Modelling the economic impact of three lameness causing diseases using herd and cow level evidence

Preventive Veterinary Medicine 95 (2010) 64–73

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Modelling the economic impact of three lameness causing diseases using herd and cow level evidence Jehan Ettema a,b,∗ , Søren Østergaard a , Anders Ringgaard Kristensen b a

University of Aarhus, Faculty of Agricultural Sciences, Department of Animal Health and Bioscience, P.O. Box 50, DK-8830 Tjele, Denmark University of Copenhagen, Faculty of Life Sciences, Department of Large Animal Sciences, Grønnegårdsvej 2, DK-1870 Frederiksberg C, Copenhagen, Denmark

b

a r t i c l e

i n f o

Article history: Received 5 February 2009 Received in revised form 1 March 2010 Accepted 2 March 2010 Keywords: Lameness Dairy cattle Stochastic simulation Hyper-distributions

a b s t r a c t Diseases to the cow’s hoof, interdigital skin and legs are highly prevalent and of large economic impact in modern dairy farming. In order to support farmer’s decisions on preventing and treating lameness and its underlying causes, decision support models can be used to predict the economic profitability of such actions. An existing approach of modelling lameness as one health disorder in a dynamic, stochastic and mechanistic simulation model has been improved in two ways. First of all, three underlying diseases causing lameness were modelled: digital dermatitis, interdigital hyperplasia and claw horn diseases. Secondly, the existing simulation model was set-up in way that it uses hyper-distributions describing diseases risk of the three lameness causing diseases. By combining information on herd level risk factors with prevalence of lameness or prevalence of underlying diseases among cows, marginal posterior probability distributions for disease prevalence in the specific herd are created in a Bayesian network. Random draws from these distributions are used by the simulation model to describe disease risk. Hereby field data on prevalence is used systematically and uncertainty around herd specific risk is represented. Besides the fact that estimated profitability of halving disease risk depended on the hyper-distributions used, the estimates differed for herds with different levels of diseases risk and reproductive efficiency. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Disorders of dairy cows’ hoofs, (inter)digital skin and legs are highly prevalent in modern dairy farming (Capion et al., 2008; Holzhauer et al., 2006; Sogstad et al., 2005; Somers et al., 2003). Because these hoof and leg disorders result in an altered locomotion, we often refer to the disorders’ clinical sign, i.e. lameness. It is especially this sign that has been associated with reduced produc-

∗ Corresponding author at: University of Aarhus, Faculty of Agricultural Sciences, Department of Animal Health and Bioscience, Bichers Alle, P.O. Box 50, Foulum, DK-8830 Tjele, Denmark. Tel.: +45 8999 1371; fax: +45 8999 1500. E-mail address: [email protected] (J. Ettema). 0167-5877/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.prevetmed.2010.03.001

tive and reproductive performance (Barkema et al., 1994; Collick et al., 1989; Green et al., 2002). Reported incidences of clinical lameness vary from 21% per lactation (Enting et al., 1997) up to 70% in a 1.5-year study period (Green et al., 2002). The detrimental effects of lameness on productivity along with its high incidence make dairy cattle lameness of large economic importance. Enting et al. (1997) estimated an economic loss of D 104 per case of clinical lameness. In an earlier simulation study Ettema and Østergaard (2006) estimated the costs per case of clinical lameness per cow-year to be D 192 in a typical Danish dairy herd. Both studies focused on lameness as one health disorder caused by a variety of claw, skin and leg disorders. Kossaibati and Esslemont (1997) clearly demonstrated the importance of considering different underlying causes of lameness.

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The objective of this study concerns specification of input parameters of a simulation model used to evaluate the economic impact of dairy cattle lameness. The complete set of these parameters, i.e. the state-of-nature of a livestock model is never known with certainty. In the earlier mentioned study with the Monte Carlo simulation model SimHerd IV (Ettema and Østergaard, 2006), cow specific probabilities for becoming diseased were calculated with a logistic regression model. Variability between animals was represented since disease occurrence was triggered stochastically by drawing a random number from a uniform distribution around the cow specific probability. However, the elements of the logistic regression model, i.e. the input parameters, were point estimates. We hereby assumed to be certain about the true value of the herd’s specific probability to become diseased. Point estimates are typically used in the state-of-nature of stochastic livestock simulation models (Carpenter, 1988; Christensen et al., 2008; Groenendaal et al., 2002; Herrero et al., 1999; Noordegraaf et al., 2002). Risk in decision making is underestimated when using point estimates in the state-of-nature (Jørgensen, 2000). In a simulation model of a scavenging chicken production system, hyper-distributions were specified representing uncertainty concerning the true value for every parameter defined in the model (McAinsh and Kristensen, 2004). Creating hyper-distributions can be done in different ways. The latter model used field data to specify the distributions, whereas Jørgensen (2000) developed a consistent way of creating prior distributions for model input parameters given expert opinion and model output. In order to decide on implementing a preventive action against a disease at a certain cost, it is not only important to have an estimate of the expected revenue but also to estimate the certainty on this estimate. A more realistic estimate on model output and its variation results from representing uncertainty in the model’s most important input parameters, i.e. disease risks. A systematic way of creating hyper-distributions for these parameters, where data on cow level disease prevalence is used in combination with information on herd level risk factors, has been described by Ettema et al. (2009). The objective of this study was to simulate the economic feasibility of reducing the risk of lameness causing diseases in a herd where disease risk is described by hyper-distributions. 2. Materials and methods 2.1. SimHerd SimHerd IV (Ostergaard et al., 2005), the model used in this study, is a dynamic (discrete, weekly time-stepping), stochastic and mechanistic Monte Carlo simulation model. SimHerd IV simulates the production and state changes in a dairy herd with additional young stock. The state of an animal is defined by age, parity, lactation stage, milk yield (actual and trades), body weight, culling status, reproductive status (estrus and pregnancy), SCC (actual and trades) and disease status. The prediction of current state is made week-by-week for each cow and heifer in the herd. The state of the individual animal is updated, and produc-

