Attachment 1: Estimation of BSE Prevalence in Canada

1\. Introduction

The purpose of this document is to estimate the prevalence of bovine
spongiform encephalopathy (BSE) in the adult cattle population of
Canada. The detection of Canada's first native BSE case was confirmed on
May 20, 2003. As of August 23, 2006, a total of nine BSE cases of
Canadian origin had been confirmed in North America (CFIA 2006). This
total includes a case of BSE that was confirmed in Washington State on
December 25, 2003. By comparison, the United Kingdom (UK) had detected
184,453 cases of BSE as of September 1, 2006 (OIE 2006a).

The number of BSE cases detected through surveillance understates the
disease prevalence because exposed animals may be incubating disease and
carrying infectious material in their tissues without presenting
clinical symptoms. Like many transmissible spongiform encephalopathies
(TSEs), BSE has an incubation period of several years. Therefore, the
disease is not detectable in its early stages with current technology.
Moreover, surveillance will miss a proportion of detectable cases.
Therefore, statistical methods are applied to the available
epidemiologic and surveillance data to estimate, with attendant
uncertainty, the prevalence of BSE in Canada.

Two related, but distinct methods were used to estimate BSE prevalence
in Canada. Given its international prominence, we used the European
Union (EU) BSurvE model (Wilesmith *et al*. 2004, 2005), recently
developed for the purpose of estimating BSE prevalence in national
herds. The BSurvE model is noteworthy for its sound epidemiologic
structure, including stratifying cattle by age and cause of death
(healthy slaughter, fallen stock, casualty slaughter, or clinical
suspect) and accounting for the relative likelihood of detecting BSE in
various strata (EFSA 2004). The primary prevalence estimation method
used in this document, referred to as the Bayesian Birth Cohort (BBC)
model, takes advantage of the BSurvE model structure to calculate BSE
surveillance point values - random sample size equivalents - represented
by targeted Canadian sampling of certain groups of cattle in which BSE
cases are more likely to be detected. The Bayesian Birth Cohort model
adopts a Bayesian statistical framework to incorporate prior information
about the decreased incidence of BSE observed in animals born after a
feed ban equivalent to the initial ruminant-to-ruminant feed ban
introduced in the UK in 1988. For the purposes of comparison and
sensitivity analysis, the prevalence of BSE in Canada also is estimated
using BSurvE.

2\. Data

2.1 BSurvE Model Structure for Input Data

Applying the BSurvE model structure to estimate a country's BSE
prevalence requires knowledge of the cattle population size and age
structure and involves important assumptions regarding the
classification of tested animals by age and cause of death, called
surveillance streams. These surveillance streams are described as:
healthy slaughter, fallen stock, casualty slaughter, or clinical suspect
(Wilesmith *et al*. 2004, 2005). In consultation with U.S. animal health
surveillance analysts, Canadian Food Inspection Agency (CFIA) officials
organized the available Canadian BSE surveillance evidence as input data
for the BSurvE model (Murray 2006).

2.2 Canadian Cattle Population Size and Age Structure

BSurvE relies on the female cattle population data because (1) the
information is more demographically stable and more readily available
than for males, and (2) females comprise the majority of the standing
adult cattle population (Wilesmith *et al*. 2005). Murray (2006) derived
the number of Canadian animals in the beef and dairy reproductive female
populations from cattle inventory data reported by Statistics Canada
(2004). Because age-specific mortality rates and slaughter rates are
unavailable for the Canadian cattle population, the population estimates
were stratified by age based on the cattle population demographics
estimated for the U.S. by the "Harvard-Tuskegee Study" (Cohen *et al*.
2003). It is reasonable to assume that the same rates would be
applicable to Canada as the cattle industries in both countries are
virtually identical. For example, the relative proportion of beef and
dairy cattle (80% and 20% respectively), management practices (such as
breeding, feeding and rearing), and slaughtering practices are
essentially the same in both countries (NASS 2006, Statistics Canada
2001). The age-specific population profiles for the beef and dairy
population were combined to give an overall estimate of the age-specific
profile of the Canadian cattle population. These data (Table 1) are
entered in BSurvE as the "idealized count" for age distribution. This
distribution results in an estimated adult (2+ years of age) Canadian
cow population of 5,979,757 animals.

Murray (2006) provides the age distribution for animals up to 20 years
of age. However, for the purpose of characterizing the age distribution,
BSurvE only accepts count data for cattle up to 16 years of age. BSurvE
uses the cattle age distribution to calculate exit constants. These
constants represent age-specific rates of removal from the herd. The
decision to exclude cattle 17 to 20 years of age results in no change in
the estimated exit rates, while the alternative of redistributing
animals estimated to be over 16 years of age into younger age groups
would have artificially altered the exit rate assumptions used in
deriving the distribution and affected the BSE surveillance point
calculations.

