DescAnalysisEpi

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This is an R Markdown document which should hopefully make the analytical steps clear and repeatable.

1. Descriptive Statistics

TABLE 1

The following shows the distribution of explanatory variables between cases (bTBPOS) and controls (bTBNeg). The matching criteria where Year, DVO, Median Herd Size and Herd Type.

Variable	bTB Status
Variable	bTBNeg, N = 4,637¹	bTBPos, N = 4,637¹
year
2015	1,774 (38%)	1,774 (38%)
2016	1,389 (30%)	1,389 (30%)
2017	1,474 (32%)	1,474 (32%)
DVO
Armagh	428 (9.2%)	428 (9.2%)
Ballymena	269 (5.8%)	269 (5.8%)
Coleraine	590 (13%)	590 (13%)
Dungannon	590 (13%)	590 (13%)
Enniskillen	566 (12%)	566 (12%)
Larne	226 (4.9%)	226 (4.9%)
Londonderry	119 (2.6%)	119 (2.6%)
Newry	688 (15%)	688 (15%)
Newtownards	515 (11%)	515 (11%)
Omagh	646 (14%)	646 (14%)
NewHerdType
Breeder	1,251 (27%)	1,251 (27%)
Dairy	1,267 (27%)	1,267 (27%)
Finisher	690 (15%)	690 (15%)
Other	1,429 (31%)	1,429 (31%)
median_herd_size	81 (41, 156)	83 (40, 173)
total_farm_area_ha	42 (26, 72)	50 (27, 84)
farm_area_category
SmallArea	583 (13%)	538 (12%)
MediumArea	938 (20%)	852 (18%)
LargeArea	1,570 (34%)	1,343 (29%)
VeryLargeArea	1,546 (33%)	1,904 (41%)
n_fields	28 (17, 44)	33 (20, 51)
n_fragments_5m	4 (2, 6)	4 (3, 7)
fragment_category
Not_fragmented	526 (11%)	488 (11%)
Little_fragmentation	2,226 (48%)	1,974 (43%)
Medium_fragmentation	1,062 (23%)	1,165 (25%)
High_fragmentation	415 (8.9%)	551 (12%)
Very_High_fragmentation	408 (8.8%)	459 (9.9%)
median_distance_fragments_km	1.52 (0.72, 3.23)	1.83 (0.86, 3.57)
fragment_distance_category
Low	798 (17%)	697 (15%)
Medium	1,338 (29%)	1,116 (24%)
High	1,282 (28%)	1,425 (31%)
Very High	1,219 (26%)	1,399 (30%)
total_shared_boundary_grazing_km	3.4 (2.0, 5.7)	4.1 (2.2, 6.7)
neighbour_contact_category
Low	763 (16%)	644 (14%)
Medium	1,086 (23%)	918 (20%)
High	1,255 (27%)	1,181 (25%)
Very High	1,533 (33%)	1,894 (41%)
NeighbourbTB	2,463 (53%)	3,284 (71%)
CountNeighbourbTB	1 (0, 1)	1 (0, 3)
¹ n (%); Median (IQR)

A plot of the distribution of same variables in the whole cattle population.

Variable	Population, N = 57,024¹
year
2015	19,008 (33%)
2016	19,008 (33%)
2017	19,008 (33%)
DVO
Armagh	5,487 (9.6%)
Ballymena	3,465 (6.1%)
Coleraine	6,450 (11%)
Dungannon	6,954 (12%)
Enniskillen	7,848 (14%)
Larne	3,882 (6.8%)
Londonderry	2,061 (3.6%)
Newry	8,934 (16%)
Newtownards	4,458 (7.8%)
Omagh	7,470 (13%)
Unknown	15
NewHerdType
Breeder	28,415 (50%)
Dairy	8,128 (14%)
Finisher	5,976 (10%)
Other	14,505 (25%)
median_herd_size	40 (19, 89)
total_farm_area_ha	31 (16, 59)
farm_area_category
SmallArea	14,164 (25%)
MediumArea	14,353 (25%)
LargeArea	14,255 (25%)
VeryLargeArea	14,252 (25%)
n_fields	24 (14, 39)
n_fragments_5m	3 (2, 6)
fragment_category
High_fragmentation	4,691 (8.2%)
Little_fragmentation	27,164 (48%)
Medium_fragmentation	12,353 (22%)
Not_fragmented	9,476 (17%)
Very_High_fragmentation	3,340 (5.9%)
median_distance_fragments_km	1.38 (0.52, 3.05)
fragment_distance_category
High	14,255 (25%)
Low	14,256 (25%)
Medium	14,256 (25%)
Very High	14,255 (25%)
Unknown	2
total_shared_boundary_grazing_km	2,842 (1,477, 4,948)
neighbour_contact_category
High	14,256 (25%)
Low	14,256 (25%)
Medium	14,256 (25%)
Very High	14,256 (25%)
NeighbourbTB	27,074 (48%)
Unknown	510
¹ n (%); Median (IQR)

SUPPLEMENTARY MATERIAL FIGURE 1

## OGR data source with driver: ESRI Shapefile 
## Source: "H:\Shapefiles\DVO_only", layer: "region_DVO"
## with 10 features
## It has 1 fields

2. Correlation between explanatory variables

Some of the potential explanatory variables are highly correlated, especially the Contact Boundary variable and Number of Fragments. The Contact Boundary is likely to be the most epidemiologically relevent but all will be investigated.

SUPPLEMENTARY MATERIAL FIGURE 2

3. UNIVARIABLE ASSOCIATIONS

3A FARM AREA

3A 1 Farm Area - Continuous

Exploratory loess plot of how mean bTB predicted positivity (binary outcome, 1/0) varies with the explanatory variable Farm Area. The relationship is not linear-there is a general increase in probability of bTB until the farm is around 500 ha in area, the a drop off. There is no biological reason for this which is not speculative.

Fig 3A in Manuscript

figMain3A

Characteristic	OR¹	95% CI¹	p-value
total_farm_area_ha	1.00	1.00, 1.00	0.5
¹ OR = Odds Ratio, CI = Confidence Interval

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
total_farm_area_ha	-3213.94	0.38	1	0.5397

How many farms biger than 500ha? Only 49

## [1] 49

3A 2 Farm Area - Categorical

Characteristic	OR¹	95% CI¹	p-value
farm_area_category
SmallArea	—	—
MediumArea	1.03	0.87, 1.21	0.8
LargeArea	1.09	0.92, 1.30	0.3
VeryLargeArea	1.87	1.55, 2.25	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Only "Very Large Farms" are at elevated risk - dichotimise the variable at this point

Characteristic	OR¹	95% CI¹	p-value
VeryLargeArea
SmallMediumLargeArea	—	—
VeryLargeArea	1.74	1.56, 1.95	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the farm area variable important in the model?

