Badgers & TB: the statistics reloaded

Badgers & TB: the statistics reloaded

Much excitement last week at the predicted recalculation of the statistics previously published by Prof Christl Donnelly which purported to show that badgers ’caused’ 50% of bTB outbreaks. This figure was, and continues to be, widely quoted by badger cull supporters, despite it having been shown to have such wide a confidence interval as to be virtually meaningless. The analysis can be found in a previous post.

Prof Donnelly’s new paper is much more honest about the statistics, almost apologetic in some ways. Her conclusion states:

The confidence intervals obtained using bootstrap sampling were wider than the profile-likelihood based intervals previously reported” (in Donnelly & Hone (2010), link at end of post). In fact they show that the 50% figure ‘has considerable uncertainty’ (CI 9.1%-100%). So on this model the transmission of bTB from badgers could be as low as 9%! In my previous post I worked out the lower limit as 14%, so this is now even more uncertain.

The lower limit

However, there is a sting in the tail of the recent paper. Donnelly chooses her data carefully and states :

The largest reduction in confirmed cattle TB incidence achieved over the course of the RBCT was that within RBCT trial areas during the first 18-month time period post-trial (that is between 12 and 30 months after the final annual proactive cull in each of the 10 proactive trial areas). The estimated reduction over this period was 54% with an overdispersion-adjusted 95% confidence interval of 38% to 66%. Because badgers were never completely eliminated from any of the culling areas and farmers moved cattle in and out of the areas, the lower confidence bound of this estimate can provide a lower bound for the average overall contribution of badgers to confirmed cattle TB in the RBCT areas.”.

By the way note the contradiction: ‘over the course of the RBCT’ includes data taken after the RBCT had finished!

Anyway, the conclusion is therefore that badgers ‘contribute’ at least 38% of bTB, a nice take-home, quotable figure for DEFRA and ministers, and not too far off her original discredited 50%.

But, Prof Donnelly, you can’t do this. You can’t take figures from one analysis, designed to show one thing, and apply it to another figure, from a totally different model, designed to show something else. And you know how I know this? I am relying on none other than you, Prof Donnelly, yourself, as a member of the ISG, who, in their report on the RBCT stated as follows (para 2.4):

‘The ISG recognised that an objective to quantify ‘the badger contribution’ implicitly assumes that there is simply a one-way transfer of infection, from badgers to cattle; whereas in reality there is an interchange of infection between the two species with disease transfer in both directions, so the contribution of badgers is not independent of the feedback from cattle. It was therefore clear that the trial could not provide anything quite as precise as a quantitative estimate of “the contribution of badgers to the risk of TB in cattle” and could directly measure only the contribution that particular forms of culling could take.’

The 38%, then, if you accept figures taken after the RBCT had finished, is an indication of the contribution of culling. The 9.1% figure comes from a model of the contribution of transmission of the disease from badgers. As the ISG (and I think Lord Krebs in an earlier document) stated, the two are not the same. And yet, there you go again, even naming this most recent paper: “The Contribution of Badgers to confirmed Tuberculosis…’, exactly what the designers of the RBCT said that it could not provide!

Direct vs Indirect Transmission

But apart from the final paragraph, the rest of Prof Donnelly’s paper seems to add up. In particular, having to go back and rework the analysis, she has come up with something new: an estimate of the amount of direct transmission of TB from badgers to cattle.

As she states, this ‘dynamical’ model: ‘also suggested that only 5.7% (bootstrap 95% CI: 0.9-25%) of the transmission to cattle herds is badger-to-cattle with the remainder of the average overall contribution from badgers being in the form of onward cattle-to-cattle transmission.’

While I am doubtful about the word ‘onward’ (suggesting that badgers were the ultimate origin of the TB, which is not assessed by the transmission model), the conclusion is very clear: up to a quarter, at most, of bTB outbreaks are directly caused by badgers alone. The rest, by far the majority, are caused either by cattle alone, or by cattle and badgers both playing a role.

So, given limited budgets in farming, should we be concentrating on cattle or badgers to ‘get on top of this disease’ as Owen Paterson and the NFU frequently put it? As even Prof Donnelly puts it, these estimates should ‘inform debate’. But it looks as though the original ISG report was right: cattle measures alone could eliminate TB from Britain, both within cattle and badgers.