Table 1. Age Distribution for Canadian Cattle Population

+------------------------------+---------------------------------------+
| Age                          | Female                                |
|                              |                                       |
| (years)                      | Cattle                                |
+------------------------------+---------------------------------------+
| 0                            | 1,194,932                             |
+------------------------------+---------------------------------------+
| 1                            | 1,104,087                             |
+------------------------------+---------------------------------------+
| 2                            | 1,065,899                             |
+------------------------------+---------------------------------------+
| 3                            | 965,795                               |
+------------------------------+---------------------------------------+
| 4                            | 856,719                               |
+------------------------------+---------------------------------------+
| 5                            | 723,068                               |
+------------------------------+---------------------------------------+
| 6                            | 561,567                               |
+------------------------------+---------------------------------------+
| 7                            | 434,748                               |
+------------------------------+---------------------------------------+
| 8                            | 331,917                               |
+------------------------------+---------------------------------------+
| 9                            | 257,258                               |
+------------------------------+---------------------------------------+
| 10                           | 201,542                               |
+------------------------------+---------------------------------------+
| 11                           | 159,075                               |
+------------------------------+---------------------------------------+
| 12                           | 126,201                               |
+------------------------------+---------------------------------------+
| 13                           | 100,468                               |
+------------------------------+---------------------------------------+
| 14                           | 80,169                                |
+------------------------------+---------------------------------------+
| 15                           | 64,071                                |
+------------------------------+---------------------------------------+
| 16                           | 51,260                                |
+------------------------------+---------------------------------------+

2.3 BSE Testing and Surveillance Data

2.3.1 December 2003 Washington State Case and Investigation Test Data

Because the animal was born in Canada, the BSE case detected in
Washington State and confirmed in December 2003 was included as a
Canadian case for the purpose of estimating the prevalence of BSE in
Canada. None of the results of tests of Canadian cattle in the U.S.
conducted during the epidemiologic investigation of the December 2003
case were included. That is, the BSE positive animal was included in the
numerator, but none of the corresponding negative results were
considered in the denominator of this analysis. Similarly, the analysis
excludes the negative results of all of the BSE tests conducted in the
course of epidemiologic investigations of the other eight BSE cases of
Canadian origin confirmed to date in North America. Thus, only those
samples collected as part of Canada's BSE surveillance program were
included in the denominator of the analysis. Excluding the negative
results from animals tested in follow-up investigations acts to
overstate prevalence, but these negative results increase confidence
that no unidentified cases are present in local association with the BSE
positive animals.

2.3.2 BSE Surveillance Streams

BSurvE requires that the BSE test data be stratified by surveillance
stream and age of animal. In accordance with World Organization for
Animal Health (OIE) guidelines for BSE surveillance (OIE 2006), Canada's
enhanced BSE surveillance program specifically targets certain risk
groups amongst which BSE cases are much more likely to be found (CFIA
2006):

-   cattle of all ages displaying clinical signs consistent with BSE
    (clinical suspects)

-   cattle over 30 months of age from the 4-D categories:

    -   animals found dead (dead stock)

    -   animals that are non-ambulatory (downers)

    -   animals presented for emergency slaughter (dying)

    -   animals sent to slaughter that are found to deviate from normal
        behavior or appearance at ante mortem inspection (diseased)

BSurvE (Wilesmith *et al*. 2004, 2005) uses four surveillance streams
which are related to the risk groups targeted in Canada as follows:

-   healthy slaughter (not included in Canada's surveillance program)

-   fallen stock (equivalent to Canada's dead stock category)

-   casualty slaughter (equivalent to Canada's categories for downers,
    dying and diseased animals)

-   clinical suspects

Animals are not specifically identified as BSE clinical suspects in the
CFIA's laboratory database. However, Murray (2006) estimated the likely
number of clinical suspects by determining which BSE related laboratory
accessions could reasonably be classified as clinical suspects on the
basis of the following selection criteria:

OIE (2006, Article 3.8.4.2) defines cattle displaying behavioral or
clinical signs consistent with BSE as those that are affected by
illnesses that are refractory to treatment AND display progressive
behavioral changes (excitability, persistent kicking when milked,
changes in herd hierarchical status, hesitation at doors, gates and
barriers) OR display progressive neurological signs without signs of
infectious illness.

To satisfy these conditions and classify an animal as a clinical
suspect, Murray (2006) determined that the pathology history would need
to indicate that an animal was suffering from a chronic condition (at
least one week), loss of productivity, weight loss AND some sort of
neurological symptom such as ataxia or behavioral changes such as
nervousness or apprehensiveness. Animals suspected of rabies also were
classified as clinical suspects. In classifying clinical suspects,
Murray (2006) ruled out: short term conditions (duration of less than
one week); injuries associated with recent calving (obturator paralysis
etc.); signs of infectious illness such as Johne\'s disease; other
explanations for locomotory disturbance such as sole ulceration;
conditions that had been present for longer than six months; and
unilateral lameness.

2.3.3 Tests from Animals of Unknown Age

Where birth records are unavailable, the age of animals may be estimated
by dentition. Historically, the age of animals tested under Canada's BSE
surveillance program has not been routinely captured. However, age
associated data is available for approximately 50% of the BSE tests
undertaken within CFIA's TSE network laboratories in 2004 and 2005. This
subset represents over 20,000 animals. Considering the large number of
animals with age data and the lack of appreciable differences in age
related trends among these years, a pooled estimate of age
stratification for each BSurvE surveillance stream was determined.
Murray (2006) used this estimate to stratify the surveillance results
for tested animals where age was unavailable.