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
farm_area_category	-3164.39	99.46	3	0.0000

Fig 3B in Manuscript

figMain3B

3A 3 Farm Area - Ordinal

For this, I create an ordered variable for farm size, and then compare a this (simpler) model to the more complex categorical model

Characteristic	OR¹	95% CI¹	p-value
farm_size_category_o	1.27	1.19, 1.34	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the ordinal variable better than the categorical one (if so could result in a simpler model) - Null hypothesis is that the simplest model is sufficient. P value is very low, which is evidence against the simpler (ordinal) model (-3182.8) and evidence for the more complex model with categorical predictors (-3164.4).

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3164.39
2	-3182.76	36.74	2	0.0000

3B FARM FRAGMENTATION

3B 1 Farm Fragmentation - Continuous

Loess plot of how bTB predicted positively (binary outcome, 1/0) varies with the explanatory variable Farm Fragmentation. The relationship is not linear-there is a general increase in probability of bTB until arpund 10 fragments, a plauteau and then a sharp increase within the most fragmented farms.

Fig 3c in Manuscript

figMain3C

Characteristic	OR¹	95% CI¹	p-value
n_fragments_5m	1.03	1.02, 1.05	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
n_fragments_5m	-3198.04	32.16	1	0.0000

3B 2 Farm Fragmentation - Categorical

Characteristic	OR¹	95% CI¹	p-value
fragment_category
Not_fragmented	—	—
Little_fragmentation	0.97	0.84, 1.11	0.7
Medium_fragmentation	1.25	1.07, 1.46	0.004
High_fragmentation	1.56	1.30, 1.88	<0.001
Very_High_fragmentation	1.36	1.12, 1.65	0.002
¹ OR = Odds Ratio, CI = Confidence Interval

Is the farm fragmentation category variable important in the model?

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
fragment_category	-3187.45	53.34	4	0.0000

Fig 3D in Manuscript

figMain3D

3B 3 Farm Fragmentation - Ordinal

Characteristic	OR¹	95% CI¹	p-value
fragment_category_o	1.14	1.09, 1.19	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the ordinal variable better than the categorical one (if so could result in a simpler model) - Null hypothesis is that the simplest model is sufficient. P value is very low, which is evidence against the simpler (ordinal) model (-3196) and evidence for the more complex model with categorical predictors (-3187.5).

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3187.45
2	-3196.04	17.18	3	0.0006

3C FRAGMENT DISPESAL

3C 1 Fragment Dispersal - Continuous

Loess plot of how mean bTB predicted positivity (binary outcome, 1/0) varies with the explanatory variable Fragment Dispersal.

Fig 3E in Manuscript

figMain3E

Explanatory variable is scaled so that it represents the change per 10km

Characteristic	OR¹	95% CI¹	p-value
median_distance_fragments_km_scaled	1.00	1.00, 1.00	0.030
¹ OR = Odds Ratio, CI = Confidence Interval

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
median_distance_fragments_km_scaled	-3211.73	4.78	1	0.0287

3C 3 Fragment Dispersal - Categorical

Conditional GLM

Characteristic	OR¹	95% CI¹	p-value
fragment_distance_category
Low	—	—
Medium	0.97	0.85, 1.11	0.6
High	1.33	1.16, 1.52	<0.001
Very High	1.35	1.19, 1.55	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the fragment distance category variable important in the model? Yes.

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
fragment_distance_category	-3188.68	50.88	3	0.0000

Fig 3F in Manuscript

figMain3F

Farms with high or very high dispersal have similar risk - dichotimise the variable at this point

Characteristic	OR¹	95% CI¹	p-value
HighVeryHighDisp
SmallMedium	—	—
HighVeryHigh	1.37	1.25, 1.49	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

3C 3 Farm Fragmentation - Ordinal

Characteristic	OR¹	95% CI¹	p-value
fragment_distance_category_o	1.14	1.09, 1.18	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the (simpler) ordinal model sufficient? P value is very low, which is evidence against the simpler (ordinal) model (-3194.8) and evidence for the more complex model with categorical predictors (-3188.7).

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3188.68
2	-3194.78	12.19	2	0.0023

3D CONTACT METRICS (i.e. shared boundary - exposure to neighbouring farms)

3D 1 Contact Metrics - Continuous

Loess plot of how bTB predicted positively (binary outcome, 1/0) varies with the explanatory variable Contact Metrics. The relationship is generally linear, with a a general decrease in probability of bTB as shared contact boundaries increases.

Fig 3G in Manuscript

figMain3G

Characteristic	OR¹	95% CI¹	p-value
total_shared_boundary_grazing_km	1.07	1.06, 1.09	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
total_shared_boundary_grazing_km	-3164.68	98.88	1	0.0000

3D 3 Contact Metrics - Categorical

Characteristic	OR¹	95% CI¹	p-value
neighbour_contact_category
Low	—	—
Medium	1.02	0.89, 1.18	0.7
High	1.20	1.04, 1.38	0.011
Very High	1.72	1.49, 1.98	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the contact category variable important in the model Yes.

Fig 3H in Manuscript

figMain3H

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
neighbour_contact_category	-3169.94	88.36	3	0.0000

3D 4 Contact Metrics - Ordinal

Characteristic	OR¹	95% CI¹	p-value
neighbour_contact_category_o	1.21	1.16, 1.27	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the ordinal model sufficient? No. P value is very low, which is evidence against the simpler (ordinal) model (-3177.3) and evidence for the more complex model with categorical predictors (-3169.9).

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3169.94
2	-3177.28	14.68	2	0.0006

3E NEIGHBOUR BTB STATUS

3E Continuous

Loess plot of how bTB predicted positively (binary outcome, 1/0) varies with the explanatory variable number of bTB Positive neighbours.

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : pseudoinverse used at 0

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : neighborhood radius 2

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : reciprocal condition number 2.026e-015

## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : There are other near singularities as well. 1

Fig 3G in Manuscript

figMain3I

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.45	1.40, 1.50	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
CountNeighbourbTB	-2920.96	586.33	1	0.0000

How is the variable distributed between case and control herds?