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tion and input consumption of the herd are calculated. Drawing random numbers from relevant probability distributions triggers individual inherent and lactational milk yield potential and discrete events, such as heat detection, conception, abortion, sex and viability of the calf, diseases, involuntary culling and death. The production and development within the herd are, thus, determined indirectly by simulation of production and change in state of the individual cow and heifer. Model behaviour could be controlled by a set of decision variables, which define certain production systems and management strategies. Involuntary culling was defined as a constant risk of 0.00193/week for all cows. Voluntary culling was based on whether the cow became pregnant within the AI period. Cows with a milk yield higher or lower than the parity specific herd-average were specified to have an AI period up to 287 or 245 days in milk, respectively. The AI periods were initiated 35 days after calving and cows were dried off 7 weeks before calving. A cow not pregnant after the AI period was replaced when a heifer entered the herd and the particular cows were the lowest yielding candidates for voluntary culling. Reproductive efficiency was assumed by a conception rate to day 14 after conception of 0.43, an abortion risk of 0.13 after day 14 and an estrus detection rate of 0.50. The first estrus cycles after calving and reproductive disorders were modelled to have a detrimental effect on insemination and conception rates. Heifers were sold in case no cows were selected for culling and a maximum number of 200 cows were reached. Heifers were bought in case herd size reached a minimum number of 180 cows. 2.2. Parameterization of three lameness causing diseases 2.2.1. Categorization of diseases In a previous simulation study, dairy cattle lameness was modelled as one health disorder where an assumption was made on the distribution of lesions causing the health disorder (Ettema and Østergaard, 2006). The literature information concerning the underlying causes was weighed according to the assumed distribution in order to get to one parameter estimate. In the current study risk factors, disease occurrence and parameters expressing the effect of the disease on production were specified for three categories of lameness causing diseases. Categorization of diseases was based on aetiology and agreement on risk factors and incorporated digital dermatitis (DD), interdigital hyperplasia (IH) and claw horn diseases (CHD). The latter category was an aggregation of the claw related diseases—sole ulcer, double sole and white line disease. The reasoning behind this categorization has been given by Ettema et al. (2009). There was however a small difference in disease categorization between this previous study and the current study. Instead of using an aggregation of three interdigital diseases as done by Ettema et al. (2009), the current study considered interdigital hyperplasia as a separate disease and excluded the other two interdigital diseases (heel horn erosion (HHE) and interdigital dermatitis (ID)). An important assumption had to be made on disease duration. The chronic nature and incurability of IH in contrast to a shorter duration and

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Table 1 Marginal posterior distributions of the logit of the probability of a third parity cow, in the third stage of lactation having digital dermatitis (DD), interdigital hyperplasia (IH) and claw horn diseases (CHD). Knowledge on disease prevalence is perfect (fixed high (FH) and fixed low (FL)) or based on disease diagnosis at trimming (1–4), lameness observations (5 and 6) and on the presence of herd level risk factorsa (7). Set

DD

IH

FH FL 1 2 3 4 5 6 7

40% 7% 40% 7% 40% 7% – – –

40% 7% 40% 7% 40% 7% – – –

CHD

LAME

N

DD

IH



a

40% 7% 40% 7% 40% 7% – – –

– – – – – – 40% 0% –

– – 180 180 45 45 45 45 –

−0.40 −2.59 −0.53 −2.74 −0.60 −2.62 −1.28 −1.65 −1.43





0.17 0.30 0.32 0.53 1.28 1.18 1.27

−0.40 −2.59 −0.17 −2.41 −0.36 −2.43 −2.17 −2.48 −2.38

CHD 





0.19 0.31 0.33 0.52 0.89 0.86 0.84

−0.40 −2.59 0.37 −1.82 0.34 −1.60 1.41 −1.56 −0.30

0.18 0.29 0.32 0.48 0.70 0.77 1.05

Herd size >125, no regular use of footbaths, zero grazing and the use of TMR.

