Darm exercise 3 J-P Männikkö
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Decision Analysis and Risk Management - 2011
25.3.2011 Calculation exercise Marko Tainio
Exercise 3
Story
City of Kuopio contacted you. They would like to hire someone to do decision analysis for the air pollution situation in Kuopio. The salary would be enormous.
Instead of interview, they will ask from you an example of your skills. The one that makes the best decision analysis model will be hired.
The test model should estimate the impact of decisions for the PM2.5 air pollution levels in Kuopio. They would also like to know if the estimate is more sensitive to dose-response data or to exposure data.
The city representatives, JT and MP, will examine models.
Data
Luckily, city decided to provide you some data for the analysis.
City has estimate that in year 2015 PM2.5 levels would be 5.0 μg/m3 if nothing is done. The concentration estimate is uncertain and they estimated that standard deviation of normal distribution would be 0.5.
They have also estimated that their decision action would lower mean PM2.5 concentrations by 2 % and cost 3 000 000 euros. The good news is that this action can be takes as many times as needed, and the impact is always 2% reduction and the cost is always 3 000 000 €. The question is: how many times should this action be taken so that it is still cost-beneficial. i.e. that the next incremential action would produce more benefit than cots?
----#: . The cost of reduction was pretty low compared to cost of death, so I increased it tenfold; seems to give more reasonable results. --Teemu R 15:10, 8 April 2011 (EEST) (type: truth; paradigms: science: comment)
For the dose-response data they recommend you to use Pope et al. 2002 epidemiological data.
Background mortality is estimated to be 883 deaths per year in year 2015.
From EU report city has also noticed that one death has economical values of 1 000 000 Euros.
Some tips that you might find useful
95% confidence interval is estimated by multiplying standard deviation with 1.96. Thus, if you know 95% CI, you can estimate standard deviation.
Some R tips that you might find useful
Normal distribution can be created with command: rnorm(1000,10,1)
- 1000 is the number of iterations
- 10 is mean
- 1 is standard deviation
Correlation between samples is done with command: Cor(sample1,sample2)
Results
City would like you to calculate following parameters:
- Mean PM2.5 concentration in 2015 in all three decisions (BAU, Option 1, Option 2)
- Cost of health effects in all three scenarios
- Comparison of health effect costs to different decision costs.
- Sensitivity of the result to dose-response and to concentration uncertainties (thus, which uncertainty has more impact to the results).
- Reviewers are lazy people so report should be short. Both report and R-code are submitted to individual Wiki page in HEANDE.
Grading
Grading will be based on:
- R-model
- Written report.
The grades can be found from here.
Purpose
This analysis seeks to answer these questions:
How many times should action to reduce PM 2.5 by 2% be taken so that it would still be cost beneficial? Assumptions: cost of action 3 million euros, cost of death 1 million euros.
Data
2015 PM2.5 levels 5.0 μg/m3 if BAU. Standard deviation of normal distribution 0.5.
Decision action would lower mean PM2.5 concentrations by 2 % and cost 3 000 000 euros, repeatable.
Dose-response data: Pope et al. 2002 epidemiological data. 10 ug/m3 change in PM 2.5 affects mortality by factor 1.06.
Background mortality is estimated to be 883 deaths per year in year 2015.
One death has economical value of 1 000 000 Euros.
Calculation
If dose-response factor to 10ug/m3 change in PM2.5 is 1,06, 5 ug/m3 PM2.5 level would result in (5/10)*(1,06-1) = 0,03 (3%) increase in mortality. Based on this it is possible to calculate the effect of 2% decrease in PM 2.5 level with the cost of 3 million euros and compare it to cost of 1 million euros per death. Calculation is presented in the following table:
| Scenario | PM 2.5 ug / m3, 2015 | Mortality | Background 2015 | Extra Deaths | Cost of deaths, me | Cost of reduction, me | Total cost |
|---|---|---|---|---|---|---|---|
| BAU | 5 | 0,03 | 883 | 26,5 | 26,5 | 0 | 26,5 |
| 1 | 4,9 | 0,0294 | 883 | 26 | 26,0 | 3 | 29,0 |
| 2 | 4,802 | 0,028812 | 883 | 25,4 | 25,4 | 6 | 31,4 |
Based on the calculations above, 3 million euros for a 2% reduction in PM 2.5 level would not be cost effective in any case compared to cost of 1 million euros per death.