2.3.4 Stratified Canadian BSE Surveillance Data

Murray (2006) provides the available Canadian BSE surveillance data
collected from 1992 through August 15, 2006, stratified by age and
surveillance stream. However, under OIE (2006), BSE surveillance points
only remain valid for 7 years. Therefore, the estimated prevalence of
BSE in Canada is based on surveillance data accumulated over a 7-year
period beginning August 16, 1999 and ending August 15, 2006. This
surveillance period includes the 9^th^ BSE case of Canadian origin
confirmed on August 23, 2006. Since the surveillance data are reported
on a calendar year basis, the number of samples for the 1999 strata was
reduced proportionately to the extra months of data captured for 2006
(i.e., the 1999 data were reduced by 62.5%, or prorated to 4.5 months).
Table 2 presents the surveillance testing data stratified in the BSurvE
format used to estimate the prevalence of BSE in Canada.

Table 2. Canadian BSE surveillance stream test data for 16 Aug. 1999 --
15 Aug. 2006

+-------+-------+-------+-------+--------+--------+--------+--------+
| Te    | Age   | F     | F     | Ca     | Ca     | Cl     | Cl     |
| sting |       | allen | allen | sualty | sualty | inical | inical |
| Year  |       | stock | stock | sla    | sla    | su     | su     |
|       |       | t     | pos   | ughter | ughter | spects | spects |
|       |       | ested | itive | tested | po     | tested | po     |
|       |       |       |       |        | sitive |        | sitive |
+-------+-------+-------+-------+--------+--------+--------+--------+
| 2006  | \<2yo | 0     | 0     | 6      | 0      | 10     | 0      |
|       |       |       |       |        |        |        |        |
| thru  |       |       |       |        |        |        |        |
|       |       |       |       |        |        |        |        |
| Aug   |       |       |       |        |        |        |        |
| 15    |       |       |       |        |        |        |        |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 2     | 333   | 0     | 233    | 0      | 0      | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 3     | 1724  | 0     | 1020   | 0      | 12     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 4     | 2072  | 0     | 1443   | 1      | 17     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 5     | 2210  | 0     | 1546   | 0      | 35     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 6     | 2425  | 1     | 1490   | 0      | 25     | 1      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 7     | 1655  | 0     | 1079   | 0      | 8      | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 8     | 2247  | 0     | 1427   | 0      | 14     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 9     | 981   | 0     | 700    | 0      | 4      | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 10    | 2255  | 0     | 1575   | 0      | 27     | 1      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 11    | 560   | 0     | 480    | 0      | 6      | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 12    | 1716  | 0     | 1447   | 0      | 14     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 13    | 568   | 0     | 423    | 0      | 10     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 14    | 799   | 0     | 755    | 0      | 10     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 15    | 811   | 0     | 818    | 0      | 6      | 1      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 16    | 414   | 0     | 368    | 0      | 0      | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 17+   | 353   | 0     | 490    | 0      | 8      | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+

Table 2 (cont'd)

  --------- -------- -------- ---------- ----------- ----------- ---------- ----------
  Testing   Age      Fallen   Fallen     Casualty    Casualty    Clinical   Clinical
  Year               stock    stock      slaughter   slaughter   suspects   suspects
                     tested   positive   tested      positive    tested     positive

  2005      \<2yo    0        0          5           0           2          0

            2        486      0          484         0           17         0

            3        3007     0          1644        0           26         0

            4        3493     0          2019        0           31         0

            5        3896     0          2271        0           53         0

            6        4387     0          2330        0           36         0

            7        2795     0          1602        0           26         1

            8        3404     0          2175        0           42         0

            9        1699     0          1125        0           20         0

            10       3778     0          2692        0           54         0

            11       950      0          798         0           17         0

            12       2504     0          2160        0           25         0

            13       755      0          703         0           14         0

            14       1101     0          923         0           16         0

            15       1163     0          1232        0           25         0

            16       302      0          352         0           9          0

            17+      559      0          549         0           14         0

  2004      \<2yo    0        0          2           0           1          0

            2        185      0          217         0           7          0

            3        1143     0          737         0           11         0

            4        1328     0          905         0           13         0

            5        1480     0          1018        0           23         0

            6        1667     0          1044        0           15         0

            7        1062     0          718         0           11         0

            8        1294     0          975         0           18         1

            9        646      0          504         0           9          0

            10       1436     0          1207        0           24         0

            11       361      0          358         0           7          0

            12       952      0          968         0           11         0

            13       287      0          315         0           6          0

            14       418      0          414         0           7          0

            15       442      0          552         0           11         0

            16       115      0          158         0           4          0

            17+      212      0          246         0           6          0
  --------- -------- -------- ---------- ----------- ----------- ---------- ----------

Table 2 (cont'd)

  --------- -------- -------- ---------- ----------- ----------- ---------- ----------
  Testing   Age      Fallen   Fallen     Casualty    Casualty    Clinical   Clinical
  Year               stock    stock      slaughter   slaughter   suspects   suspects
                     tested   positive   tested      positive    tested     positive

