Stochastic Modeling Approach Model Structure

When the pathway model is considered for assessing the human health risk caused by the BSE agent, an event tree may need to follow a risk pathway from the BSE-infected cattle to the vCJD patients (Fig. 24.1). Ideally, the number of vCJD occurrences should be estimated from the number of BSE-infected cattle in the total cattle population in order to obtain the absolute risk to the human population. However, the number of BSE cases (Part 1) and the vCJD cases (Part 3) can be estimated only under certain assumptions with considerable uncertain input parameters. It is of concern that modeling all events through this pathway results in amplifying uncertainty in the model outputs. Since the purpose is to evaluate the impact of alternative testing schemes on the risk to human health, Part 2 provides enough information to see those effects although the difference of absolute risk is not acquired. In quantitative risk assessments, modeling is often focused on only the key process of the risk pathway to compare different scenarios. This could remove unnecessary uncertainty from

Fig. 24.1 Meai pathway for Number of BSE infected animals modeling -

BSE infected animal to be slaughtered

Human exposure to BSE infectivity

Part l

Prediction of total number of infected animal

Part 2

Effect of alternation of testing strategies

Number of vCJD cases in human

Part 3

Prediction of total number of vCJD cases the risk assessment models, but still contributes to decision-making. In Part 2, the purpose of modeling is specified more concretely by comparing the efficacy of screening tests when a BSE-infected animal is slaughtered under different testing schemes.

The model structure is outlined in Fig. 24.2. First, the model estimates infectivity accumulated in the brain stem of infected cattle at the time of slaughter. Then, the estimated infectivity is examined and determines whether the titer is higher than the detection limit of the screening test. The infected cattle with negative results are expected to enter the food chain, while the whole carcass of positive animals is removed. The different age targeting test schemes are incorporated into the model to compare their impact on outputs.

The unit of the risk measurement is another important item to be carefully selected in the risk assessment model. This is profoundly associated with structures and outputs of the model. The choice of unit should be made considering the end point of risk assessment and the ease of treating it in the model. Since the aim of modeling here is to assess the relative change of the exposure by different scenarios, murine intracerebral ID50 (m.i.c. ID50) units can be used as the unit of measure for infectivity. This avoids related uncertainty on the

BSE infected cattle

J

1

<_

Infectivity of cattle at slaughter

J

1

<_

Test age at slaughterhouse

Screening test

Age at infection Age at slaughter Incubation period

Growth of infectivity

Test age at slaughterhouse

Screening test

Detected

Detection limit of test

Overlooked

Fig. 24.2 Model structure

Infectivity to human conversions from mouse units to cattle/human units and enables use of mouse bioassay data directly. Stochastic effects can be generated by Monte Carlo simulation.

Modeling Infectivity of Cattle at Slaughter

The central part of this risk assessment model is to model the infectivity of cattle at slaughter. To estimate the infectivity at slaughter, we need to know when the infected cattle are slaughtered during the incubation period and how much infectivity is accumulated at that stage. We could assume that each infected individual has a unique incubation period, Inc_period, derived from the assumed distribution of incubation periods. If this animal is infected at age of Inf_age, the potential age of the disease development, D_age, is described by adding Inc_period to Inf_age.

Dage = Infage + Incperiod

The underlying assumption here is that incubation period is not affected by the age at infection. Age of slaughter, S_age, is estimated from the age distribution of slaughtered cattle derived from the national data. Since we know the time of clinical onset, D_age, the time period until clinical onset at slaughter, C_period, can be calculated by subtracting S_age from D_age.

If D_age < S_age, we could assume that an infected animal develops the disease on a farm and does not come to a slaughterhouse. The process of modeling until this point is described in Fig. 24.3.

Incubation Period Distribution

2 3 ; 4 5 Incaperiod

Fig. 24.3 Incubation period distribution and modeling approach for time left at slaughtering before estimated clinical development

Inf_age

2 3 ; 4 5 Incaperiod

Incubation Period Distribution

Cattle Age

D_age

The infectivity titer of the spinal cord at clinical stage, C_titer, was measured by mouse bioassay. If we know the way that the infectivity titer increases during the incubation period, the infectivity titer at slaughter, S_titer, can be estimated from C_period, the time period until clinical onset at slaughter, and C_titer. It could be assumed that the infectivity in cattle increased during the incubation period with infectivity titer doubling in a certain period, Do_period. The model calculates infectivity at the time of slaughter backward from the infectivity of C_titer by the time period of C_period, assuming that cattle develop clinical signs when the infectivity reaches a certain level. This also assumes that BSE infectivity increases in a similar way before clinical development irrespective of the duration of incubation period. The equation for calculating infectivity at the time of slaughter, S_titer, is as follows:

Then, if S_titer is higher than the estimated detection limits of the applied test, the infected animal is detected. If it is lower, the infected cattle are overlooked and enter the food chain.

