### Cost benefit calculations

#### Posted by ChristlDonnelly on 09 Jun 2010 at 11:28 GMT

Cost benefit calcuations (Response to ‘Cost benefits’ query)
Helen E. Jenkins1, Rosie Woodroffe2, Christl A. Donnelly1*

1 Department of Infectious Disease Epidemiology, Imperial College London, London, United Kingdom
2 Institute of Zoology, London, United Kingdom

* E-mail: c.donnelly@imperial.ac.uk

Based on the most recent results (posted on 14 May 2010 as the comment “Analysis of further data on the impacts on cattle TB incidence of repeated badger culling”), in the time period from one year after the last proactive cull to 31 January 2010 (the post-trial period), the incidence of confirmed cattle herd breakdowns in the proactive culling areas was 37.0% lower (95% CI: 25.3% to 46.8% lower) than in survey-only areas. In areas up to 2km outside proactive trial areas, this incidence was 3.6% lower (95% CI: 29.0% lower to 31.0% higher) than outside survey-only areas.

Following the methods used in our PLoS ONE paper, the costs and benefits are then calculated assuming:

an idealised circular area of 150 sq km,

a herd density of 1.25/sq km and

a background incidence of 0.08 breakdowns/herd/year.

As before: “During a five-year culling period, annual proactive culling in the circular area would be expected to prevent 23.2% of 75 breakdowns inside the culled area (17.4 breakdowns prevented), while increasing the number of breakdowns on adjoining land by 24.5% (prompting 12.1 additional breakdowns), giving an overall total of 5.3 breakdowns prevented.”

Just to be clear, these values were obtained as follows:

150 sq km x 1.25 herds/sq km = 187.5 herds (on average)

187.5 herds x 0.08 breakdowns/herd/year x 5 years = 75 breakdowns (in the absence of culling).

23.2% x 75 breakdowns = 17.4 breakdowns prevented.

For the adjoining land the calculations are:

99 sq km x 1.25 herds/sq km = 123.75 herds (on average)

123.75 herds x 0.08 breakdowns/herd/year x 5 years = 49.5 breakdowns (in the absence of culling).

24.5% x 49.5 breakdowns = 12.1 additional breakdowns.

Taken together this gives an overall total of 5.3 breakdowns prevented, representing a savings of £143,100 at £27,000/breakdown (Defra 2005). (Please note that this is a rounded figure – the Defra document gives the precise figure £26,762, of which £6,603 arises from “spread to other herds prevented”.)

The cost of conducting five annual culls over a 150 sq km area, 75% of which was accessible for culling, was estimated as follows:

150 sq km x 75% accessible = 112.5 sq km accessible

112.5 sq km accessible x £3,800/ sq km/year x 5 years = £2,137,500, rounded to £2.14 million for cage trapping (based on Defra 2005 estimate of the cost of cage trapping per sq km per year)

112.5 sq km accessible x £2,400/sq km/year x 5 years = £1,350,000, or £1.35 million, for snaring or gassing (based on Defra 2005 estimate of the costs of snaring or gassing per sq km per year)

It is then possible to calculate the number of years that the post-culling effects observed to date would have to last for the total savings to equal these costs.

Within the circular area:

150 sq km x 1.25 herds/sq km = 187.5 herds (on average) [as before]

187.5 herds x 0.08 breakdowns/herd/year x 12.5 years = 187.5 breakdowns (in the absence of culling).

37.0% x 187.5 breakdowns = 69.4 breakdowns prevented.

For the adjoining land the calculations are:
99 sq km x 1.25 herds/ sq km = 123.75 herds (on average) [as before]

124.25 herds x 0.08 breakdowns/herd/year x 12.5 years = 123.75 breakdowns (in the absence of culling).

3.6% x 123.75 breakdowns = 4.5 breakdowns prevented.

Taken together this gives an overall total of 73.9 breakdowns prevented, representing a savings of £1,995,300 at £27,000/breakdown (Defra 2005). Adding this to the savings achieved while culling was ongoing (£143,100) gives a total of £2,138,400. Thus, 12.5 years of post-culling benefits of a 37.0% reduction inside the circular culling area and only a 3.6% reduction on adjoining land are required for savings to equal the costs of five years of culling using cage trapping. Analogous calculations demonstrate that 7.5 years of post-culling benefits are required for savings to equal the costs of five years of culling using snaring or gassing.

As the size of the culled area increases (and thus the ratio of culled land to adjoining land up to 2km outside the culled land increases), these durations decrease but remain at least 11.1 years of post-culling benefits required to equal the costs of five years of culling using cage trapping and at least 5.8 years of post-culling benefits required to equal the costs of culling using snaring or gassing (as above based on Defra 2005 estimates for culling costs and average breakdown cost).

Note that, in making these calculations, we have not applied a discounting rate, which could be used to compute all cost and benefits into present-value terms relating to the point at which the first cull was undertaken. If such a discounting rate were applied, it would extend the duration of post-culling benefit required for the total present-value benefits (savings associated with prevented breakdowns) to match the total present-value costs. This is because all of the costs are incurred in the first five years (with five culls) whereas the benefits are realized over a substantially longer timescale.

We cannot predict how long the post-culling effects of widespread repeated badger culling will last. Thus, we will continue to monitor the effects of badger culling on TB incidence in and around areas subjected to proactive culling within the Randomised Badger Culling Trial.

References:
Defra (2005) Cost benefit analysis of badger management as a component of bovine TB control in England: Defra. Available: http://www.defra.gov.uk/f... Accessed 2010 June 3.

Funding: The authors gratefully acknowledge the support of the United Kingdom Department of Environment, Food and Rural Affairs (Defra; http://www.defra.gov.uk/i...) for this work. CAD thanks the United Kingdom Medical Research Council (http://www.mrc.ac.uk/inde...) for Centre funding. HEJ thanks the Medical Research Council for a studentship.

No competing interests declared.