curability of ID and HHE made it difficult to maintain the aggregation. 2.2.2. Hyper-distributions The fundamental difference with previous simulation studies performed with SimHerd was the use of hyper-distributions describing disease risk. Traditionally, state-of-nature parameters (˚O ) in SimHerd are described with fixed estimates. In the current study however, nine state-of-nature parameters representing three disease risks for three categories of parity were described by a joint posterior distribution. The objective was to perform herd specific simulations where additional information was available on model parameters. The joint posterior distribution was formulated given observations (y) that were made in the specific herd, O (˚O |y). Bayesian statistics using Markov chain Monte Carlo (MCMC) based methods, i.e. Winbugs (Spiegelhalter et al., 2004) were used to systematically create these distributions. The Gibbs sampler was the particular Markov chain algorithm used to generate the sequence of samples from the joint probability distributions. A full description of the probability structure is given by Ettema et al. (2009). The posterior distributions were based on prior knowledge of disease prevalence in the entire population, combined with different kinds and quantities of herd and cow specific evidence (y). For every (i) replicate of the simulation model, a state-of-nature ˚O was randomly drawn from the joint probability distribution resulting in three parity specific risks for three lameness causing diseases; one state-of-nature consisted of 9 parameters. By running 1000 replicates with SimHerd where 1000 different states of nature were used, uncertainty around herd level risk was represented. In this simulation study, the goal was to simulate certain management strategies in a specific (fictitious) herd using different hyper-distributions which represent different levels of knowledge. In Table 1 an overview is given of 9 different sets of marginal probability distributions used in this study for the probability’s logit value for having three lameness causing diseases. Logit values are presented, instead of the respective probabilities. This was done because all logit values, in contrast to the corresponding probability values, were normally distributed and could

therefore be presented by two parameters (mean, SD). In this table, only distributions for parity 3 are presented, the remaining 6 distributions for cows of parity 1 and 2 are not presented here. The 9 distribution sets represent knowledge available on the specific herd for which 9 different types and amounts of data were gathered. In the first two sets, fixed estimates were used indicating high and low disease prevalence (high fixed (FH) and low fixed (FL)), respectively. These fixed estimates represented the traditional way of describing disease risk in SimHerd. As can be seen from the absence of a standard deviation for these sets, uncertainty on disease risk was ignored. In sets 1 and 2 there was information available on disease presence in the specific herd which was diagnosed during trimming of 180 cows. The prevalence of each of the three diseases was diagnosed and amounted to 40% and 7%, respectively. The same diseases prevalence was found for sets 3 and 4, respectively. However, this evidence was based on 45 cows instead of 180. As can be seen from the standard deviations, certainty on disease prevalence decreased where evidence was based on fewer cows. Information on locomotion score of 45 cows was collected in the specific herd and the joint posterior knowledge was represented by distribution sets 5 and 6. The information on locomotion score indicated presence of clinical lameness among 40% and 0% of the cows, respectively. As described by Ettema et al. (2009), the conditional probability of lameness given the presence of the three diseases (P(Lame+ |Disease+)) was 0.48 for CHD and only 0.05 and 0.14 for DD and IH, respectively. The degree to which belief was updated for distribution sets 5 and 6, indicated by the standard deviation of the hyper-distributions, depended on the conditional probabilities for the three diseases. In set 7 there was only information available on herd level risk factors present in the specific herd. To study the effect of disease risks’ different levels and degrees of certainty on the profitability of a preventive action estimated by simulation, draws from the joint distributions were used in SimHerd. By only using every 20th draw from the Gibb’s sampler, independence between the samples was guaranteed.

2.2.3. Calibration of disease prevalence The effect of lactation stage (days in milk, DIM) on the risk of a disease in SimHerd was specified with a 3-phase

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despite the fact that fixed estimate for disease risk (white plots) was used. The same calibration procedure was performed for the other 2 diseases and comparable results as presented in Fig. 1 were realized. Hereby it was assumed that CHD was observable during the entire lactation and a cow could only suffer from one episode during one lactation. It was furthermore assumed that 40% of all cows went through a second episode of CHD (Lischer, 2000). interdigital hyperplasia was assumed to be chronic and therefore also present later on and in following lactations (Enevoldsen et al., 1991).

Fig. 1. Prevalence of digital dermatitis (DD) as described by hyperdistributions (model input, white boxes) and prevalence of DD as simulated by SimHerd IV (model output, grey boxes) for different sets of hyper-distributions describing disease risk (Table 1). The box plot shows outliers, smallest non-outlier observation, lower quartile, median, upper quartile and largest non-outlier observation.

