Bayesian network Case examples Advanced Herd Managem ent October 2 - PDF document

Bayesian network Case examples Advanced Herd Managem ent October 2 nd 2 0 0 7 Tina Birk Jensen Outline 1 . PigLam e m odel � Background of the m odel � The qualitative part of the m odel � The quantitative part of the m odel � Elicitation of probabilities � Output variables � Exam ple of use ( Esthauge) 2 . Mycoplasm a net � Background of the m odel � The m odel � Consequences of Mycoplasm a 1

Background Leg disorders in finishers: An economical problem for farmers due to: - Increased work load - Cost of treatments - Reduced productivity - Risk of condemnations - A negative impact on animal welfare Background Causes of leg disorders 1 . I nfectious Mycoplasma hyosynoviae, Erysipelothrix rhusiopathiae, Haemophilus parasuis, Streptococcus suis 2 . Environm ental Fracture, lesion to the claw wall, lesion to the claw sole 3 . I nherited Osteochondrosis manifesta, osteochondrosis dissecans Control strategies against leg disorders will depend on the cause category 2

Leg disorder Herd Pig Info Info Leg disorder 3

Herd Pig Info Info Leg disorder Strategy Strategy Strategy 1 2 3 Purpose of the PigLame model To estimate probability distributions of different manageable causes of leg disorders in finisher herds 4

PigLame model Bayesian Netw orks • A set of variables and directed edges betw een variables • Each variable has a finite set of m utually exclusive states • The variables and edges form a directed acyclic graph • To each variable A w ith parents B 1 ….B n , there is attached the probability table P( A| B 1 ,….,B n ) Bayesian network A B Bayes Theorem : ( ) ( ) ( ) P B | A P A i i = | P A B i + + + ( | ) ( ) ( | ) ( ) ... ( | ) ( ) P B A P A P B A P A P B A P A 1 1 2 2 n n 5

Bayesian network W hy use Bayesian Netw ork approach for the PigLam e m odel? • Static m odel • Express the biological variation and represent uncertainty • I nform ation can flow in the opposite direction of the causality • Evidence about som e input variables can tell us som ething about variables that are not observable ”Hypothesis variables” Object-oriented Bayesian network The object diagram for the PigLam e m odel Herd class Herd size Production Purchase Pen density Floor type Straw Pig class Gender Disease Diagnostic test Lean meat percent 6

Qualitative structure of the PigLame model • Tw o classes: Herd class and pig class • Background for the qualitative structure is based on evidence from published literature Qualitative structure of the PigLame model 7

Feed strat Breed Pen Herd Produc- Floor Straw Purchase Weight den size tion Environmental Infectious Inherited Herd class Environmental Infectious Inherited TailBite Arth_risk Gender LMP Fracture Claw wall Claw sole Myco Strep Erysi Haemo OCM OCD PigLame Path2 Clinic2 Path3 Bac1 Path4 Bac2 Path5 Bac3 Path6 Bac4 Path1 Clinic1 Path7 Path8 Path9 ObsLame Pig class 8

The quantitative part of the PigLame model The probabilities in the model are based on: - Literature - Expert opinions The quantitative part of the model Probabilities elicited from the literature How to get the probabilities into the model Example: Meat Percent OCM OCD 9

The quantitative part of the model Probabilities elicited from the literature I ncrease in the LMP of one percentage point OR= 1 .0 3 ( OCM) OR= 1 .0 5 ( OCD) ⎛ ⎞ Pno ⎜ ⎟ ⎜ ⎟ OR − ⎝ 1 ⎠ pno = Form ula: Pyes ⎛ ⎞ Pno + ⎜ ⎟ 1 OR − ⎝ ⎠ 1 Pno Assum e: P( OCM) = 0 .5 P( OCD) = 0 .2 The quantitative part of the model Level Odds Ratio Probability P(OCM| 0 percent) OR 0 = 1.03 0 = 1 0.5 OR 1 = 1.03 1 = 1.03 P(OCM| 1 percent) 0.507 P(OCM| 2 percent) OR 2 = 1.03 2 = 1.06 0.515 P(OCM| 3 percent) OR 3 = 1.03 3 = 1.09 0.522 OR 4 = 1.03 4 = 1.13 P(OCM| 4 percent) 0.530 P(OCM| 5 percent) OR 5 = 1.03 5 = 1.16 0.537 Level Odds Ratio Probability P(OCD| 0 percent) OR 0 = 1.05 0 = 1 0.2 P(OCD| 1 percent) OR 1 = 1.05 1 = 1.05 0.208 P(OCD| 2 percent) OR 2 = 1.05 2 = 1.10 0.216 P(OCD| 3 percent) OR 3 = 1.05 3 = 1.16 0.225 P(OCD| 4 percent) OR 4 = 1.05 4 = 1.22 0.234 P(OCD| 5 percent) OR 5 = 1.05 5 = 1.28 0.242 10