  2003      \<2yo    0        0          0           0           1          0

            2        19       0          39          0           11         0

            3        117      0          131         0           18         0

            4        136      0          161         0           21         0

            5        152      0          181         0           35         0

            6        171      0          185         2           24         0

            7        109      0          128         0           18         0

            8        133      0          173         0           28         0

            9        66       0          90          0           14         0

            10       147      0          214         0           36         0

            11       37       0          64          0           11         0

            12       98       0          172         0           17         0

            13       29       0          56          0           9          0

            14       43       0          73          0           10         0

            15       45       0          98          0           17         0

            16       12       0          28          0           6          0

            17+      22       0          44          0           9          0

  2002      \<2yo    0        0          1           0           2          0

            2        6        0          52          0           18         0

            3        38       0          178         0           28         0

            4        45       0          219         0           33         0

            5        50       0          246         0           56         0

            6        56       0          253         0           38         0

            7        36       0          174         0           28         0

            8        43       0          236         0           44         0

            9        22       0          122         0           21         0

            10       48       0          292         0           57         0

            11       12       0          86          0           18         0

            12       32       0          234         0           26         0

            13       10       0          76          0           15         0

            14       14       0          100         0           16         0

            15       15       0          134         0           26         0

            16       4        0          38          0           10         0

            17+      7        0          60          0           15         0
  --------- -------- -------- ---------- ----------- ----------- ---------- ----------

Table 2 (cont'd)

  --------- -------- -------- ---------- ----------- ----------- ---------- ----------
  Testing   Age      Fallen   Fallen     Casualty    Casualty    Clinical   Clinical
  Year               stock    stock      slaughter   slaughter   suspects   suspects
                     tested   positive   tested      positive    tested     positive

  2001      \<2yo    0        0          0           0           2          0

            2        0        0          20          0           25         0

            3        0        0          68          0           39         0

            4        0        0          84          0           45         0

            5        0        0          94          0           77         0

            6        0        0          97          0           52         0

            7        0        0          67          0           39         0

            8        0        0          90          0           61         0

            9        0        0          47          0           29         0

            10       0        0          112         0           79         0

            11       0        0          33          0           25         0

            12       0        0          90          0           36         0

            13       0        0          29          0           20         0

            14       0        0          38          0           23         0

            15       0        0          51          0           36         0

            16       0        0          15          0           14         0

            17+      0        0          23          0           20         0

  2000      \<2yo    0        0          0           0           2          0

            2        0        0          12          0           18         0

            3        0        0          40          0           28         0

            4        0        0          50          0           33         0

            5        0        0          56          0           56         0

            6        0        0          57          0           38         0

            7        0        0          39          0           28         0

            8        0        0          54          0           44         0

            9        0        0          28          0           21         0

            10       0        0          66          0           58         0

            11       0        0          20          0           18         0

            12       0        0          53          0           26         0

            13       0        0          17          0           15         0

            14       0        0          23          0           16         0

            15       0        0          30          0           26         0

            16       0        0          9           0           10         0

            17+      0        0          14          0           15         0
  --------- -------- -------- ---------- ----------- ----------- ---------- ----------

Table 2 (cont'd)

+-------+-------+-------+-------+--------+--------+--------+--------+
| Te    | Age   | F     | F     | Ca     | Ca     | Cl     | Cl     |
| sting |       | allen | allen | sualty | sualty | inical | inical |
| Year  |       | stock | stock | sla    | sla    | su     | su     |
|       |       | t     | pos   | ughter | ughter | spects | spects |
|       |       | ested | itive | tested | po     | tested | po     |
|       |       |       |       |        | sitive |        | sitive |
+-------+-------+-------+-------+--------+--------+--------+--------+
| 1     | \<2yo | 0     | 0     | 0      | 0      | 1.125  | 0      |
| 999\* |       |       |       |        |        |        |        |
|       |       |       |       |        |        |        |        |
| (     |       |       |       |        |        |        |        |
| 37.5% |       |       |       |        |        |        |        |
| of    |       |       |       |        |        |        |        |
| total |       |       |       |        |        |        |        |
| in    |       |       |       |        |        |        |        |
| st    |       |       |       |        |        |        |        |
| rata) |       |       |       |        |        |        |        |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 2     | 0     | 0     | 1.5    | 0      | 10.5   | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 3     | 0     | 0     | 5.25   | 0      | 16.125 | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 4     | 0     | 0     | 6.75   | 0      | 18.75  | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 5     | 0     | 0     | 7.5    | 0      | 32.25  | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 6     | 0     | 0     | 7.875  | 0      | 21.75  | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 7     | 0     | 0     | 5.25   | 0      | 16.125 | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 8     | 0     | 0     | 7.125  | 0      | 25.5   | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 9     | 0     | 0     | 3.75   | 0      | 12.375 | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 10    | 0     | 0     | 9      | 0      | 33     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 11    | 0     | 0     | 2.625  | 0      | 10.5   | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 12    | 0     | 0     | 7.125  | 0      | 15     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 13    | 0     | 0     | 2.25   | 0      | 8.625  | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 14    | 0     | 0     | 3      | 0      | 9.375  | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 15    | 0     | 0     | 4.125  | 0      | 15     | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 16    | 0     | 0     | 1.125  | 0      | 5.625  | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+
|       | 17+   | 0     | 0     | 1.875  | 0      | 8.625  | 0      |
+-------+-------+-------+-------+--------+--------+--------+--------+

\*Data prorated for 1999. See accompanying text.

