Dear Mr Major,

You wrote: “I see that there are noticeable differences between culling benefits in the culling area at the end of months 30 and 36 after one year after culling ceased. This can be seen by comparing values in Table 1 reported in February (this report) and Table 1 reported in July in the posting by Prof Donnelly titled "Analysis of further data (to 2 July 2010)". What is the reason for this?”

Our paper, published in February, only included data up to July 2009. This meant that the estimate for 31 to 36 month post-trial only consisted of 3.9 triplet-years of data (see Table 1). Full data are accrued over 5 triplet-years (i.e. 10 triplets x 6 months each = 5 triplet-years). The full data for this time interval (all 5 triplet-years) were available in the analysis of data available as of January 2010 (published as a comment in May 2010). You will note there was very little change between the estimate published in May 2010 and the estimate published in July 2010 (based on data up to July 2010). These later estimates, based on the full data, are more reliable than that published in February, based on incomplete data. To reduce such potential confusion in future, we have scheduled our next analysis to be based on data up to March 2011, rather than January 2011.

Regarding the paper published in February 2010, you wrote: “The best fitting straight line through the points in Table 1 of this report gives a 10% reduction in culling benefit every 6 months. However a 14.3% reduction was reported. How was this 14.3% calculated?”

The 14.3% was calculated by estimating a linear trend in the estimates on a log scale, using weighted least squares regression so that less precise estimates receive less weight. The 14.3% figure does not itself represent a reduction in cattle TB incidence; it is instead a measure of the estimated impact of badger culling on cattle TB incidence is changing. It might be easier for us to illustrate with the fitted values.

Time period Estimate Fitted value
(post-trial)
----------------------------------------------------------------
Months 1-6 -52.7% -54.2%
Months 7-12 -41.1% -47.7%
Months 13-18 -49.4% -40.2%
Months 19-24 -27.8% -31.7%
Months 25-30 -35.0% -21.9%
Months 31-36 9.9% -10.8%

You wrote: “According to the best fitting straight line in data reported in July, the reduction in culling benefit every 6 months after culling ceased is 4%. Are there any plans to report a lower figure which reflects cattle incidence in the 12 months leading up to July 2010? As far as I am aware the last figure reported is 14.3%.”

A similar analysis was performed on the data up to July 2010, again estimating a linear trend in the estimates on a log scale. The equivalent figure was 7.0%; in other words the benefit of culling was going away less quickly. Again, it might be easier for us to illustrate with the fitted values.

Time period Estimate Fitted value
(post-trial)
----------------------------------------------------------------
Months 1-6 -52.2% -47.8%
Months 7-12 -40.5% -44.1%
Months 13-18 -49.1% -40.2%
Months 19-24 -27.2% -36.0%
Months 25-30 -30.3% -31.6%
Months 31-36 -8.4% -26.8%
Months 37-42 -31.4% -21.7%
Months 43-48 -25.0% -16.2%

Other trends might, of course, be fitted to the estimates. In any case, it is clear that the benefits of culling have diminished during the post-trial period.

Christl A. Donnelly1*, Helen E. Jenkins1, Rosie Woodroffe2
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