Exam ple: P( Fracture| fully slatted floors) Exam ple: P( Fracture| fully slatted floors) Consider 100 pigs examined individually at a herd visit. The herd has fully slatted floors in the pens. How often do you, during the examination expect to find a pig with a fracture? 11

Always (almost) 100 Exam ple: P( Fracture| fully slatted floors) 85 Usually 75 Consider 100 pigs examined individually Often at a herd visit. The herd has fully slatted floors in the pens. As often as not 50 How often do you, during the examination expect to find a pig with a fracture? Sometimes 25 Once in a while 15 (Almost) never 0 The quantitative part of the PigLame model From the literature • 46 conditional probabilities From experts • > 150 conditional probabilities • 6 experts • Not randomly distributed 12

The quantitative part of the model The ”output” nodes • I nfectious, environm ental and inherited express the m agnitude of the cause-category at herd level • Considered as a continuous variable • Need to m ake a discretization of the node • Logit m ethod The nodes have 1 0 states • Environmental Infectious Inherited TailBite Arth_risk Gender LMP Fracture Claw wall Claw sole Myco Strep Erysi Haemo OCM OCD PigLame Path2 Clinic2 Path3 Bac1 Path4 Bac2 Path5 Bac3 Path6 Bac4 Path1 Clinic1 Path7 Path8 Path9 ObsLame Pig class 13

The quantitative part of the model The ”output” nodes Exam ple: Inherited OCM OCD The quantitative part of the model The ”output” nodes ( 1 ) I nherited= Logit( P( OCM| I nherited) ) + 0 C ( 2 ) I nherited= Logit( P( OCD| I nherited) ) + C Then w e get: P( OCM| I nherited) = Logit -1 ( I nherited – 0 C) ( 1 ’) ( 2 ’) P( OCD| I nherited) = Logit -1 ( I nherited – C) 14

The quantitative part of the model The ”output” nodes Assum e: P( OCM| I nherited) = 0 .5 P( OCD| I nherited) = 0 .2 Then: P( OCM| I nherited) = Logit -1 ( I nherited – 0 C ) = 0 .5 ( 1 ’) P( OCD| I nherited) = Logit -1 ( I nherited – C) = 0 .2 ( 2 ’) W hich gives: C= -1 .3 9 I nherited ( OCM) = 0 I nherited ( OCD) = 1 .3 9 The quantitative part of the model The ”output” nodes P( OCM| 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 I nherited) I nherited -2.20 -1.39 -0.85 -0.41 0 0.41 0.85 1.39 P( OCD| 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 I nherited) I nherited 0.81 0 0.54 0.98 1.39 1.79 2.23 2.77 15

Perspectives • Probability distributions for the three cause- categories of leg disorders can serve as inputs for future econom ic calculations • First step in developing an econom ic m odel for leg disorders in finisher herds Mycoplasma net Outline � Background of the model � The model � Consequences of Mycoplasma Literature: Otto, L. and Kristensen, C.S., 2 0 0 4 : A biological netw ork describing infection w ith Mycoplasm a hyopnem oniae in sw ine herds. Preventive Veterinary Medicine, 6 6 , 1 4 1 - 1 6 1 . 16

Mycoplasma hyopneumonia • Cause enzootic pneumonia in finishers • Important in the intensive pig production • Can exist latent in the herd • Outbreak: 50-70 percent of the finishers have lung lesions • A well documented disease Mycoplasma net Purpose To develop a tool for evaluating the economic consequences of different control strategies against Mycoplasma The decisions are often based on intuition from farmers, advisors and vets 17

Mycoplasma net Building the m odel: Biological m odel : - Based on biological knowledge Econom ic m odel : - Economic risk due to the biological variation Risk factors Disease level Productivity Economics Constibution margin 18

Risk factors Control stragegy Diagnostics Disease level Productivity Economics Constibution margin Mycoplasma net I nput Risk factors: -Herd size -Production type -Purchase policy -Season -Region 19

Mycoplasma net I nput Diagnostics: - Clinical examination - Serology examination - Postmortem examination Determines the disease level with more precision Mycoplasma net I nput Control strategy: (Any action with the aim to change the level of disease) Short term strategy: Medication Vaccination Long term strategy: Change in mangement Change in production system 20

Mycoplasma net Output: Probability distribution: - Disease level - Production outcome - Economical outcome 21

The states of the variables Label Text Risk factors Herd size States: 1-1000 / 1001-3000 / 3001-5000 / 5001- All in all out States: Yes / no Seson States: Sept. / Dec. / Mar. / Jun. Diagnostics Clinical examination States: Zero / low / middle / high Serologic examination States: Zero / low / middle / high Postmortem examination States: 0-1% / 1-10% / 10-20% / 20%- Productivity outcome Change in daily weight gain States: 0g / -30g / -60g / -90g Change in feed conversion rate States: 0 / 0-0.15 / 0.15-0.30 / 0.30-0.45 Change in mortality States: 0% / ½% / 1% / 1½% The economic part Contribution margin = TR – VC TR: The income from the slaughterhouse VC: Weaner price Cost of feed Dead pigs Labor cost Control strategy Diagnosis 22