2.4 Feed Ban Evidence

Canada introduced a feed ban in 1997. The Canadian BSE surveillance
program has been intensified since the first native case was detected in
2003, and the surveillance data available to date indicate that the
country's feed ban has kept the level of disease in subsequent birth
year cohorts at a low level. Due to BSE's long incubation period and the
low prevalence of BSE in Canada, however, the available surveillance
data provides limited information about the trajectory of disease
incidence over time. However, implementation of feed mitigations has
been demonstrated to dramatically decrease the risk of new BSE cases,
and this knowledge provides information about the status of disease
before consideration of the animal health surveillance data. For the
purpose of this analysis, empirical evidence following the 1988 UK feed
ban provides prior information about the effect of a reasonably
effective feed ban on the incidence of BSE. These data are used as
surrogate data to predict the decline in prevalence in Canadian cattle
cohorts born after the 1997 Canadian ban.

Retrospective analysis of the incidence of BSE by birth year cohort
demonstrated that the UK's BSE epidemic was on the upswing before a
ruminant-to-ruminant feed ban was introduced in July 1988, but the
incidence of disease declined rapidly for each cohort of cattle born
after the ban (Schreuder *et al*. 1997). As clearly shown in the
epidemic curve (Figure 1), the UK ruminant-to-ruminant feed ban
introduced in 1988 substantially decreased the number of new cases in
subsequent birth year cohorts, although it was insufficient to eradicate
the disease immediately.

![](media/image1.wmf){width="4.834722222222222in"
height="2.8513888888888888in"}

Figure 1. Cumulative incidence of BSE in the UK by birth year cohort.

Source: Schreuder *et al*. (1997)

Applying the method described by Schreuder *et al*. (1997) to the
cumulative UK BSE surveillance data available as of November 2005 (DEFRA
2005), Animal and Plant Health Inspection Service (APHIS) Centers for
Epidemiology and Animal Health (CEAH) staff updated the cumulative
incidence for each UK birth year cohort (Table 3). In comparison to the
initial ruminant-to-ruminant feed ban introduced in the UK in 1988, the
Canadian feed ban introduced in 1997 is considered equivalent or more
restrictive, prohibiting feeding of most mammalian proteins to
ruminants. In 1994, the UK feed ban was amended to become a more
restrictive mammalian-to-ruminant feed ban. Therefore, the UK-based
evidence about the effect of a feed ban on BSE prevalence was
incorporated into the analysis for Canadian cohorts born in the first
five years following Canada's 1997 rule. Thus, the Canadian feed ban was
assumed to be at least as effective as the first five years of the
initial UK feed ban (Table 3).

Table 3. Observed (UK) and Expected (Canada) Decline in BSE Incidence by
Birth Year Cohort Following Feed Ban Introduction

+------+-------+------+-----------+----------+-------+--------------+
| Y    | UK    | BSE  | P         | Canadian | Years | Expected     |
| ears | Birth | c    | roportion |          | since | proportion   |
| s    | c     | ases | of the    | Birth    | feed  | of the 1997  |
| ince | ohort | in   | 1987/88   |          |       | Canadian     |
| feed |       | the  | UK        | cohort   | ban   | cohort's     |
| ban  |       | UK   | cohort's  |          |       | incidence \* |
|      |       | co   |           |          |       |              |
|      |       | hort | incidence |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 0    | 19    | 3    | 1.0000    | 1997     | 0     | 1.0000       |
|      | 87/88 | 9201 |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 1    | 19    | 1    | 0.4223    | 1998     | 1     | 0.4223       |
|      | 88/89 | 6556 |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 2    | 19    | 1    | 0.2817    | 1999     | 2     | 0.2817       |
|      | 89/90 | 1044 |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 3    | 19    | 5036 | 0.1285    | 2000     | 3     | 0.1285       |
|      | 90/91 |      |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 4    | 19    | 4348 | 0.1109    | 2001     | 4     | 0.1109       |
|      | 91/92 |      |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 5    | 19    | 3231 | 0.0824    | 2002     | 5     | 0.0824       |
|      | 92/93 |      |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 6    | 19    | 2517 | 0.0642    | 2003     | 6     | n/a          |
|      | 93/94 |      |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 7    | 19    | 1675 | 0.0427    | 2004     | 7     | n/a          |
|      | 94/95 |      |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+
| 8    | 19    | 444  | 0.0113    | 2005     | 8     | n/a          |
|      | 95/96 |      |           |          |       |              |
+------+-------+------+-----------+----------+-------+--------------+

\*Assuming Canadian feed ban was as effective as the initial UK feed ban
in its first five years.

Additional information provided by Cohen *et al*. (2003) indicates that
the prevalence of BSE is expected to decline in the U.S. in response to
the domestic feed ban. U.S. epidemiologists reviewed records and
conducted site visits to Canadian facilities to evaluate the Canadian
feed ban, its implementation and compliance. USDA (2005) concluded that
the Canadian feed ban is not substantially different from the U.S. feed
ban. Because the Canadian ban is similar to the U.S. ban and deemed to
be effectively enforced, the decline predicted by Cohen *et al*. (2003)
would likely apply to the Canadian population as well. In sum, knowledge
of the effect of a feed ban provides substantial information about BSE
prevalence before consideration of the surveillance data.