## # A tibble: 2 x 3
##   bTBStatus   med    mx
##   <fct>     <int> <int>
## 1 bTBNeg        1    11
## 2 bTBPos        1    14

3E Binary

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.20	2.01, 2.41	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Is the count of bTB positive neighbours variable important in the model Yes.

	loglik	Chisq	Df	Pr(>\|Chi\|)
NULL	-3214.12
NeighbourbTB	-3056.18	315.88	1	0.0000

3D 4 Contact Metrics - Ordinal

Characteristic	OR¹	95% CI¹	p-value
neighbour_contact_category_o	1.21	1.16, 1.27	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3169.94
2	-3177.28	14.68	2	0.0006

4 Assess confounding & effect modification between each explanatory variable and bTB positive neighbours

4A FARM AREA

1. Continuous area & Binary neighbours (not in main MS)

Characteristic	OR¹	95% CI¹	p-value
total_farm_area_ha	1.00	1.00, 1.00	0.2
NeighbourbTB	2.22	2.03, 2.43	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
total_farm_area_ha	1.00	1.00, 1.00	0.002
NeighbourbTB	2.59	2.28, 2.93	<0.001
total_farm_area_ha * NeighbourbTB	1.00	1.00, 1.00	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
total_farm_area_ha	1.00	1.00, 1.00	0.5	1.00	1.00, 1.00	0.2	1.00	1.00, 1.00	0.002
NeighbourbTB	2.20	2.01, 2.41	<0.001	2.22	2.03, 2.43	<0.001	2.59	2.28, 2.93	<0.001
total_farm_area_ha * NeighbourbTB							1.00	1.00, 1.00	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

2. Continuous area & Continuous neighbours (not in MS)

Characteristic	OR¹	95% CI¹	p-value
total_farm_area_ha	1.00	1.00, 1.00	0.003
CountNeighbourbTB	1.46	1.41, 1.51	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
total_farm_area_ha	1.00	1.00, 1.00	0.7
CountNeighbourbTB	1.51	1.44, 1.57	<0.001
total_farm_area_ha * CountNeighbourbTB	1.00	1.00, 1.00	0.012
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
total_farm_area_ha	1.00	1.00, 1.00	0.5	1.00	1.00, 1.00	0.003	1.00	1.00, 1.00	0.7
CountNeighbourbTB	1.45	1.40, 1.50	<0.001	1.46	1.41, 1.51	<0.001	1.51	1.44, 1.57	<0.001
total_farm_area_ha * CountNeighbourbTB							1.00	1.00, 1.00	0.012
¹ OR = Odds Ratio, CI = Confidence Interval

3. Categorical area & Binary neiehgbours (not in MS)

Characteristic	OR¹	95% CI¹	p-value
farm_area_category
SmallArea	—	—
MediumArea	0.88	0.74, 1.04	0.13
LargeArea	0.88	0.74, 1.06	0.2
VeryLargeArea	1.35	1.11, 1.65	0.003
NeighbourbTB	2.12	1.93, 2.33	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
farm_area_category
SmallArea	—	—
MediumArea	1.24	0.98, 1.55	0.069
LargeArea	1.03	0.82, 1.30	0.8
VeryLargeArea	1.80	1.40, 2.32	<0.001
NeighbourbTB	3.65	2.78, 4.79	<0.001
farm_area_category * NeighbourbTB
MediumArea * NeighbourbTB	0.45	0.32, 0.63	<0.001
LargeArea * NeighbourbTB	0.62	0.45, 0.85	0.003
VeryLargeArea * NeighbourbTB	0.51	0.38, 0.71	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
farm_area_category
SmallArea	—	—		—	—		—	—
MediumArea	1.03	0.87, 1.21	0.8	0.88	0.74, 1.04	0.13	1.24	0.98, 1.55	0.069
LargeArea	1.09	0.92, 1.30	0.3	0.88	0.74, 1.06	0.2	1.03	0.82, 1.30	0.8
VeryLargeArea	1.87	1.55, 2.25	<0.001	1.35	1.11, 1.65	0.003	1.80	1.40, 2.32	<0.001
NeighbourbTB	2.20	2.01, 2.41	<0.001	2.12	1.93, 2.33	<0.001	3.65	2.78, 4.79	<0.001
farm_area_category * NeighbourbTB
MediumArea * NeighbourbTB							0.45	0.32, 0.63	<0.001
LargeArea * NeighbourbTB							0.62	0.45, 0.85	0.003
VeryLargeArea * NeighbourbTB							0.51	0.38, 0.71	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

4. Categorical area & Continuous neighbours (not in MS)

Characteristic	OR¹	95% CI¹	p-value
farm_area_category
SmallArea	—	—
MediumArea	0.90	0.76, 1.07	0.2
LargeArea	0.85	0.71, 1.02	0.085
VeryLargeArea	1.18	0.96, 1.44	0.11
CountNeighbourbTB	1.43	1.38, 1.48	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
farm_area_category
SmallArea	—	—
MediumArea	1.13	0.92, 1.39	0.2
LargeArea	0.93	0.75, 1.15	0.5
VeryLargeArea	1.43	1.14, 1.79	0.002
CountNeighbourbTB	1.90	1.61, 2.22	<0.001
farm_area_category * CountNeighbourbTB
MediumArea * CountNeighbourbTB	0.69	0.57, 0.83	<0.001
LargeArea * CountNeighbourbTB	0.80	0.67, 0.95	0.010
VeryLargeArea * CountNeighbourbTB	0.73	0.62, 0.87	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
farm_area_category
SmallArea	—	—		—	—		—	—
MediumArea	1.03	0.87, 1.21	0.8	0.90	0.76, 1.07	0.2	1.13	0.92, 1.39	0.2
LargeArea	1.09	0.92, 1.30	0.3	0.85	0.71, 1.02	0.085	0.93	0.75, 1.15	0.5
VeryLargeArea	1.87	1.55, 2.25	<0.001	1.18	0.96, 1.44	0.11	1.43	1.14, 1.79	0.002
CountNeighbourbTB	1.45	1.40, 1.50	<0.001	1.43	1.38, 1.48	<0.001	1.90	1.61, 2.22	<0.001
farm_area_category * CountNeighbourbTB
MediumArea * CountNeighbourbTB							0.69	0.57, 0.83	<0.001
LargeArea * CountNeighbourbTB							0.80	0.67, 0.95	0.010
VeryLargeArea * CountNeighbourbTB							0.73	0.62, 0.87	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

