mid Case Oil Value = $10/ BO Probability = 0.50– High Case Oil Value = $15/ BO Probability = 0.25

• Oil value is the present day value of production, after taking into account all Operating and capital costs, all taxes, etc

Should we drill this well?

Drill?

No.

YesSuccess?

No0.90

Yes0.1

Reserves?

L0.25

M

0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

0.5

H0.25

Success?

No0.90

Yes0.1

Reserves?

L0.25

M

0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

0.5

H0.25

Probability for Branch

0.1*0.25*0.25 = 0.00625

0.1*0.25*0.25 = 0.00625

0.1*0.25*0.25 = 0.00625

0.1*0.25*0.25 = 0.00625

0.90

0.1*0.25*0.5 = 0.0125

0.1*0. 5*0.25 = 0.0125

0.1*0. 5*0.25 = 0.0125

0.1*0. 5*0.5 = 0.025

0.1*0.25*0.5 = 0.0125

Note: Probabilities for all uncertainty nodes must sum to 1.000

Uncertainty Node

1

2

3

4

5

6

7

8

9

10

Calculate Expected Value of all outcomes

– Sum these up to give Expected Value after exploration drilling

Branch Probability Reserves Oil ValueExpected Value

mmBO $/BO mm$1 0.0063 0.1 5 0.0032 0.0125 0.1 10 0.0133 0.0063 0.1 15 0.0094 0.0125 1 5 0.0635 0.0250 1 10 0.2506 0.0125 1 15 0.1887 0.0063 10 5 0.3138 0.0125 10 10 1.2509 0.0063 10 15 0.938

10 0.9000 0 10 0.0001.0000 3.025

Drill?

No.

YesSuccess?

No0.90

Yes0.1

Reserves?

L0.25

M

0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

0.5

H0.25

EV = $3.025mm

Drill?

No.

YesSuccess?

EV = $3.025mm

The Decision tree has been “Rolled Back” to give the value at the “Success” uncertainty node.

The cost of drilling the well is not included in this analysis yet.

If the option to drill is selected, the Expected Value would be -$5mm (the cost of the Exploration well) + $3.025mm ( the EV of the well if drilled)

As this is less than the alternative of not drilling, you SHOULD decide to not drill the well

-$5mm

$0mm

Top branch = -5+3.025= -1.975

Bottom Branch= 0

What Probability of success would justify drilling the well?

For a decision to drill, the value of the well needs to be greater than the cost

of the exploration well.

First work out the value of the well ASSUMING it is successful.

Reserves?

L0.25

M

0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

M0.5

H0.25

Value?

L0.25

0.5

H0.25

Probability for Branch

0.25*0.25 = 0.0625

0.25*0.25 = 0.0625

0.25*0.25 = 0.0625

0.25*0.25 = 0.0625

0.25*0.5 = 0. 125

0. 5*0.25 = 0.125

0. 5*0.25 = 0. 125

0. 5*0.5 = 0. 25

0.25*0.5 = 0. 125

1

2

3

4

5

6

7

8

9

Value of the well ASSUMING success

Branch Probability Reserves Oil ValueExpected Value

mmBO $/BO mm$1 0.0625 0.1 5 0.0312 0.1250 0.1 10 0.1253 0.0625 0.1 15 0.0944 0.1250 1 5 0.6255 0.2500 1 10 2.5006 0.1250 1 15 1.8757 0.0625 10 5 3.1258 0.1250 10 10 12.5009 0.0625 10 15 9.375

1.0000 30.250

Calculate the Probability of Success needed to justify drilling • Expected Value (EV) of the Well =

Probability of Success * EV of Success+ (1-Probability of Success)* EV of Failure

• In this case EV of failure is zero

• To justify drilling, the EV of the well must be equal to or greater than $5mm cost to drill the Exploration well.Ps* (EV)success => Expl Well Cost

• Ps => Expl Well cost / (EV) success= 5 / 30.25

= 0.1653