Input Parameters

Age at Infection

Epidemiological studies in the UK have suggested an age-dependent risk of BSE infection, and younger animals have a higher risk of infection (Arnold & Wilesmith, 2003; Ferguson et al., 1997; Anderson et al., 1996; Wilesmith, Ryan, Hueston, & Hoinville, 1992). Supervie and Costagliola (2007) and Calavas, Supervie, Morignat, Costagliola, and Ducrot (2007) considered that the BSE infection in France mostly occurred in cattle between 6 and 12 months of age by using mathematical modeling studies. The first year of life is presumed to be a high-risk period for BSE infection in the international guidelines (OIE, 2007). Age at infection could vary among countries due to the difference in cattle management systems. We assumed even probability of infection during the first year of life according to OIE guidelines.

Incubation Period

Anderson et al. (1996) derived a gamma distribution for the BSE incubation period from the UK epidemic. Later, Ferguson et al. (1997) reported that a mechanistic distribution was better fitted using a similar approach. Calavas et al. (2007) fitted a gamma distribution with slightly different parameters to the French BSE epidemic. These distributions are based on the analysis of the epidemiological data on the BSE epidemic in specific countries, mostly in the UK. However, the number of BSE cases observed in the UK is substantially higher than those in other countries, such as Japan, and thus the exposure of cattle to BSE infectivity differs. Lower exposure dose is known to prolong the incubation period in a cattle bioassay study (Wells et al., 2007). For countries with a small number of BSE cases, it is impossible to estimate the incubation period from the original data. Therefore, we used a gamma distribution derived from the UK epidemic for the assumed incubation distribution. Then, the influence of lower exposure dose was tested by shifting the distribution toward a longer time period in the sensitivity analysis. Because of the large uncertainty regarding incubation period in the field, the influence of incubation period needs to be examined by sensitivity analysis with alternative distributions in any case.

Age at Slaughter

Age at slaughter depends on the demography and cattle management system in situations considered. In countries where beef industries are dominant, age at slaughter is generally younger than the intensive dairy countries. In Japan, the detailed data are obtained from the database of cattle identification system as detailed in Fig. 24.4.

Infectivity at Clinical Stage

Clinically affected cattle are considered to have infectivity of between 103 and 105 m.i.c. ID50/g in the central nervous system (CNS) (SSC, 2002). In the bovine unit, Comer and Huntly (2003) proposed to use a log-normal distribution with a mean of 90 bovine oral ID50/g of CNS tissues for risk assessment study, while Cooper and Bird (2002) used 10 b.o. ID50/g in their risk assessment. Attack rate studies using cattle indicated one cattle oral ID50 was equal to 1028 m.i.c./i.p.

120,000

100,000

2 60,000

n 40,000

20,000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Age (months)

Fig. 24.4 Age distribution of slaughtered cattle in Japan

ID50/g (95% CI: 102 1-103 5) (Wells et al., 2007). For use of the unit of infectiv-ity, route of inoculation, animal species, and breed of host need to be considered carefully. We assumed an infectivity of 104 7 m.i.c. ID50 (median value of 103 and 105 m.i.c. ID50) at clinical onset.

Doubling Time

Many models assumed that the infectivity in cattle increased during the incubation period, with infectivity titer doubling every 1.5 or 2 months (Comer & Huntly, 2003; de Koeijer et al., 2004; Ferguson & Donnelly, 2003). The exponential growth of infectivity, which is described in terms of the time required to double infectivity (doubling time), was derived from a scrapie pathogenesis study in hamsters (Beekes, Baldauf, & Diringer, 1996).