5. Binary Area & Continuous neighbours (in MS)

Characteristic	OR¹	95% CI¹	p-value
VeryLargeArea
SmallMediumLargeArea	—	—
VeryLargeArea	1.35	1.20, 1.52	<0.001
CountNeighbourbTB	1.43	1.38, 1.48	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
VeryLargeArea
SmallMediumLargeArea	—	—
VeryLargeArea	1.46	1.25, 1.69	<0.001
CountNeighbourbTB	1.47	1.40, 1.54	<0.001
VeryLargeArea * CountNeighbourbTB
VeryLargeArea * CountNeighbourbTB	0.94	0.88, 1.01	0.10
¹ OR = Odds Ratio, CI = Confidence Interval

The univariable model is improved by the addition of bTB positive neighbours

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3165.04
2	-2908.74	512.60	1	0.0000

No evidence that an interaction term is needed

	loglik	Chisq	Df	P(>\|Chi\|)
1	-2908.74
2	-2907.38	2.73	1	0.0987

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
VeryLargeArea
SmallMediumLargeArea	—	—		—	—		—	—
VeryLargeArea	1.74	1.56, 1.95	<0.001	1.35	1.20, 1.52	<0.001	1.46	1.25, 1.69	<0.001
CountNeighbourbTB	1.45	1.40, 1.50	<0.001	1.43	1.38, 1.48	<0.001	1.47	1.40, 1.54	<0.001
VeryLargeArea * CountNeighbourbTB
VeryLargeArea * CountNeighbourbTB							0.94	0.88, 1.01	0.10
¹ OR = Odds Ratio, CI = Confidence Interval

coefficient changes - 10% rule for farm area and neighbour bTB status

There is some confounding between area and neighbours with bTB - after controlling for bTB status of neighbours, the relationship between area and bTB risk is smaller

## [1] "22% difference between non adjusted and asjusted coefficient"

## [1] "1% difference between non adjusted and asjusted coefficient"

Explore confounding more - what's going on?

Larger farms more are likely to have bTB positive neighbours. The table below shows that 75% of larger farms have at least 1 bTB positive neighbour, compared to only 37% of smaller farms

## # A tibble: 4 x 5
##   farm_area_category    Q1   med    Q3   max
##   <fct>              <dbl> <dbl> <dbl> <dbl>
## 1 SmallArea              0     0     1     5
## 2 MediumArea             0     1     1     8
## 3 LargeArea              0     1     2    11
## 4 VeryLargeArea          1     1     3    14

Fig4Area

Looking only at the presence/absence of bTB positive neighbours - almost twice as many very large farms had at least one bTB positive neighbour.

Variable	SmallArea, N = 1,121¹	MediumArea, N = 1,790¹	LargeArea, N = 2,913¹	VeryLargeArea, N = 3,450¹
NeighbourbTB	414 (37%)	956 (53%)	1,776 (61%)	2,601 (75%)
¹ n (%)

4B FARM FRAGMENTATION

1. Continuous fragmentation & binary neighbours (not in MS)

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.16	1.97, 2.37	<0.001
n_fragments_5m	1.01	1.00, 1.03	0.020
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.16	1.86, 2.51	<0.001
n_fragments_5m	1.01	0.99, 1.04	0.3
NeighbourbTB * n_fragments_5m	1.00	0.97, 1.03	>0.9
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
n_fragments_5m	1.03	1.02, 1.05	<0.001	1.01	1.00, 1.03	0.020	1.01	0.99, 1.04	0.3
NeighbourbTB	2.20	2.01, 2.41	<0.001	2.16	1.97, 2.37	<0.001	2.16	1.86, 2.51	<0.001
NeighbourbTB * n_fragments_5m							1.00	0.97, 1.03	>0.9
¹ OR = Odds Ratio, CI = Confidence Interval

2. Continuous fragmentation & Continuous neighbours (not in MS)

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.45	1.40, 1.51	<0.001
n_fragments_5m	0.99	0.98, 1.00	0.2
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.51	1.44, 1.59	<0.001
n_fragments_5m	1.00	0.99, 1.02	0.7
CountNeighbourbTB * n_fragments_5m	0.99	0.99, 1.00	0.019
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
n_fragments_5m	1.03	1.02, 1.05	<0.001	0.99	0.98, 1.00	0.2	1.00	0.99, 1.02	0.7
CountNeighbourbTB	1.45	1.40, 1.50	<0.001	1.45	1.40, 1.51	<0.001	1.51	1.44, 1.59	<0.001
CountNeighbourbTB * n_fragments_5m							0.99	0.99, 1.00	0.019
¹ OR = Odds Ratio, CI = Confidence Interval

3. Categorical fragmentation and binary neighbours (not in MS)

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.16	1.97, 2.37	<0.001
fragment_category
Not_fragmented	—	—
Little_fragmentation	0.88	0.77, 1.02	0.094
Medium_fragmentation	1.05	0.90, 1.23	0.6
High_fragmentation	1.28	1.05, 1.55	0.013
Very_High_fragmentation	1.01	0.83, 1.24	0.9
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	1.68	1.30, 2.17	<0.001
fragment_category
Not_fragmented	—	—
Little_fragmentation	0.76	0.62, 0.93	0.007
Medium_fragmentation	0.96	0.76, 1.22	0.7
High_fragmentation	1.20	0.88, 1.65	0.3
Very_High_fragmentation	0.71	0.47, 1.08	0.11
NeighbourbTB * fragment_category
NeighbourbTB * Little_fragmentation	1.37	1.03, 1.83	0.030
NeighbourbTB * Medium_fragmentation	1.24	0.90, 1.71	0.2
NeighbourbTB * High_fragmentation	1.20	0.81, 1.78	0.4
NeighbourbTB * Very_High_fragmentation	1.72	1.06, 2.77	0.027
¹ OR = Odds Ratio, CI = Confidence Interval

The univariable model is improved by the addition of bTB positive neighbours

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3187.45
2	-3043.59	287.72	1	0.0000

No evidence that an interaction term is needed

## <!-- html table generated in R 4.1.0 by xtable 1.8-4 package -->
## <!-- Tue Sep 14 11:50:35 2021 -->
## <table border=1>
## <tr> <th>  </th> <th> loglik </th> <th> Chisq </th> <th> Df </th> <th> P(&gt;|Chi|) </th>  </tr>
##   <tr> <td> 1 </td> <td align="right"> -3043.59 </td> <td align="right">  </td> <td align="right">  </td> <td align="right">  </td> </tr>
##   <tr> <td> 2 </td> <td align="right"> -3040.05 </td> <td align="right"> 7.08 </td> <td align="right"> 4 </td> <td align="right"> 0.1315 </td> </tr>
##    </table>