3\. Methods

3.1 BSurvE Model

The BSurvE model was developed to provide a method for evaluation of
national surveillance data and optimization of national surveillance
strategies for BSE (Wilesmith *et al*. 2004). BSurvE uses epidemiologic
information about the disease that was accumulated during the UK and
European outbreaks to predict parameters such as incubation period of
BSE, probable length of an infected animal's life, and the dynamics of
disease expression in infected animals. BSurvE combines this information
with country-specific demographic information about a national herd
(size and age distribution) and national BSE surveillance data to
achieve a set of point values for samples taken from cattle of different
age and surveillance streams---healthy slaughter, fallen stock, casualty
slaughter, or clinical suspect. The points represented by an animal
tested for BSE are based on the relative likelihood that the disease
would be detected in an animal leaving the herd at a particular age and
by a particular surveillance stream. Under this scheme, one point is
equivalent to an animal randomly selected for testing from the national
herd (Wilesmith *et al*. 2004).

The BSurvE model is implemented as a Microsoft^©^ Excel™ spreadsheet
application. The analysis herein based on the BSurvE model was performed
using BSurvE Version 06.03 (downloaded March 22, 2006 from
[http://www.bsurve.com](http://www.bsurve.com/) ). The BSurvE
spreadsheet model and documentation are available on the BSurvE website
(<http://www.bsurve.com/forum/forum.asp?$sid=&id=10> ). The BSurvE
website includes updates made to the BSurvE model when a new version is
released and documentation that provides detailed description of the
underlying functions of the model as well as step by step user
instructions.

For the purpose of estimating the prevalence of BSE in Canada, BSurvE
was used in two ways. First, for the purposes of estimating the
prevalence of BSE in Canada using the Bayesian Birth Cohort (BBC) model
including the UK feed ban evidence, BSE surveillance point values
allocated to the 1991-2005 birth year cohorts were calculated by
entering individual surveillance year data (Table 2) into the BSurvE
model and then summing the BSE surveillance points calculated by the
model for each birth cohort over the 7-year surveillance period ending
August 15, 2006. Note that Murray (2006, Table 26) presents BSE
surveillance points allocated to each birth cohort accumulated over more
than 14 years, dating back to the 1992 surveillance year.

Second, for the purposes of comparison, the prevalence of BSE in Canada
also is estimated using the unembellished BSurvE model application
intended for application to countries where BSE is non-endemic, or where
the infection rate is independent of birth year cohort, with animals
from different birth year cohorts having the same underlying probability
of infection. The BSurvE model developers refer to this prevalence
estimation method as BSurvE Prevalence B (Wilesmith *et al*. 2004,
2005). The latter BSE prevalence estimation method makes no assumptions
about feed ban efficacy and relies on the surveillance data alone. In
contrast to OIE (2006), which permits accumulation of BSE surveillance
points over 7 years, BSurvE (Version 06.03, downloaded 3/22/06 from
[http://www.bsurve.com](http://www.bsurve.com/) ) allows entry of no
more than 5 years of surveillance data at a time. Therefore, for the
purposes of estimating the prevalence of BSE in Canada using BSurvE
Prevalence B, testing data (Table 2) were combined for 1999-2002 for
entry into the model. Recall that the surveillance points calculated by
BSurvE depend on the age and health strata of animals when they are
tested and that BSurvE Prevalence B assumes a constant probability of
infection over time. In contrast to BSurvE Prevalence B, the BSurvE
application intended for application to countries where BSE is endemic
(BSurvE Prevalence A) is designed to permit an assessment of changes in
BSE prevalence across birth year cohorts. As discussed below, however,
the Canadian BSE surveillance data provide no statistical basis for
distinguishing BSE prevalence among birth year cohorts. Therefore,
BSurvE Prevalence B is used here to provide a sensitivity analysis of
the effect of incorporating the UK feed ban data on the estimated BSE
prevalence in Canada, and more importantly, the overall results of the
risk assessment.

3.2 Bayesian Birth Cohort Model

The Bayesian Birth Cohort (BBC) model combines prior evidence about the
effect of a ruminant-to-ruminant feed ban on BSE dynamics with the
surveillance points calculated by the BSurvE model, resulting in a more
precise estimate of BSE prevalence. Like the BSurvE model, the BBC model
prevalence estimate refers to all BSE-infected animals, regardless of
whether they would be detectable or showing clinical signs. As a
starting point, this method assumes that prevalence may be anything from
0 to 100% (i.e., the prior assumption was that prevalence is uniformly
distributed between 0 and 100%). The model then updates the Canadian
prevalence estimate based on the detected BSE cases, the expected
decline in BSE incidence by birth year cohort following the first five
years of the Canadian feed ban (Table 3), and the BSurvE point total for
each birth year cohort assumed to contribute adult animals to the
current standing population (birth years 1991-2005). The analysis
considers animals tested over the 7 year surveillance period ending
August 15, 2006; however, the surveillance points associated with
animals born prior to 1991 do not enter the analysis under the BBC model
because BSurvE only accepts data for cattle up to 16 years of age. To
date, no BSE cases of Canadian origin have been detected in animals born
prior to 1991.

The BBC model assumes that prevalence is constant for birth year cohorts
1991-97, with 1998 being the first cohort influenced by the 1997 feed
ban. The prevalence of BSE in the adult cattle alive in 2006 was
estimated as the weighted sum of the individual birth cohorts'
prevalence levels, where the weights are the proportion of infected
animals in each birth cohort that remain alive in 2006. The BBC model
was implemented using two Bayesian analytical methods: Gibbs sampling
and Sampling-Importance-Resampling (SIR).

