9 bTB case numbers, aggregated Poisson/negative binomial models
10 Introduction
Here, we are exploring an aggregated Poisson model of bTB cases per year. Its a crude but useful approach to explore incidence risk ratios over time.
As reminder of cases and population (based on AIM data on 1st May), below are some plots. Naturally, population is problematic for trader herds as the population is fluctuating a lot more than for the other herd types as animals are constantly coming and going.
10.1 Cases over time
10.2 Population:
11 Poisson models
In this first model, I include herd type and year as covariates.
Next, to adjust for counts of events over time, we included an offset term based on population to focus on rates (instead of counts).
Its now really interesting that trader herds are positively significant with a large effect size. It suggests that there are a lot of bTB cases in trader herds considering their population.
11.1 Combined offset
Above we included population as an offset. However, for curiosity, we included a double offset below, not only accounting for population but also the number of tests (at animal level) conducted in the year (based solely on SICTT):
The results are perhaps strange at first (the massive IRR estimate for trader) but I think they make sense. The large effect on trader herds is saying that when you account for testing effort and the population, we see a strong effect of trader herds. Trader herds have a high IRR in the first model but its attentuated when the number of tests are brought in. In essence, its saying that we we see a lot of bTB cases considering the population size and number of tests conducted on trader herds. The per head, per test value is high. Trader herds will not have as many SICTT tests as other herd types (I would imagine a lot of the time if bTB is detected, they send their animals to slaughter so the amount of tests (at animal level) conducted during follow-up will be lower etc).
This is a bit nuance and admittedly strange to have two offsets (but it is permitted in a model).
For now, we am leaving out this combined offset and from here on, we will just include population as the offset which is a more standard approach.
11.2 Model without trader herds
Trader herds are problematic here because we are taking a snapshot of their population (which is changing a lot). We still believe that this approach is ok - the small numbers for the count of cases within traders is not really an issue, we see similar numbers in store herds. Repeating this by month would be a really useful exercise and one we should (we dont have a count of animals in every herd for the 1st of each month, just 1st Jan/May/Sept. It would involve a bit of work to estimate these but something we want to do at some stage). We would end up with very few cases in some months though.
So with that in mind, we have repeated the model without trader herds:
11.2.1 Dispersion test
# Overdispersion test
dispersion ratio = 114.772
Pearson's Chi-Squared = 7345.429
p-value = < 0.001Over dispersion present, repeat using negative binomial.
12 Negative binomial models
12.1 All herds
12.2 Trader herds removed
12.3 Estimated rates (per 1000)
Here, I’ve estimated marginal means and plots of these.
herd_type_ml_description year response SE df asymp.LCL asymp.UCL
Beef 2015 2.231 0.1560 Inf 1.945 2.560
Dairy 2015 3.028 0.2120 Inf 2.639 3.474
Store 2015 0.643 0.0459 Inf 0.559 0.740
Fattener 2015 3.033 0.2130 Inf 2.643 3.481
Mixed 2015 2.502 0.1760 Inf 2.180 2.872
Beef 2008 4.315 0.3010 Inf 3.763 4.948
Dairy 2008 5.855 0.4090 Inf 5.106 6.714
Store 2008 1.244 0.0883 Inf 1.083 1.430
Fattener 2008 5.866 0.4100 Inf 5.115 6.727
Mixed 2008 4.839 0.3380 Inf 4.219 5.550
Beef 2009 3.473 0.2430 Inf 3.028 3.983
Dairy 2009 4.712 0.3300 Inf 4.108 5.405
Store 2009 1.001 0.0712 Inf 0.871 1.151
Fattener 2009 4.721 0.3310 Inf 4.116 5.416
Mixed 2009 3.895 0.2730 Inf 3.395 4.468
Beef 2010 3.227 0.2260 Inf 2.813 3.702
Dairy 2010 4.379 0.3070 Inf 3.817 5.024