Characteristic	Unadjusted Analysis			Adjusted Analysis			Adjusted Analysis (Interaction
Characteristic	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value	OR¹	95% CI¹	p-value
fragment_category
Not_fragmented	—	—		—	—		—	—
Little_fragmentation	0.97	0.84, 1.11	0.7	0.88	0.77, 1.02	0.094	0.76	0.62, 0.93	0.007
Medium_fragmentation	1.25	1.07, 1.46	0.004	1.05	0.90, 1.23	0.6	0.96	0.76, 1.22	0.7
High_fragmentation	1.56	1.30, 1.88	<0.001	1.28	1.05, 1.55	0.013	1.20	0.88, 1.65	0.3
Very_High_fragmentation	1.36	1.12, 1.65	0.002	1.01	0.83, 1.24	0.9	0.71	0.47, 1.08	0.11
NeighbourbTB	2.20	2.01, 2.41	<0.001	2.16	1.97, 2.37	<0.001	1.68	1.30, 2.17	<0.001
NeighbourbTB * fragment_category
NeighbourbTB * Little_fragmentation							1.37	1.03, 1.83	0.030
NeighbourbTB * Medium_fragmentation							1.24	0.90, 1.71	0.2
NeighbourbTB * High_fragmentation							1.20	0.81, 1.78	0.4
NeighbourbTB * Very_High_fragmentation							1.72	1.06, 2.77	0.027
¹ OR = Odds Ratio, CI = Confidence Interval

4. Categorical fragmentation and Continuous neighbours (in MS)

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.45	1.40, 1.51	<0.001
fragment_category
Not_fragmented	—	—
Little_fragmentation	0.83	0.72, 0.96	0.014
Medium_fragmentation	0.96	0.81, 1.12	0.6
High_fragmentation	1.06	0.87, 1.30	0.6
Very_High_fragmentation	0.73	0.59, 0.91	0.004
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.44	1.25, 1.65	<0.001
fragment_category
Not_fragmented	—	—
Little_fragmentation	0.78	0.66, 0.94	0.008
Medium_fragmentation	0.97	0.79, 1.18	0.7
High_fragmentation	1.17	0.90, 1.52	0.2
Very_High_fragmentation	0.80	0.59, 1.07	0.13
CountNeighbourbTB * fragment_category
CountNeighbourbTB * Little_fragmentation	1.07	0.92, 1.24	0.4
CountNeighbourbTB * Medium_fragmentation	1.00	0.86, 1.16	>0.9
CountNeighbourbTB * High_fragmentation	0.95	0.81, 1.12	0.5
CountNeighbourbTB * Very_High_fragmentation	0.97	0.83, 1.14	0.7
¹ OR = Odds Ratio, CI = Confidence Interval

The univariable model is improved by the addition of bTB positive neighbours

	loglik	Chisq	Df	P(>\|Chi\|)
1	-3187.45
2	-2909.70	555.50	1	0.0000

No evidence that an interaction term is needed

##  ##  ## <table border=1> ## <tr> <th> </th> <th> loglik </th> <th> Chisq </th> <th> Df </th> <th> P(>|Chi|) </th> </tr> ## <tr> <td> 1 </td> <td align="right"> -2909.70 </td> <td align="right"> </td> <td align="right"> </td> <td align="right"> </td> </tr> ## <tr> <td> 2 </td> <td align="right"> -2906.31 </td> <td align="right"> 6.80 </td> <td align="right"> 4 </td> <td align="right"> 0.1471 </td> </tr> ## </table>

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

fragment_category

Not_fragmented — — — — — —

Little_fragmentation 0.97 0.84, 1.11 0.7 0.83 0.72, 0.96 0.014 0.78 0.66, 0.94 0.008

Medium_fragmentation 1.25 1.07, 1.46 0.004 0.96 0.81, 1.12 0.6 0.97 0.79, 1.18 0.7

High_fragmentation 1.56 1.30, 1.88 <0.001 1.06 0.87, 1.30 0.6 1.17 0.90, 1.52 0.2

Very_High_fragmentation 1.36 1.12, 1.65 0.002 0.73 0.59, 0.91 0.004 0.80 0.59, 1.07 0.13

CountNeighbourbTB 1.45 1.40, 1.50 <0.001 1.45 1.40, 1.51 <0.001 1.44 1.25, 1.65 <0.001

CountNeighbourbTB * fragment_category

CountNeighbourbTB * Little_fragmentation 1.07 0.92, 1.24 0.4

CountNeighbourbTB * Medium_fragmentation 1.00 0.86, 1.16 >0.9

CountNeighbourbTB * High_fragmentation 0.95 0.81, 1.12 0.5

CountNeighbourbTB * Very_High_fragmentation 0.97 0.83, 1.14 0.7

¹ OR = Odds Ratio, CI = Confidence Interval

Confounding in fragmentation - looks like the presence of bTB positive neighbours confounds the relationship with fragmentation and breakdown risk.

## [1] "14% difference between non adjusted and adjusted coefficient" ## [2] "24% difference between non adjusted and adjusted coefficient" ## [3] "32% difference between non adjusted and adjusted coefficient" ## [4] "46% difference between non adjusted and adjusted coefficient"

## [1] "1% difference between non adjusted and adjusted coefficient"

Explore confounding more - what's going on?

Larger farms more are likely to have bTB positive neighbours. The table below shows that 75% of larger farms have at least 1 bTB positive neighbour, compared to only 37% of smaller farms

## # A tibble: 5 x 5 ## fragment_category Q1 med Q3 max ## <fct> <dbl> <dbl> <dbl> <dbl> ## 1 Not_fragmented 0 0 1 5 ## 2 Little_fragmentation 0 1 2 11 ## 3 Medium_fragmentation 0 1 2 14 ## 4 High_fragmentation 1 2 3 13 ## 5 Very_High_fragmentation 1 2 4 14

Fig4Frag

Variable Not_fragmented, N = 1,014¹ Little_fragmentation, N = 4,200¹ Medium_fragmentation, N = 2,227¹ High_fragmentation, N = 966¹ Very_High_fragmentation, N = 867¹

NeighbourbTB 461 (45%) 2,298 (55%) 1,531 (69%) 725 (75%) 732 (84%)

¹ n (%)