3.2.1 Gibbs Sampling

Gibbs Sampling is a Monte Carlo Markov Chain (MCMC) statistical method
(Vose 2000). MCMC methods are based on an iterative updating scheme that
is repeated until the sequence of parameter vectors converges. In
general, Bayesian Monte Carlo procedures update uncertainty with forward
and backward propagation of the model (Brand and Small 1995). Vose
(2006) recommended this method for implementing the BBC model and
provided exemplar computer code using WinBUGS (Bayesian Inference Using
Gibbs Sampling), a freeware statistical application. WinBUGS (Version
1.4.1, downloaded January 2006 from
<http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml> ) was used to
implement the BBC model using the code presented in Appendix 1. Two
chains were initiated in WinBUGS to monitor convergence with starting
values for prevalence (p) equal to 0.1 and 0.0001. A total of 100,000
iterations were performed, and data from the last 20,000 iterations were
used for prevalence estimation.

3.2.2 Sampling-Importance-Resampling (SIR)

Using the same model inputs described above, an alternative Bayesian
method was used to verify the BBC model results obtained using WinBUGS.
In contrast to the iterative Gibbs sampling method,
Sampling-Importance-Resampling (SIR) is a noniterative algorithm used to
simulate Bayesian posterior distributions (Rubin 1988). This procedure
is also referred to as a weighted bootstrap (Smith and Gelfand 1992). In
SIR, *m* samples are drawn from an initial approximation to the desired
distribution, and then *l* \< *m* samples are randomly drawn from the
first finite sample (*m*) with probability proportional to their
importance (i.e., sampling weight). The rationale of the SIR algorithm
is based on the fact that as *m/l* → ∞ , the *l* sample values represent
independent draws from the desired posterior distribution (Rubin 1988).

In essence, the iterative MCMC procedures like Gibbs sampling converge
on the desired posterior as the number of iterations approaches
infinity, whereas the non-iterative SIR procedure converges to the
desired posterior as the initial sample (*m*) gets infinitely larger
than the resample (*l*). The SIR algorithm provides a useful check on
the Gibbs procedure because the former is not prone to \"getting stuck
in a rut\" (i.e., converging to local rather than global maxima). A
disadvantage of the SIR algorithm is that its computational efficiency
depends on having a good first approximation (prior), whereas the
iterative procedures can be monitored for convergence and stopped once
the convergence criteria are met.

The SIR algorithm proceeds by using Monte Carlo simulation methods to
generate a first approximation to the pre-feed ban prevalence (*p*)
uncertainty distribution that captures the entire range of feasible
parameter values, evaluating the likelihood of discrete *p* values given
the surveillance evidence, and then resampling from the uncertainty
distribution proportional to importance weights (normalized likelihoods)
of the discrete *p* values. The likelihood of *p*, given the
surveillance evidence, is calculated assuming a binomial likelihood
function:

$$\text{Lik}\left( p|s \right) = \prod_{\text{1991}}^{\text{2005}}{\text{Binomial}\left( \text{s,n,p} \right)}$$

where: s~i~ = number of BSE cases detected in the *i^th^* birth year
cohort

n~i~ = number of BSurvE points for the *i^th^* birth year cohort

p~1991~ = p~1992~ = \... = p~1997~ = *p*

p~1998~ = 0.4223\**p*

p~1999~ = 0.2817\**p*

p~2000~ = 0.1285\**p*

p~2001~ = 0.1109\**p*

p~2002~ = 0.0824\**p*

p~2003~ = 0.0824\**p*

p~2004~ = 0.0824\**p*

p~2005~ = 0.0824\**p*

The resampling weights (w) are equal to normalized likelihood values for
discrete uncertainty realizations of *p*:

$$w_{m} = \frac{\text{Lik}\left( p_{m} \right)}{\sum_{}^{}{\text{Lik}(p)}}$$

Monte Carlo methods are used to resample from the uncertainty
distribution for *p*, which is assumed to follow a beta distribution,
the conjugate prior to the binomial (Vose 2000):

$$p\text{\textasciitilde}\text{Beta}(\alpha,\beta)$$

Based on the mean and variance obtained from the Monte Carlo simulation
of *p*, the parameters of the beta distribution are estimated by the
method of matching moments (Evans *et al*. 1993):

$$\begin{array}{r}
\hat{\alpha} = \overline{x}\left\{ \lbrack\overline{x}(1 - \overline{x})\text{/s}^{2}\rbrack - 1 \right\} \\
\hat{\beta} = (1 - \overline{x})\left\{ \lbrack\overline{x}(1 - \overline{x})\text{/s}^{2}\rbrack - 1 \right\}
\end{array}$$

Based on the posterior for *p* obtained from these parameter estimates,
the prevalence in the current adult standing cattle population in Canada
is estimated as the weighted sum of the individual birth cohorts'
prevalence levels, where the weights are the proportion of infected
animals in each birth cohort that remain alive in 2006. The SIR method
was implemented using Palisades^©^ \@Risk™ (Ver. 4.5), an add-on to
Microsoft^©^ Excel™ (Ver. 9.0). Monte Carlo simulation was performed
with Latin Hypercube sampling (10,000 iterations).