Store 2010 0.930 0.0664 Inf 0.809 1.070
Fattener 2010 4.387 0.3080 Inf 3.823 5.034
Mixed 2010 3.619 0.2540 Inf 3.154 4.153
Beef 2011 2.691 0.1890 Inf 2.345 3.089
Dairy 2011 3.652 0.2560 Inf 3.182 4.191
Store 2011 0.776 0.0555 Inf 0.675 0.893
Fattener 2011 3.659 0.2570 Inf 3.188 4.200
Mixed 2011 3.018 0.2120 Inf 2.629 3.465
Beef 2012 2.694 0.1890 Inf 2.348 3.090
Dairy 2012 3.655 0.2560 Inf 3.186 4.193
Store 2012 0.777 0.0553 Inf 0.676 0.893
Fattener 2012 3.662 0.2570 Inf 3.192 4.202
Mixed 2012 3.021 0.2120 Inf 2.633 3.467
Beef 2013 2.374 0.1670 Inf 2.069 2.725
Dairy 2013 3.222 0.2260 Inf 2.808 3.697
Store 2013 0.685 0.0489 Inf 0.595 0.787
Fattener 2013 3.228 0.2270 Inf 2.812 3.705
Mixed 2013 2.663 0.1870 Inf 2.320 3.056
Beef 2014 2.399 0.1680 Inf 2.091 2.753
Dairy 2014 3.256 0.2280 Inf 2.837 3.735
Store 2014 0.692 0.0494 Inf 0.602 0.796
Fattener 2014 3.262 0.2290 Inf 2.842 3.743
Mixed 2014 2.691 0.1890 Inf 2.344 3.088
Beef 2016 2.189 0.1530 Inf 1.908 2.512
Dairy 2016 2.970 0.2080 Inf 2.589 3.408
Store 2016 0.631 0.0450 Inf 0.549 0.726
Fattener 2016 2.976 0.2090 Inf 2.594 3.415
Mixed 2016 2.455 0.1720 Inf 2.139 2.817
Beef 2017 2.243 0.1570 Inf 1.956 2.573
Dairy 2017 3.044 0.2130 Inf 2.654 3.492
Store 2017 0.647 0.0460 Inf 0.563 0.744
Fattener 2017 3.050 0.2140 Inf 2.658 3.499
Mixed 2017 2.516 0.1770 Inf 2.193 2.887
Beef 2018 2.366 0.1660 Inf 2.062 2.714
Dairy 2018 3.210 0.2250 Inf 2.799 3.682
Store 2018 0.682 0.0485 Inf 0.593 0.784
Fattener 2018 3.216 0.2250 Inf 2.803 3.689
Mixed 2018 2.653 0.1860 Inf 2.312 3.044
Beef 2019 2.275 0.1590 Inf 1.983 2.610
Dairy 2019 3.087 0.2160 Inf 2.691 3.541
Store 2019 0.656 0.0467 Inf 0.571 0.754
Fattener 2019 3.093 0.2170 Inf 2.696 3.548
Mixed 2019 2.552 0.1790 Inf 2.224 2.928
Beef 2020 3.004 0.2100 Inf 2.620 3.444
Dairy 2020 4.076 0.2840 Inf 3.555 4.673
Store 2020 0.866 0.0613 Inf 0.754 0.995
Fattener 2020 4.084 0.2850 Inf 3.561 4.683
Mixed 2020 3.369 0.2350 Inf 2.938 3.863
Beef 2021 2.712 0.1890 Inf 2.365 3.109
Dairy 2021 3.680 0.2570 Inf 3.209 4.219
Store 2021 0.782 0.0553 Inf 0.681 0.898
Fattener 2021 3.687 0.2570 Inf 3.215 4.227
Mixed 2021 3.041 0.2130 Inf 2.652 3.488
Beef 2022 3.028 0.2110 Inf 2.641 3.471
Dairy 2022 4.108 0.2860 Inf 3.584 4.709
Store 2022 0.873 0.0617 Inf 0.760 1.003
Fattener 2022 4.116 0.2870 Inf 3.590 4.719
Mixed 2022 3.395 0.2370 Inf 2.961 3.893
Beef 2023 3.575 0.2490 Inf 3.119 4.097
Dairy 2023 4.851 0.3370 Inf 4.233 5.559
Store 2023 1.031 0.0726 Inf 0.898 1.183
Fattener 2023 4.860 0.3380 Inf 4.240 5.571
Mixed 2023 4.009 0.2790 Inf 3.498 4.596
Beef 2024 5.515 0.3830 Inf 4.813 6.318
Dairy 2024 7.483 0.5190 Inf 6.531 8.573
Store 2024 1.590 0.1120 Inf 1.386 1.825
Fattener 2024 7.497 0.5210 Inf 6.543 8.590
Mixed 2024 6.185 0.4300 Inf 5.397 7.087
Confidence level used: 0.95
Intervals are back-transformed from the log scale 12.4 Dispersion test
# Overdispersion test
dispersion ratio = 1.300
p-value = 0.22412.5 Trader population - ADD IN
13 Notes/ideas
- We think the trader results are really interesting and would be of interest for policymakers but we do have to keep in mind the issues with this approach. Worth doing a separate analysis on trader herds specifically, even just highlighting the fact that their prevalence/numbers are going up. The fact that they are going up isnt all that surprising but coupled with the small numbers, its interesting that they are getting “caught” at all. This is primarily driven by slaughter surveillance. So in essence there are probably two cohorts of herds within trader herds. Those that just trade (and so dont send animals to slaughter) and those that do a bit of everything (looking for a quick sale etc).
- in the double offset model, i just looked at count of SICTTs, could expand on that to include count of animals tested at slaughter plant.
- Update from AIM data: From the 2023 movement data, approximately a third of trader sales were to slaughterhouses (32.7 %), 39 % exports, 23% farm to farm, and 5 % via marts.