A Bayesian Belief Network to Infer Incentive Mechanisms to Reduce Antibiotic Use in Livestock Production

Figures & data

Fig. 1 Conceptual model of the causal relationships among key variables.

Table 1 Definition and descriptive statistics of the manifest variables used in the BBN model (N = number of observations).

Description (Unit)	Year								Overall
	2007 (N = 26)		2008 (N = 41)		2009 (N = 42)		2010 (N = 32)
	Mean	sd	Mean	sd	Mean	sd	Mean	sd	Mean	sd
Capital depreciation costs (€/animal/year)	27.4	22.6	32.9	38.4	38.6	52.0	34.5	41.1	33.9	41.1
Feed conversion ratio (Dimensionless)	2.89	0.18	2.91	0.22	2.86	0.21	2.87	0.21	2.88	0.21
Gross margin over feed (€/animal/year)	55.1	18.7	85.0	19.5	49.1	16.9	72.7	14.7	66.0	23.0
General costs (€/animal/year)	9.9	7.0	13.1	14.7	13.3	18.9	12.5	11.2	12.4	14.3
Gross margin of the farm (€/animal/year)	-52.1	49.1	-15.1	80.9	-52.5	42.3	-8.3	97.9	-31.5	73.2
Mortality of pigs (%)	2.9	1.1	3.1	2.4	3.3	3.4	2.5	1.0	3.0	2.3
Number of treatment days(Day/animal year)	18.5	12.7	23.4	16.9	17.7	12.9	13.6	12.1	18.6	14.3
Revenue to costs ratio (%)	82.1	8.9	94.6	12.0	83.3	9.4	93.3	8.6	88.6	11.4
Solvency rate (%)	65.9	23.3	62.1	23.5	57.5	24.0	57.5	24.8	60.4	23.9
Veterinary costs (€/animal/year)	2.9	1.5	3.6	1.8	2.9	1.8	2.8	1.6	3.1	1.7
Spread in gross margin over feed (€/animal)	38.6	12.9	40.2	15.9	40.0	15.9	39.6	16.8	39.7	15.5
Spread in gross margin of the farm (€/animal)	54.5	31.5	61.5	75.1	62.9	75.7	64.9	84.6	61.4	71.2

Table 2 Correlationmatrix between antibiotic use (NDD and other manifest variables used to infer the latent factors.

	NDD	DepCost	FCR	FeedMargin	GenCost	GrossMargin	Mortality	RCR	Solvency	VetCost	DeltaFeed	DeltaGross
NDD	1
DepCost	0.156	1
	(0.310)
FCR	0.249	-0.199	1
	(0.103)	(0.196)
FeedMargin	0.238	-0.056	-0.101	1
	(0.119)	(0.719)	(0.514)
GenCost	0.101	0.880 *	-0.093	-0.243	1
	(0.513)	(0.000)	(0.547)	(0.111)
GrossMargin	0.384 *	0.572 *	-0.093	0.371 *	0.399 *	1
	(0.010)	(0.000)	(0.547)	(0.013)	(0.007)
Mortality	0.263	-0.068	0.274	-0.264	-0.016	-0.063	1
	(0.085)	(0.660)	(0.072)	(0.083)	(0.916)	(0.685)
RCR	0.331 *	0.288	0.072	0.558 *	0.135	0.772 *	0.011	1
	(0.028)	(0.058)	(0.643)	(0.000)	(0.384)	(0.000)	(0.943)
Solvency	-0.275	0.154	-0.146	-0.029	0.180	-0.008	-0.173	0.022	1
	(0.071)	(0.319)	(0.343)	(0.852)	(0.242)	(0.958)	(0.261)	(0.889)
VetCost	0.293	0.112	0.040	0.025	0.055	-0.067	0.016	-0.220	-0.092	1
	(0.053)	(0.470)	(0.799)	(0.874)	(0.723)	(0.667)	(0.918)	(0.150)	(0.551)
DeltaFeed	0.288	0.026	0.120	0.200	-0.042	0.193	0.387 *	0.201	-0.156	0.285	1
	(0.058)	(0.869)	(0.439)	(0.194)	(0.786)	(0.210)	(0.009)	(0.191)	(0.312)	(0.060)
DeltaGross	0.158	0.938 *	-0.188	0.023	0.807 *	0.669 *	-0.124	0.376 *	0.129	0.102	0.225	1
	(0.306)	(0.000)	(0.220)	(0.880)	(0.000)	(0.000)	(0.421)	(0.012)	(0.406)	(0.509)	(0.141)

Significance levels are shown between brackets,* P< 0.05

Table 3 Rotated factor loadings of manifest variables.

	Factor1	Factor2
NDD	-0.043	0.632
DepCost	0.958	0.080
FCR	-0.271	0.245
GenCost	0.877	-0.055
GrossMargin	0.483	0.647
RCR	0.198	0.668
Solvency	0.258	-0.270
VetCost	-0.012	0.143
DeltaFeedMargin	-0.093	0.514
DeltaGrossMargin	0.902	0.234

Table 4 Evidence statistics of the variables used in the BBN model.

	Input					Factor 1				Factor 2
Evidence ^*	Very low	Low	Average	High	Very high	Very low	Low	Average	High	Very high	Very low	Low	Average	High	Very high
Default	20%	20%	20%	20%	20%	29%	12%	6%	7%	47%	6%	23%	14%	25%	31%
NDD ^*	0%	0%	0%	0%	100%	42%	11%	5%	7%	35%	0%	2%	7%	25%	66%
DeltaFeedMargin ^*	0%	0%	0%	0%	100%	38%	11%	6%	7%	38%	1%	11%	9%	21%	57%
DeltaGrossMargin ^*	0%	0%	0%	0%	100%	6%	23%	14%	25%	31%	6%	23%	14%	25%	31%
DepCost ^*	0%	0%	0%	0%	100%	8%	5%	3%	4%	80%	6%	23%	14%	25%	31%
GenCost ^*	0%	0%	0%	0%	100%	21%	11%	7%	7%	54%	6%	23%	14%	25%	31%
GrossMargin ^*	0%	0%	0%	0%	100%	22%	9%	5%	6%	59%	0%	2%	7%	27%	64%
RCR ^*	0%	0%	0%	0%	100%	40%	11%	5%	7%	37%	0%	7%	7%	27%	58%

* Evidence on all other variables are set as default, the probabilities for the two factors were rounded.

Fig. 2 Probability distributions of Factor 1 with different evidences on the manifest variables.

Fig. 3 Probability distributions of Factor 2 with different evidences on the manifest variables.

Fig. 4 The Bayesian Belief Network (BBN) with evidence of Factor 1 and Factor 2 in GeNie.