linear spline function (f(DIM)) (Ostergaard et al., 2005). For a cow at a certain DIM, the value of the spline function was subsequently used as the intercept in the logit function for disease onset. The values specified by the hyper-distributions in Table 1 however, represented disease prevalence since this was the unit of the observations. In order to use information about prevalence from the hyper distribution in the logit function for disease onset in SimHerd, a calibration was necessary. First of all, by assuming a value for disease duration, the simulation model was run with random draws from the hyper-distributions and model output for disease prevalence was compared to the prevalence described by the hyper-distributions. Accordingly, the simulation model was run again where all random draws were multiplied with the same factor until desirable model output for prevalence was produced. The models output for incidence were therefore a result of the assumed duration and the calibrated prevalence. A case of DD was assumed to be observable for 42 days after onset (Nielsen et al., 2009) and it was further assumed that at an average herd level prevalence (20% (Ettema et al., 2009)) a cow with DD can be observed as positive during 147 days of the lactation, i.e. a cow contracts on average 3.5 episodes of digital dermatitis. It is important to note here that only 1 out of the 3.5 episodes were assumed to be detected and treated. Fig. 1 shows the results of the calibration process. Grey box plot number 7 represents the simulated prevalence of DD by SimHerd when the corresponding hyper distribution set (Table 1) was used to describe disease risk. Accordingly, the prevalence described by this hyper distribution set is represented by white box plot number 7. Due to the stochastic nature of the model, variation in simulated prevalence (grey plots for FH and FL) was present

2.2.4. Risk factors Depending on the cow’s lactation stage, parity, milk yield potential, previous cases of the disease and access to pasture a cow specific probability of becoming diseased was calculated for every week of simulation. The parity specific estimates drawn from the joint distributions were transformed from prevalence into lactation stage specific risks for disease onset. Parameters of the earlier mentioned spline function were calibrated in a way that resulted in correct SimHerd output for prevalence in the different lactation stages. The differences in simulated prevalence in the lactation stages corresponded to the ones that resulted from the logistic regression analysis of this data (Ettema et al., 2009). The modelled herd in this study implemented zero grazing in its management (Table 1); there was therefore no high or a low risk season specified. Finally, milk yield potential was quantified as a risk factor for all three lameness causing diseases. The increased odds of contracting a disease in comparison to an average producing cow were quantified with an OR per kg of energy corrected milk (ECM) that the cow has the potential to produce more in comparison to an average producing cow. For all three lameness causing diseases this OR was set at 1.046 (Fleischer et al., 2001). 2.2.5. Effect parameters The parameters used in SimHerd representing the effects of lameness on production, reproduction and survival data are summarized in Table 2. A literature study was used to specify these effect parameters. Feed intake was modelled as the intake of net energy measured in feeding units (FE) necessary to realize milk production, maintenance and fetus growth. These three processes were described by functions (lactation curve, body condition curve and growth curve, respectively). As a result of lower milk yield and weight loss, feed intake was reduced in the corresponding amounts. The estimate for reduced milk yield due to clinical lameness caused by CHD was based on the study of Bicalho et al. (2008). Their estimate of a daily milk loss of 3.7% over the entire lactation was considered least biased, since it was based on a retrospective matched cohort design and an analysis of covariance. Besides, the cases of clinical lameness in their study were caused by diseases of the laminitic kind, which fitted our definition of CHD best. Hernandez et al. (2002) found a 1.8% lower milk yield in lactations where cows were treated for clinical lameness due to digital dermatitis. The same result was found

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Table 2 Assumed effects of digital dermatitis (DD), interdigital hyperplasia (IH) and claw horn diseases (CHD) on production, reproduction and survival.

Reduced milk yield (per lactation)a Daily body weight loss (%)b Relative decline per day in the effect on weight lossb Reduced conception rate (risk ratio)c Duration reduced conception rate (days)c Riske of involuntary cullingf Riske of sudden death/euthanasiag a b c d e f g

DD

IH

CHD

0.5% 0.03 −0.026 0.89 42 0.14% 0.16%

1.8% 0.03 −0.026 0.86 e.o.l.d 0% 0%

3.7% 0.12 −0.026 0.43 140 3.64% 4.2%

References used: Argaez-Rodriguez et al. (1997), Hernandez et al. (2002), Bicalho et al. (2008). References used: Van Arendonk et al. (1984), Enting et al. (1997). References used: Collick et al. (1989), Argaez-Rodriguez et al. (1997), Melendez et al. (2003). Until the end of lactation. During week of onset. References used: Thomsen et al. (2004), Enemark (2007). References used: Rajala-Schultz and Gröhn (1999), Thomsen et al. (2004).