4B FRAGMENT DISPERSAL

1. COntinuous dispersal and binary neighbours (not in MS)

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.20 2.01, 2.41 <0.001

median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.7

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.35 2.11, 2.61 <0.001

median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.031

NeighbourbTB * median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.018

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.030 1.00 1.00, 1.00 0.7 1.00 1.00, 1.00 0.031

NeighbourbTB 2.20 2.01, 2.41 <0.001 2.20 2.01, 2.41 <0.001 2.35 2.11, 2.61 <0.001

NeighbourbTB * median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.018

¹ OR = Odds Ratio, CI = Confidence Interval

2. Continuous dispersal and continuous neighbours (not in MS)

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.45 1.40, 1.50 <0.001

median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.5

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.54 1.47, 1.60 <0.001

median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.007

CountNeighbourbTB * median_distance_fragments_km_scaled 1.00 1.00, 1.00 <0.001

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

median_distance_fragments_km_scaled 1.00 1.00, 1.00 0.030 1.00 1.00, 1.00 0.5 1.00 1.00, 1.00 0.007

CountNeighbourbTB 1.45 1.40, 1.50 <0.001 1.45 1.40, 1.50 <0.001 1.54 1.47, 1.60 <0.001

CountNeighbourbTB * median_distance_fragments_km_scaled 1.00 1.00, 1.00 <0.001

¹ OR = Odds Ratio, CI = Confidence Interval

3. Binary dispersal and binary neighbours (not in MS)

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.14 1.95, 2.34 <0.001

HighVeryHighDisp

SmallMedium — —

HighVeryHigh 1.23 1.12, 1.35 <0.001

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.18 1.91, 2.49 <0.001

HighVeryHighDisp

SmallMedium — —

HighVeryHigh 1.26 1.09, 1.45 0.001

NeighbourbTB * HighVeryHighDisp

NeighbourbTB * HighVeryHigh 0.96 0.81, 1.15 0.7

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

HighVeryHighDisp

SmallMedium — — — — — —

HighVeryHigh 1.37 1.25, 1.49 <0.001 1.23 1.12, 1.35 <0.001 1.26 1.09, 1.45 0.001

NeighbourbTB 2.20 2.01, 2.41 <0.001 2.14 1.95, 2.34 <0.001 2.18 1.91, 2.49 <0.001

NeighbourbTB * HighVeryHighDisp

NeighbourbTB * HighVeryHigh 0.96 0.81, 1.15 0.7

¹ OR = Odds Ratio, CI = Confidence Interval

4. Binary dispersal and continuous neighbours (in MS)

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.44 1.39, 1.49 <0.001

fragment_distance_category

Low — —

Medium 0.84 0.73, 0.97 0.016

High 1.01 0.87, 1.17 0.9

Very High 1.01 0.88, 1.16 0.9

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.63 1.44, 1.84 <0.001

fragment_distance_category

Low — —

Medium 0.83 0.70, 0.99 0.037

High 1.09 0.91, 1.30 0.4

Very High 1.19 1.00, 1.41 0.053

CountNeighbourbTB * fragment_distance_category

CountNeighbourbTB * Medium 0.97 0.84, 1.12 0.7

CountNeighbourbTB * High 0.88 0.77, 1.01 0.068

CountNeighbourbTB * Very High 0.83 0.73, 0.95 0.007

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

fragment_distance_category

Low — — — — — —

Medium 0.97 0.85, 1.11 0.6 0.84 0.73, 0.97 0.016 0.83 0.70, 0.99 0.037

High 1.33 1.16, 1.52 <0.001 1.01 0.87, 1.17 0.9 1.09 0.91, 1.30 0.4

Very High 1.35 1.19, 1.55 <0.001 1.01 0.88, 1.16 0.9 1.19 1.00, 1.41 0.053

CountNeighbourbTB 1.45 1.40, 1.50 <0.001 1.44 1.39, 1.49 <0.001 1.63 1.44, 1.84 <0.001

CountNeighbourbTB * fragment_distance_category

CountNeighbourbTB * Medium 0.97 0.84, 1.12 0.7

CountNeighbourbTB * High 0.88 0.77, 1.01 0.068

CountNeighbourbTB * Very High 0.83 0.73, 0.95 0.007

¹ OR = Odds Ratio, CI = Confidence Interval

The univariable model is improved by the addition of bTB positive neighbours

loglik Chisq Df P(>|Chi|)

1 -3188.68

2 -2914.72 547.92 1 0.0000

An interaction term is needed:

loglik Chisq Df P(>|Chi|)

1 -2914.72

2 -2907.27 14.91 3 0.0019

## [1] "13% difference between non adjusted and adjusted coefficient" ## [2] "24% difference between non adjusted and adjusted coefficient" ## [3] "25% difference between non adjusted and adjusted coefficient"

## [1] "0% difference between non adjusted and adjusted coefficient"

Investigate relationships

## # A tibble: 4 x 5 ## fragment_distance_category Q1 med Q3 max ## <fct> <dbl> <dbl> <dbl> <dbl> ## 1 Low 0 0 1 6 ## 2 Medium 0 1 2 10 ## 3 High 0 1 2 13 ## 4 Very High 0 1 2 14

Fig4Disp

Variable Low, N = 1,495¹ Medium, N = 2,454¹ High, N = 2,707¹ Very High, N = 2,618¹

NeighbourbTB 626 (42%) 1,411 (57%) 1,918 (71%) 1,792 (68%)

¹ n (%)

4C CONTACT METRICS

1. COntinuous contact and binary neighbours (not in MS)

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.06 1.88, 2.27 <0.001

total_shared_boundary_grazing_km 1.04 1.03, 1.06 <0.001

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.31 1.99, 2.68 <0.001

total_shared_boundary_grazing_km 1.07 1.04, 1.10 <0.001

NeighbourbTB * total_shared_boundary_grazing_km 0.97 0.94, 1.00 0.050

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

total_shared_boundary_grazing_km 1.07 1.06, 1.09 <0.001 1.04 1.03, 1.06 <0.001 1.07 1.04, 1.10 <0.001

NeighbourbTB 2.20 2.01, 2.41 <0.001 2.06 1.88, 2.27 <0.001 2.31 1.99, 2.68 <0.001