As an example, infectivity growth curves with a doubling time of 1, 2, or 4 months with a 60-month incubation period are shown in Fig. 24.5. Shorter doubling time, which means rapid increase of infectivity, results in a steeper growth curve of infectivity in the final stage of the incubation period as detailed in Fig. 24.5. These assume steep rises of infectivity at the final stage. In the model that we described, the rapid increase of infectivity causes the rapid decrease of infectivity toward the beginning of the incubation period, since the level of infectivity at the end of the incubation period is defined in advance. We assumed that the doubling time is somewhere between 1 and 2 months for each individual animal and applied a uniform distribution between the two values in the model. This parameter must be tested by the sensitivity analysis.

10000

9000

Q 7000

1 month

6000

Q 7000

6000

2000

1000

2000

1000

Months from infection

Fig. 24.5 Growth of the BSE infectivity during incubation period with a doubling time of 1,2, or 4 months

Detection Limit of Infectivity by Test

In the evaluation of screening tests (SSC, 1999), 20 of 20 samples diluted 102fold from the original brain samples of BSE-infected cattle with infectivity of 1031 m.i.c. ID50/g were positive with ELISA, and 18 of 20 samples diluted 1025fold were positive using the same ELISA kit. Detection limits can work on the all-or-nothing basis to determine individual animal test results, as we used 103.1 m.i.c. ID50/g for the threshold value. Alternatively, chance effect can be built into the model using a binomial probability.

Outputs

Here, we described results of the comparison of the impact of different testing scenarios on BSE infectivity destined for the human food chain in Japan. The details of parameters used are described in a published article (Tsutsui & Kasuga, 2006). The maximum expected fraction of BSE-infected cattle that would be detected by screening tests occurs when all slaughtered cattle are tested (Table 24.1). But even taking this scheme, the fraction was only 20%. Testing only cattle aged over 20 or 24 months retains more than 96% efficacy when compared with all cattle testing scheme, while testing only cattle beyond 30 months would retain 77%. It is considered that those overlooked animals below the age limits have relatively low infectivity, because these cattle are mostly in the early stages of the incubation period. Infectivity entering the human food chain is further reduced by the removal of risk materials such as brain and spinal cord at slaughterhouses, as our original study indicated (Tsut-sui & Kasuga, 2006).

The result of sensitivity analysis is shown in Fig. 24.6. Among the input parameters, the time required for doubling BSE infectivity has a significant impact on the probability of detecting BSE-infected cattle by screening tests. The probability of detection becomes considerably higher for all testing strategies, except testing those cattle beyond 30 month of age, when doubling time was assumed to be longer than 1 month. As the infectivity at slaughter was calculated backward from the infectivity at clinical onset assuming an exponential decrease, the larger doubling time generated a higher level of infectivity long before clinical onset. Concerning the impact of prolonged incubation period, the assumed distribution of the incubation period was shifted by 0.5,

Table 24.1 Detection probability of the BSE-infected cattle at slaughterhouse with different testing strategies

Testing

Detection probability

Ratio

All cattle

20.3%

Base

Over 20 mo

20.1%

0.99

Over 24 mo

19.5%

0.96

Over 30 mo

15.5%

0.77

60%

—♦—

Test all

50%

-B-

Test over 20mo

—A—

Test over 24mo

40%

—X—

Test over 30mo

Number of months required to double infectivity

60%

Test all

50%

-B-

Test over 20mo

—A—

Test over 24mo

40%

—X —

Test over 30mo

50%

—•—-

Test all

—B—

Test over 20mo

40%

—A—

Test over 24mo

-X-

Test over 30mo

Detection limit (m.i.c.ID50)

Base 0.5 year 1 year

Delay of incubation period

1.5 year

Fig. 24.6 The result of sensitivity analysis

1.0, and 1.5 years in order to express the delay in clinical onset. Delaying clinical onset reduced the probability of detection for all testing schemes, while the degree of reduction was smaller when cattle over 30 months are tested. This is because the longer incubation period resulted in lower infectivity at the time of slaughter. The effects of alternative values on detection limits for the screening tests were also analyzed. Lowering the detection limit slightly improved the probability of detection. However, the impact on the probability of detection was rather limited.

Was this article helpful?

0 0
Beauty for Newbies

Beauty for Newbies

Do you feel like an ugly duckling sometimes? Doesn't it seem like everyone else seems to know the best ways to present themselves, from their hair, to their skin, to their makeup?

Get My Free Ebook


Post a comment