Do badgers get TB from cattle?

The answer to this seems obvious: yes. And the original Donnelly & Hone model ddn’t take it into account. The recent paper does address this problem by taking out data where this happened to an obvious degree: in three areas where Foot and Mouth delayed TB testing and removal of cattle. As well as causing a huge spike of bTB nationally (arguably the main cause of the extent of the current outbreak) this produced a large number of TB-infected badgers. As the model has not accounted for this source of TB (cattle-badger-cattle), the authors have taken out the three triplets involved. It makes the figures even less convincing:

This corresponds to an average overall contribution of badgers to confirmed cattle TB of 42% (bootstrap 95% CI: 0.0%-100%). The estimated average percentage of transmission to cattle herds that was badger-to-cattle was 3.7% (bootstrap 95% CI: 0.0-100%)”.

So now the model really does show nothing at all! Not surprising perhaps, as the RBCT was not set up to show this, as the ISG report stated.

The main point though is that the refinement actually lowers the main estimate of badgers being the direct source of bTB in cattle to a tiny 3.7%!

What is the betting that Owen Paterson and the NFU don’t exactly bust a gut to quote this figure in their press releases?

And finally…does the Donnelly & Hone model tell us anything about badger culling vs vaccination?

Donnelly & Hone’s 2010 paper (see below for link) in fact has no mention of the original 50% figure at all. This was first trotted out in Parliament following the announcement of the badger culls, and backed up by a letter from Donnelly to DEFRA explaining how she arrived at the figure. It was this letter which enabled my previous analysis to debunk the figure.

However, the 2010 paper does have one important conclusion that seems to have been overlooked:

‘the best fitting model included frequency-dependent transmission between cattle herds and badger-herd transmission proportional to the proportion of badgers infectious for Bovine TB’.

So it is the prevalence of Bovine TB amongst badgers rather than the density of badgers that seems ot be important. The paper goes to to state:

‘the results imply that reducing the prevalence of Bovine TB in badgers, such as by effective vaccination of badgers, may be important in reducing TB incidence in cattle herds’.

The authors go on to recommend an RBCT-style trial, but using vaccination instead of culling.

The reason that vaccination was suggested here was that the RBCT, far from reducing the prevalence of Bovine TB in badgers (as claimed by Owen Paterson and the NFU), actually increased it. So, by this model, culling would actually increase TB among cattle without any perturbation effects. Of course, as we know, culling did reduce cattle TB inside the cull zones, so there must be factors not taken into account in the model. The recent analysis points to what they could be: that badgers are very seldom the direct origin of TB in cattle, but in some way play an intermediary or facilitating role in cattle to cattle transmission.

In short, badgers may help spread bTB in some way, but it is cattle that mainly take the blame for new outbreaks.

Jamie McMillan

Briantspuddle

16 October 2013

Donnelly & Hone (2010): Association-between-Levels-of-TB-in-Cattle-Herds-and-Badgers

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2 thoughts on “Badgers & TB: the statistics reloaded

  1. Tom Rigby

    Hi Jamie, interesting analysis of complex data but is it not the case that all of the breakdowns caused by ‘the perturbation effect’ must have been badger-to-cattle?

    Reply
    1. furtlefinch Post author

      Thanks Tom, good question. It is always hard to interpret a mathematical model, but what I think this one shows is the degree of transmission from one animal to the next, and not the overall effect of any variable on the prevalence of bTB. The model is showing that an average of 3-6% is caused by DIRECT transmission from badger to cattle. Presumably the rest is cattle-cattle. But there is a part of this where badgers also play a role in herd breakdowns without being the direct source. Donnelly called this ‘amplification’ of infection from badgers by cattle. But it could be amplification of cattle-sourced infections by badgers.

      The perturbation effect increases the badger-related transmission, but I don’t think we can tell whether it affects the direct or ‘amplified’ proportions, or both.

      Interestingly today’s press has details of a social study of badgers which suggests that social disruption affects TB-infected badgers more than healthy ones, which may explain why the perturbation effect is so marked.

      Reply

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