NeighbourbTB * total_shared_boundary_grazing_km 0.97 0.94, 1.00 0.050

¹ OR = Odds Ratio, CI = Confidence Interval

2. Continuous contact and continuous neighbours (not in MS)

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.44 1.39, 1.50 <0.001

total_shared_boundary_grazing_km 1.00 0.99, 1.02 0.8

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.58 1.50, 1.66 <0.001

total_shared_boundary_grazing_km 1.03 1.01, 1.05 0.003

CountNeighbourbTB * total_shared_boundary_grazing_km 0.99 0.98, 0.99 <0.001

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

total_shared_boundary_grazing_km 1.07 1.06, 1.09 <0.001 1.00 0.99, 1.02 0.8 1.03 1.01, 1.05 0.003

CountNeighbourbTB 1.45 1.40, 1.50 <0.001 1.44 1.39, 1.50 <0.001 1.58 1.50, 1.66 <0.001

CountNeighbourbTB * total_shared_boundary_grazing_km 0.99 0.98, 0.99 <0.001

¹ OR = Odds Ratio, CI = Confidence Interval

3. Categorical contact & binary neighbours (not in MS)

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.10 1.91, 2.31 <0.001

neighbour_contact_category

Low — —

Medium 0.92 0.80, 1.06 0.3

High 0.97 0.84, 1.12 0.7

Very High 1.25 1.08, 1.46 0.003

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

NeighbourbTB 2.34 1.86, 2.93 <0.001

neighbour_contact_category

Low — —

Medium 0.89 0.74, 1.07 0.2

High 1.11 0.91, 1.35 0.3

Very High 1.37 1.10, 1.71 0.005

NeighbourbTB * neighbour_contact_category

NeighbourbTB * Medium 1.04 0.78, 1.39 0.8

NeighbourbTB * High 0.78 0.59, 1.04 0.090

NeighbourbTB * Very High 0.84 0.64, 1.12 0.2

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

neighbour_contact_category

Low — — — — — —

Medium 1.02 0.89, 1.18 0.7 0.92 0.80, 1.06 0.3 0.89 0.74, 1.07 0.2

High 1.20 1.04, 1.38 0.011 0.97 0.84, 1.12 0.7 1.11 0.91, 1.35 0.3

Very High 1.72 1.49, 1.98 <0.001 1.25 1.08, 1.46 0.003 1.37 1.10, 1.71 0.005

NeighbourbTB 2.20 2.01, 2.41 <0.001 2.10 1.91, 2.31 <0.001 2.34 1.86, 2.93 <0.001

NeighbourbTB * neighbour_contact_category

NeighbourbTB * Medium 1.04 0.78, 1.39 0.8

NeighbourbTB * High 0.78 0.59, 1.04 0.090

NeighbourbTB * Very High 0.84 0.64, 1.12 0.2

¹ OR = Odds Ratio, CI = Confidence Interval

4. Categorical contact & continuous neighbours (in MS)

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.44 1.39, 1.49 <0.001

neighbour_contact_category

Low — —

Medium 0.91 0.79, 1.05 0.2

High 0.95 0.82, 1.10 0.5

Very High 1.02 0.87, 1.19 0.8

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic OR¹ 95% CI¹ p-value

CountNeighbourbTB 1.46 1.29, 1.66 <0.001

neighbour_contact_category

Low — —

Medium 0.79 0.66, 0.94 0.009

High 0.85 0.71, 1.02 0.074

Very High 1.22 1.01, 1.46 0.035

CountNeighbourbTB * neighbour_contact_category

CountNeighbourbTB * Medium 1.21 1.03, 1.42 0.023

CountNeighbourbTB * High 1.11 0.96, 1.29 0.2

CountNeighbourbTB * Very High 0.90 0.79, 1.03 0.12

¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic Unadjusted Analysis Adjusted Analysis Adjusted Analysis (Interaction)

OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value OR¹ 95% CI¹ p-value

neighbour_contact_category

Low — — — — — —

Medium 1.02 0.89, 1.18 0.7 0.91 0.79, 1.05 0.2 0.79 0.66, 0.94 0.009

High 1.20 1.04, 1.38 0.011 0.95 0.82, 1.10 0.5 0.85 0.71, 1.02 0.074

Very High 1.72 1.49, 1.98 <0.001 1.02 0.87, 1.19 0.8 1.22 1.01, 1.46 0.035

CountNeighbourbTB 1.45 1.40, 1.50 <0.001 1.44 1.39, 1.49 <0.001 1.46 1.29, 1.66 <0.001

CountNeighbourbTB * neighbour_contact_category

CountNeighbourbTB * Medium 1.21 1.03, 1.42 0.023

CountNeighbourbTB * High 1.11 0.96, 1.29 0.2

CountNeighbourbTB * Very High 0.90 0.79, 1.03 0.12

¹ OR = Odds Ratio, CI = Confidence Interval

The univariable model is improved by the addition of bTB positive neighbours

loglik Chisq Df P(>|Chi|)

1 -3169.94

2 -2919.27 501.35 1 0.0000

No evidence that an interaction term is needed

loglik Chisq Df P(>|Chi|)

1 -2919.27

2 -2897.13 44.27 3 0.0000

coefficient changes - 10% rule for contact metrics and neighbour bTB status

## [1] "11% difference between non adjusted and adjusted coefficient" ## [2] "20% difference between non adjusted and adjusted coefficient" ## [3] "41% difference between non adjusted and adjusted coefficient"

## [1] "0.53% difference between non adjusted and adjusted coefficient"

Explore confounding more - what's going on?

## # A tibble: 4 x 5 ## neighbour_contact_category Q1 med Q3 max ## <fct> <dbl> <dbl> <dbl> <dbl> ## 1 Low 0 0 1 6 ## 2 Medium 0 0 1 8 ## 3 High 0 1 2 8 ## 4 Very High 1 2 3 14

Fig4Contact

Variable Low, N = 1,407¹ Medium, N = 2,004¹ High, N = 2,436¹ Very High, N = 3,427¹

NeighbourbTB 503 (36%) 991 (49%) 1,548 (64%) 2,705 (79%)

¹ n (%)

Variable	Not_fragmented, N = 1,014¹	Little_fragmentation, N = 4,200¹	Medium_fragmentation, N = 2,227¹	High_fragmentation, N = 966¹	Very_High_fragmentation, N = 867¹
NeighbourbTB	461 (45%)	2,298 (55%)	1,531 (69%)	725 (75%)	732 (84%)
¹ n (%)