by Argaez-Rodriguez et al. (1997). Neither of these studies found this result to be significant. However, due to a lack of better estimates the loss of 1.8% was used in this study for both DD and IH. In the paragraph on calibration of model input parameters, it was mentioned that a cow affected by DD on average is affected 3.5 times. In the study of Hernandez et al. (2002) no information on the number of episodes or the duration of the episode was available. For the current study it was assumed that the 1.8% lactational milk loss was spread out over the 3.5 cases per affected cow. Every episode of DD therefore resulted in a 0.5% milk loss. 2.2.6. Treatment costs of lameness causing diseases The costs of treating a lame cow differ across countries, across farms, across underlying diseases causing lameness and across people responsible for treating the cow (Enting et al., 1997; Ettema and Østergaard, 2006; Guard, 1999; Kossaibati and Esslemont, 1997). Finally, the selection criteria for treatment and therefore the severity of the treated case of lameness contribute to the variation. Prices and treatment costs used to quantify the technical output of the simulation model were set in a way that was representative for a typical Danish dairy farm (Table 3). Treatment costs for this study were based on current rates for the treatment procedures by Danish veterinarians, professional hoof trimmers, farmers and routine hoof trimming. For this study it was assumed that an equal proportion (25%) of lameness caused by DD and CHD was treated by each of the four procedures mentioned above. For DD the earlier mentioned number of 3.5 episodes per affected cow was used to divide treatment costs, as was done for the effect of DD on milk yield. In other words, only 1 out of 3.5 cases were treated. It was finally assumed that a case of CHD was treated a second time in 40% of the cases (Lischer, 2000). For the treatment of interdigital hyperplasia (IH), it was assumed that none of them was treated as an acute case, but all at periodic trimming. 2.3. Design of the simulation study Thirty six scenarios were run with the simulation model in order to estimate the impact of halving disease risks given different levels of information on disease presence

and in order to establish whether these estimates were herd specific. 2.3.1. Economic feasibility of halving the risk of all lameness causing diseases For scenario 1 the simulation model was run where disease risk was described with a fixed estimate representing a high risk (set FH in Table 1). This scenario was accordingly compared to a simulation where disease risk was halved. The same pair wise comparison was performed for a herd with poor reproductive performance. This additional evaluation was performed to demonstrate the fact that disease impact and profitability of preventive actions are herd specific. Conception rate to day 14 after conception was set to 0.38 in this herd with poor reproduction instead of 0.43 and estrus detection rate was set to 0.40 instead of 0.50.

Table 3 Examples of prices and costs (in D ), representative for Danish conditions in 2008, used to evaluate the results of the SimHerd model. Factor

Price

Milk Livestock

D 0.38 per kg ECMa Slaughter cows: D 0.94 per kg BW; bull calves: D 107; springing heifers: D 1477; dead cows: −D 72/animal Total ration for cows D 0.20 per FEb and for dry cows D 0.16 per FE Milk replacer: D 2.4 per kg; concentrates: D 0.30 per FE; roughage: D 0.17 per FE; grazing first and second year: D 0.60 and D 1.20/day Claw horn diseases: D 52; digital dermatitis: D 47; interdigital hyperplasia: D 8; milk fever: D 95; Dystocia: D 107; retained placenta: D 38; Metritis: D 44; left displaced abomesum: D 89; Ketosis: D 44; Mastitis: D 54 Cowsc : D 40 per cow/year; heifersc : D 13 per heifer/year; AI: D 16/AI 4% per year

Feed cows Feed heifers

Veterinary cost

Other costs Interest rate of herd value a

Energy corrected milk. Feeding unit. c Average costs for bedding, milk recording, pregnancy test, additional veterinary assistance and drugs. b

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Table 4 Mean and standard deviation (sd) of the annual technical effects in a scenario with a high risk of all lameness causing diseases and the mean differences with a scenario where all three risks are halved for a herd with average and poor reproduction, using SimHerd IV. Average reproduction High risk

Poor reproduction Difference

High risk

Mean

SD

ALL-half

Mean

SD

ALL-half

197.9 9140 6528 41.1 1.07 401 198.1 0 3.8

0.13 41.4 19.2 0.87 0.009 1.5 5.13 – 1.1

+0.23 +176.2 +103.8 −2.90 −0.002 −3.5 −0.21 0 +2.8

188.2 8913 6396 42.0 0.92 416 165.4 2.2 0

2.59 48.9 23.5 0.91 0.010 1.8 5.42 1.04 –

+6.9 +303.5 +173.4 −1.05 +0.03 −3.3 +10.33 −1.94 0

DDe Prevalence (%) Casesd Affected cowsd Cases per cow

41 420 91 4.6

1.2 4.4 1.0 0.05

−18.7 −189.6 −23.4 −1.21

43 435 81 5.4

1.2 4.6 1.0 0.08

−19.3 −195.7 −17.3 −1.61

IHf Prevalence (%) Casesd

38 40

1.2 1.0

−16.9 −17.9

35 35

1.9 1.0

−15.4 −14.7

CHDg Prevalence (%) Casesd

37 49

1.1 1.1

−15.5 −20.6

34 43

1.1 1.0

−13.4 −17.0

Other disease treatmentsd Dead cowsd

71 7.1

1.4 0.47

59 6.7

1.4 0.48

Cow-years Milk yield (kga ), ECMb Feed intakea , FEc Replacement rate Calves borna Calving interval Heifer-years Bought heifersd Sold heifersd

a b c d e f g

+3.3 −1.00

Difference

+3.3 −0.88

Per cow-year. Energy corrected milk. Feeding unit. Per 100 cow-years. Digital dermatitis. Interdigital hyperplasia. Claw horn diseases.

The above-described estimation of economic feasibility of halving disease risk was performed for a situation where disease risk was high (FH). The same comparison was performed for a situation where disease risk was low (FL).

Besides estimating the feasibility of an incentive that halves disease risks in a herd with average reproductive performance (scenarios 9–22), this was also done for a herd with poor reproductive performance in scenarios 23–36.