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.35	2.11, 2.61	<0.001
median_distance_fragments_km_scaled	1.00	1.00, 1.00	0.031
NeighbourbTB * median_distance_fragments_km_scaled	1.00	1.00, 1.00	0.018
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.54	1.47, 1.60	<0.001
median_distance_fragments_km_scaled	1.00	1.00, 1.00	0.007
CountNeighbourbTB * median_distance_fragments_km_scaled	1.00	1.00, 1.00	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.14	1.95, 2.34	<0.001
HighVeryHighDisp
SmallMedium	—	—
HighVeryHigh	1.23	1.12, 1.35	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.18	1.91, 2.49	<0.001
HighVeryHighDisp
SmallMedium	—	—
HighVeryHigh	1.26	1.09, 1.45	0.001
NeighbourbTB * HighVeryHighDisp
NeighbourbTB * HighVeryHigh	0.96	0.81, 1.15	0.7
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.44	1.39, 1.49	<0.001
fragment_distance_category
Low	—	—
Medium	0.84	0.73, 0.97	0.016
High	1.01	0.87, 1.17	0.9
Very High	1.01	0.88, 1.16	0.9
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.63	1.44, 1.84	<0.001
fragment_distance_category
Low	—	—
Medium	0.83	0.70, 0.99	0.037
High	1.09	0.91, 1.30	0.4
Very High	1.19	1.00, 1.41	0.053
CountNeighbourbTB * fragment_distance_category
CountNeighbourbTB * Medium	0.97	0.84, 1.12	0.7
CountNeighbourbTB * High	0.88	0.77, 1.01	0.068
CountNeighbourbTB * Very High	0.83	0.73, 0.95	0.007
¹ OR = Odds Ratio, CI = Confidence Interval

Variable	Low, N = 1,495¹	Medium, N = 2,454¹	High, N = 2,707¹	Very High, N = 2,618¹
NeighbourbTB	626 (42%)	1,411 (57%)	1,918 (71%)	1,792 (68%)
¹ n (%)

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.06	1.88, 2.27	<0.001
total_shared_boundary_grazing_km	1.04	1.03, 1.06	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.31	1.99, 2.68	<0.001
total_shared_boundary_grazing_km	1.07	1.04, 1.10	<0.001
NeighbourbTB * total_shared_boundary_grazing_km	0.97	0.94, 1.00	0.050
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.44	1.39, 1.50	<0.001
total_shared_boundary_grazing_km	1.00	0.99, 1.02	0.8
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.58	1.50, 1.66	<0.001
total_shared_boundary_grazing_km	1.03	1.01, 1.05	0.003
CountNeighbourbTB * total_shared_boundary_grazing_km	0.99	0.98, 0.99	<0.001
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.10	1.91, 2.31	<0.001
neighbour_contact_category
Low	—	—
Medium	0.92	0.80, 1.06	0.3
High	0.97	0.84, 1.12	0.7
Very High	1.25	1.08, 1.46	0.003
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
NeighbourbTB	2.34	1.86, 2.93	<0.001
neighbour_contact_category
Low	—	—
Medium	0.89	0.74, 1.07	0.2
High	1.11	0.91, 1.35	0.3
Very High	1.37	1.10, 1.71	0.005
NeighbourbTB * neighbour_contact_category
NeighbourbTB * Medium	1.04	0.78, 1.39	0.8
NeighbourbTB * High	0.78	0.59, 1.04	0.090
NeighbourbTB * Very High	0.84	0.64, 1.12	0.2
¹ OR = Odds Ratio, CI = Confidence Interval

Characteristic	OR¹	95% CI¹	p-value
CountNeighbourbTB	1.46	1.29, 1.66	<0.001
neighbour_contact_category
Low	—	—
Medium	0.79	0.66, 0.94	0.009
High	0.85	0.71, 1.02	0.074
Very High	1.22	1.01, 1.46	0.035
CountNeighbourbTB * neighbour_contact_category
CountNeighbourbTB * Medium	1.21	1.03, 1.42	0.023
CountNeighbourbTB * High	1.11	0.96, 1.29	0.2
CountNeighbourbTB * Very High	0.90	0.79, 1.03	0.12
¹ OR = Odds Ratio, CI = Confidence Interval

Variable	Low, N = 1,407¹	Medium, N = 2,004¹	High, N = 2,436¹	Very High, N = 3,427¹
NeighbourbTB	503 (36%)	991 (49%)	1,548 (64%)	2,705 (79%)
¹ n (%)

DescAnalysisEpi

Georgina Milne

01 Sep 2021

R Markdown

1. Descriptive Statistics

TABLE 1

2. Correlation between explanatory variables

3. UNIVARIABLE ASSOCIATIONS

3A FARM AREA

3A 1 Farm Area - Continuous

3A 2 Farm Area - Categorical

3A 3 Farm Area - Ordinal

3B FARM FRAGMENTATION

3B 1 Farm Fragmentation - Continuous

3B 2 Farm Fragmentation - Categorical

3B 3 Farm Fragmentation - Ordinal

3C FRAGMENT DISPESAL

3C 1 Fragment Dispersal - Continuous

3C 3 Fragment Dispersal - Categorical

Conditional GLM

3C 3 Farm Fragmentation - Ordinal

3D CONTACT METRICS (i.e. shared boundary - exposure to neighbouring farms)

3D 1 Contact Metrics - Continuous

3D 3 Contact Metrics - Categorical

3D 4 Contact Metrics - Ordinal

3E NEIGHBOUR BTB STATUS

3E Continuous

3E Binary

3D 4 Contact Metrics - Ordinal

4 Assess confounding & effect modification between each explanatory variable and bTB positive neighbours

4A FARM AREA

1. Continuous area & Binary neighbours (not in main MS)

2. Continuous area & Continuous neighbours (not in MS)

3. Categorical area & Binary neiehgbours (not in MS)

4. Categorical area & Continuous neighbours (not in MS)

5. Binary Area & Continuous neighbours (in MS)

4B FARM FRAGMENTATION

1. Continuous fragmentation & binary neighbours (not in MS)

2. Continuous fragmentation & Continuous neighbours (not in MS)

3. Categorical fragmentation and binary neighbours (not in MS)

4. Categorical fragmentation and Continuous neighbours (in MS)

4B FRAGMENT DISPERSAL

1. COntinuous dispersal and binary neighbours (not in MS)

2. Continuous dispersal and continuous neighbours (not in MS)

3. Binary dispersal and binary neighbours (not in MS)

4. Binary dispersal and continuous neighbours (in MS)

4C CONTACT METRICS

1. COntinuous contact and binary neighbours (not in MS)

2. Continuous contact and continuous neighbours (not in MS)

3. Categorical contact & binary neighbours (not in MS)

4. Categorical contact & continuous neighbours (in MS)