2.3.2. Economic feasibility when using 9 different sets of hyper-distributions After having used fixed estimates for disease risk in the first eight scenarios, hyper-distributions were used to describe disease risk in scenarios 9–15. One thousand samples were drawn from the different sets of joint posterior distributions (sets 1–7 in Table 1) specifying parity specific disease risk for the three lameness causing diseases (set 1 in scenario 9, set 2 in scenario 10, etc.). Accordingly the simulation model was run 1000 times where a different draw from the joint posterior distribution was used for each replicate. In order to estimate the economic benefit of an incentive that could half the risk of all lameness causing diseases, the simulation model was run with the same 1000 draws in scenario 16–22, where the weekly disease risk that resulted from the calibration process was divided by 2. By running these 14 scenarios in addition to using fixed estimates, an incentive that halves disease risk was evaluated for 9 different levels and degrees of certainty on disease prevalence.

2.4. Simulation procedure and analysis of the results A scenario in which the risk, described with point estimates, for all lameness causing diseases was at a level that resulted in a prevalence representative for the population was simulated over 10 years; the resulting herd was used as the initial herd for all other scenarios in order to eliminate the effect of the arbitrary start herd. After creation of this initial herd, all scenarios were simulated over 20 years with 1000 replications. The high number of replications and long simulation horizon were chosen in order to obtain a precise estimate of the results. Total margin was calculated as the sales income minus the variable costs for cows and additional young stock. Labour and management costs were generally not included, except for the labour involved with treatment of diseases (Table 3). Each replication of the model was considered as an independent observation. To avoid the influence of the initial herd, only the average results over the last 15 years of the 20-year simulation were studied.

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Table 5 Mean and standard deviation (sd) of the annual economic effects in a scenario with a high risk of all lameness causing diseases and the mean differences with a scenario where all three risks are halved for a herd with average and poor reproduction, using SimHerd IV. Average reproduction

Poor reproduction

High risk Mean Sales (×1000 D ) Milk Cows Heifers Calves Total Purchase (×1000 D ) Feed, cows Feed, heifers Treatments Insemination Miscellaneousa Total Margin Total (×1000 D ) Per cow-year (D ) Per kg ECM (D ) a

SD

Difference

High risk

ALL-half

Mean

Difference SD

ALL-half

686.5 37.3 11.3 11.4

3.18 0.96 3.17 0.19

+13.80 −1.32 +8.25 −0.01

636.5 36.8 0.1 9.2

10.89 0.96 0.09 0.24

+45.68 +2.04 +0.23 +0.80

746.5

4.74

+20.72

682.7

11.49

+48.75

252.6 86.9 26.6 10.6 35.6

0.79 2.26 0.31 0.16 0.51

+4.29 −0.04 −8.11 −0.25 0.00

235.6 72.5 23.6 8.5 37.6

3.75 2.38 0.47 0.23 2.29

+15.28 +4.56 −6.63 +0.46 −3.63

412.4

3.29

−4.12

377.8

5.25

+9.93

2.81 13.8 0.0011

+24.84 +123.5 +0.0100

6.9 18.1 0.0014

+38.82 +142.5 +0.0095

334.1 1688 0.185

304.9 1620 0.182

Other costs cows, other costs heifers, interest on operating capital.

3. Results 3.1. Technical and economic impact of three lameness causing diseases In Tables 4 and 5 technical and economic consequences of a scenario where all three disease risks are at a high level, in contrast to a scenario where risk of all three diseases was halved, are presented. Fixed estimates were used for disease risk (distribution set FH from Table 1). Tables 4 and 5 contain results for herds with average and poor reproductive performance. In a herd with a high risk for DD and average reproductive performance, 91% of all cows were affected with DD at least once. On average, affected cows experienced 4.6 episodes of DD and were therefore affected during 193 days of their lactation. By halving the cow’s risk, the total number of cases per cow-year dropped by 45%, 23 fewer cows were affected by DD and the average number of episodes per affected cow dropped from 4.6 to 3.4. Halving the risk of IH and CHD resulted in 45% and 42% fewer cases per cowyear, respectively. The average number of cows present in the herd (cow-years) increased by 0.23 when all three disease risks were halved. Other important changes in technical results were the decrease in replacement rate and calving interval and a 176 kg higher milk yield per cowyear. A herd with poor reproductive performance had fewer cow-years to begin with; halving disease risk increased average herd size by 6.9 cow-years. The change in replacement rate was actually less in a herd with poor reproduction when disease risks were halved; cows were not replaced since there were no heifers available to replace them with. Instead of selling heifers, as was done in a herd with average production, 2 heifers per 100 cow-years had

to be bought. By halving all three disease risks, the problem of heifer shortage was almost solved. Milk yield per cowyear increased twice as much as was the case for a herd with average reproductive performance. Halving disease risk of all three lameness causing diseases in a herd with average and poor reproduction increased total gross margin by D 24,840 and D 38,820, respectively. The profitability at the herd level was 56% higher if the herd had poor reproductive performance. When expressing gross margin per cow-year, profitability was 15% higher: the margin increased by D 143 and D 123 per cow-year for a herd with poor and average reproduction, respectively. 3.1.1. Low risk herd, with average reproduction When halving the risk of all diseases in a low risk herd (set FL Table 1), margin per cow-year increased with D 29.3 instead of D 123.5. In a herd with poor reproduction and a low risk for all diseases, herd size was maintained. The increase in cow-years when halving disease risks was therefore of the same magnitude as was the case for a herd with average reproduction and high disease risk. When halving the risk of all diseases in a low risk herd, instead of D 142.5, margin per cow-year increased by D 28.1. 3.2. Economic feasibility of halving diseases risks using hyper-distributions For the results presented in Tables 4 and 5 the simulation model used fixed estimates for disease risk, i.e. sets FH and FL of Table 1. In Fig. 2, the change in gross margin per cow-year is displayed when, beside FH and FL, 7 different sets of hyper-distributions were used and all disease risks were halved in a herd with average reproduction.

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4. Discussion 4.1. Calibration and direct use of data on prevalence

Fig. 2. Change of gross margin per cow-year as an effect of halving the risk of all three lameness causing diseases when using 9 different sets of hyper-distributions describing disease risk, using SimHerd IV. The box plot shows outliers, smallest non-outlier observation, lower quartile, median, upper quartile and largest non-outlier observation.

The resulting change in margin per cow-year and the SD when using 7 hyper-distributions in a herd with average and poor reproduction are displayed in Table 6. In the case in which only herd reproductive efficiency was known to be average, herd size exceeded 125 cows, footbaths were not regularly used and zero grazing and TMR was implemented, an incentive that halved all three disease risks was expected to result in a higher margin per cow-year of D 78. This estimate is uncertain, but with 95% confidence to be between D 25 and D 130. If accordingly an effort was made to collect information on the prevalence of lame cows, prevalence of hoof lesions among 45 and 180 cows indicating that the problem was small (sets 6, 4, 2, respectively), the expected revenue resulting from the incentive decreased and belief in the estimate increased. Conversely, by adding more proof of lameness and the underlying disease being present in the herd (represented by distribution sets 7, 5, 3) the expected revenue increased, as did certainty about it. Table 6 Change in gross margin per cow-year (median and standard deviation, SD) as a result of halving disease risks when using fixed estimates for disease risk (high risk (FH) and low risk (FL)) and 7 different distributions for herds with average and poor reproduction, using SimHerd IV. Hyper distribution

Average reproduction

Poor reproduction

Set

Median

SD

Median

SD

FH FL 1 2 3 4 5 6 7

123.5 29.3 125.2 31.5 118.9 40.6 104.7 59.7 77.7

20.06 22.06 19.94 22.57 20.68 23.86 26.41 29.82 26.16

142.5 28.1 138.6 30.9 135.7 39.0 115.0 61.4 84.6

27.48 21.72 27.26 23.13 27.01 25.58 31.00 34.90 32.22

To the author’s knowledge, information on prevalence collected in the field has not been used directly and systematically in a cow-based simulation model of a dairy herd. The problem of only having knowledge on observable output from the simulation model (disease prevalence) and making it coherent with knowledge on the simulation model’s structure and input parameters is very relevant for mechanistic simulation models like SimHerd IV. As described by Jørgensen (2000) prior distributions are adjusted until desirable model output is produced. In our study however, the prior distributions were created systematically using Bayesian statistics. The process of adjusting the prior distributions was not performed by creating new distributions; instead each random draw from the distributions was multiplied with a “factor”. When comparing model output on disease prevalence to prevalence described by the hyper-distributions (Fig. 1), it can be concluded that the simulation model’s disease prevalence results were much like the prevalence described by the hyper-distributions. The results from the model were distributed more normally than the hyper-distributions; judging from a univariate analysis, the distributions were less skewed and fewer extreme values were produced by the model. Our current study demonstrated the concept of using field data on disease prevalence for specification of cow level disease risk in a consistent way. This was one of two improvements to the model’s functionality; the other improvement was the consistent handling of parameter uncertainty. The marginal distributions represented knowledge from the population, herd specific knowledge on presence of risk factors and cow level information on the presence of diseases and their common cause, lameness. 4.2. Disease duration For this study the duration for a single case of DD was assumed to be 42 days (Nielsen et al., 2009). Furthermore, it was assumed that a cow that has had one episode of DD was at higher risk of experiencing another episode. Whether this was a problem cow that persists in the infectious stage of DD (Holzhauer et al., 2008) or a reoccurring case was not very relevant for the approach of simulating the disease in this study, i.e. one long lasting disease episode compared to several short lasting episodes resulted in the same prevalence and the same number of animals affected by DD. The relationship between prevalence (P), incidence (I) and duration (D) can be described by P = I × D/(I × D + 1) (Dohoo et al., 2003). This formula can be rewritten where incidence becomes a function of prevalence and duration I = (P/D)/(1 − P). Assuming duration to be twice as long, results in halving of the incidence, given certain prevalence. This formula is only valid in stable populations, but by assuming different durations, a comparable relationship was found in a simulated dairy herd. Besides a result on overall incidence per cow-year, an estimate on the number of times an affected cow suffered from an episode of DD was also derived from the simulation model’s

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output. This figure of 3.5 cases was used to divide the effect on milk production and treatment costs. In case a longer duration would have been assumed, a lower number of cases per affected cow would have been the result, which then would have been used to divide reduced milk yield and treatment costs. The diseases CHD and IH were assumed to last the entire, remaining lactation and to be chronic, respectively. For these assumptions, the above-described considerations concerning the duration of DD should be kept in mind. For modelling the lameness causing diseases, especially DD and IH, it was necessary to make assumptions on reoccurrence rates, milk loss and other important parameters. This highlights the need for better knowledge on the effects of these production diseases. 4.3. Interpretation of results for different hyper-distributions The results presented in Fig. 2 and Table 6 should be interpreted in terms of the expected economic profitability of an incentive, given different degrees of belief in disease risk. Normality of the distributions in Fig. 2 was studied by a univariate analysis. Due to too little and too much variation, sets 4 and 5 were not distributed normally, respectively. Based on a visual inspection of the histogram and qq-plot the deviation from normality was small. By considering the results to be normally distributed and by assuming that full uncertainty was represented in our simulation model, a probability can be calculated for a certain incentive, costing D X per cow-year, to be profitable. With the integral of the normal distribution from X to plus-infinity, the probability that the economic gain exceeds X can be calculated. For a herd with average reproduction, the expected profitability of the incentive was D 78 with a standard deviation of 26 (set 7 in Fig. 2 and Table 6). By assuming that the incentive costs D 40 per cow-year, the best guess of the expected profit of this decision was D 38 per cow-year. The probability that the incentive’s revenues exceeded the costs (the incentive results in a profit) was 0.92. When more information was added on lameness prevalence being 0% (set 6), hoof trimming of 45 cows and hoof trimming of 180 cows indicating a 7% prevalence of all diseases (sets 4 and 2), the expected profitability of this incentive decreased. Besides, the probability of this incentive being profitable decreased to 0.75, 0.51 and 0.35, respectively. Information on disease risk accumulated and the simulation model was run with the resulting hyper-distributions describing disease risk. Subsequently, certainty about the model’s outcome increased and for this particular example, belief in profitability decreased. Whether the calculated probabilities are too low for the decision maker to initiate an intervention depends on the decision makers risk averseness. In this straightforward illustration of the results’ application, the costs of gathering information were not included. Especially trimming cows is costly and should be considered in a full economic evaluation. Furthermore, beneficial effects of an extra trimming have been reported (Manske et al., 2002a) but were not included in this study. Since only 9 of the simulation model’s parameters were described by a hyper distribution, over 1000 parameters remain fixed.

Uncertainty in the model’s outcome should therefore not be assumed as fully represented. 4.4. Opportunities for application The specific herd and data used for the posterior estimates were fictitious and served merely as an illustration of SimHerd’s use of hyper-distributions. An interesting application of the Bayesian Network would be one where information on both lameness prevalence and hoof trimming registration were combined. It is likely that real life data would supply evidence on a certain disease being a problem instead of all diseases being prevalent among either 7% or 40% of the cows, as how we described the network. In addition, preventive strategies mainly effective against certain diseases could be evaluated; for example using rubber floors only benefits control of claw horn diseases (Benz, 2002) whereas topical treatment or footbaths mainly benefit control of the infectious diseases (Manske et al., 2002b; Shearer and Hernandez, 2000). Illustration of this study’s two new main concepts, i.e. using hyper-distributions, and using field data on prevalence, was addressed in this study. Demonstrating a real life application is an obvious next step. 4.5. Dynamic aspect of the simulation model The network creating the hyper-distributions was static, in contrast to the simulation model being dynamic. The creation of hyper parameters describing disease risk was done for the present situation in the specific herd. Every sample from the distribution was used by the simulation model to forecast the cows’ life in weekly steps. Hereby, the value of the drawn sample did not change over time. However, a more correct approach would have been a changing disease risk in time due to herd effects or preventive measures. Correlation of disease risk in the future herd with the risk in the present situation decreases as time goes by. Without updating the network with new herd specific information, the best guess for the future disease risk is to move towards the population mean. Besides, as time goes by, certainty about the disease risk decreases. In this first set-up of an existing Monte Carlo simulation model using hyper-distributions, the network was kept static. 5. Conclusion The use of hyper-distributions describing disease risk by an existing dynamic, stochastic and mechanistic simulation model of a dairy herd was demonstrated. Through the described process of calibration, systematic use can be made of different types and amounts of field data on disease prevalence. The uncertainty in input parameters is reflected in the uncertainty of the simulation model’s output, which is important in decision support in livestock systems. An improvement has been made in describing uncertainty. However, it should be realized that uncertainty in model outcome is still underestimated.

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