4\. Results

4.1 BSurvE Points by Birth Year Cohort

Table 4 presents the BSE surveillance points calculated by BSurvE from
the Canadian BSE surveillance data and the Canadian BSE cases by birth
year cohort. The increase in surveillance points between the 2004 to
2005 birth year cohorts is due to the larger number of animals tested in
the clinical and casualty surveillance streams for the 2005 cohort. This
can be seen by comparing the one-year age class in Murray (2006, Tables
23 and 24).

Table 4. BSurvE Points and BSE Cases by Birth Year Cohort

  ------------------- ---------------------------- -----------------------
  Birth year          BSurvE Points                BSE Cases

  1991                24,737                       1

  1992                35,814                       0

  1993                61,914                       0

  1994                115,950                      0

  1995                183,528                      0

  1996                225,473                      2

  1997                217,155                      2

  1998                173,111                      1

  1999                142,290                      0

  2000                150,111                      2

  2001                128,565                      0

  2002                59,090                       1

  2003                13,894                       0

  2004                558                          0

  2005                2,170                        0
  ------------------- ---------------------------- -----------------------

4.2 No Statistically Significant Differences between Birth Year Cohorts

To determine whether there is any empirical basis for distinguishing BSE
prevalence among Canadian birth year cohorts, we consider the BSurvE
points calculated for the Canadian 1991-2005 birth year cohorts.
Recalling that one BSurvE point is equivalent to one randomly sampled
animal, multiple comparison tests were performed using BSE surveillance
points accumulated for birth year cohorts as inputs to statistical
methods designed to detect differences among random samples. The results
indicate that the available surveillance data provide no empirical basis
for distinguishing BSE prevalence among Canadian birth year cohorts. (To
maintain an overall type I (false positive) error rate when conducting
multiple comparisons tests, the comparison-wise error rate must be
adjusted. To maintain an overall type I error rate of 5 percent, with
105 pairwise comparisons, the comparison-wise type I error rate (CER) is
set to 0.05 percent (Sidak 1967). The multiple comparison test was
repeated, removing the 1991 through 2002 cohorts in sequence and
modifying the CER accordingly to maintain the overall type I error rate
of 5 percent. In each application of the test, there were no
statistically significant differences in BSE prevalence among birth year
cohorts. Similarly, no statistically significant differences were found
in a simple pairwise comparison of birth cohorts born before (1991-1997)
or after (1998-2005) feed ban introduction. In summary, analysis of the
Canadian BSE surveillance data provides no statistical basis for
distinguishing BSE prevalence among birth year cohorts. Therefore, a
single prevalence was estimated for the standing adult cattle
population.

In addition to the lack of statistical evidence to distinguish among
cohort prevalence estimates, there are biological reasons why birth
cohorts should not be considered independent. Animals born within one or
two years of a positive case have a similar likelihood of being exposed
to the feed sources responsible for infecting the case (given no
information about feed mitigations). Knowledge of BSE incidence in
animals born in each of the 3 to 7 years prior to the birth date of a
BSE case would also influence the prediction of the current prevalence,
because infected tissues from these animals could have been recycled
into the feed of the case's birth cohort (again assuming no knowledge of
feed mitigations).

4.3 Prevalence Estimates

The WinBUGS implementation of the BBC model resulted in an expected
prevalence value of 0.68 per million. In comparison, the SIR
implementation of the BBC model resulted in an expected prevalence value
of 0.65 per million. The 95% confidence levels also were virtually the
same, 1.1 and 1.0 per million, respectively. Due to the negligible
difference in the two results, the expected value of the Bayesian Birth
Cohort model was taken as 0.68 per million.

Table 5 summarizes the results of the estimation of BSE prevalence in
the standing Canadian adult cattle population as of August 15, 2006.
Based on the expected prevalence value under the BBC model and the
estimated adult herd size (Table 1), the expected number of BSE-infected
animals in the standing Canadian adult cattle population is 4.1. By
comparison, the expected value obtained under BSurvE Prevalence B is 3.9
per million, which corresponds to an estimated 23.2 BSE-infected animals
in the standing Canadian adult cattle population.

Table 5. Estimated Prevalence of BSE in Canada

  -------------------- ---------------------------- ---------------------
  **Prevalence in      **Bayesian birth cohort      **BSurvE Prevalence B
  adult cattle         method (BBC) with UK feed    estimate without
  population**         ban data**                   including feed ban
                                                    data**

  Expected value       0.68 \* 10^-6^               3.9 \* 10^-6^

  95% confidence level 1.1 \* 10^-6^                6.8 \* 10^-6^
  -------------------- ---------------------------- ---------------------

It is important to note that the estimated prevalence distribution
presented here represents uncertainty and not variability. At a given
point in time, the proportion (i.e., probability) of infected animals in
the population is a fixed value, but the exact magnitude of the value is
uncertain. Further, assuming the probability of infection remains
constant, the actual number of infected cattle in the population would
still vary randomly about the mean of the probability distribution over
time. Similarly, if we repeatedly draw a sample of animals from a
population with a fixed prevalence (i.e., fixed probability of
infection), the proportion of infected animals would vary randomly
between samples. Assuming a constant probability of infection, the
random variability in the number of BSE infected animals in the adult
cattle population would follow a binomial distribution that is described
by the prevalence and size of the population (Vose 2000). For a large
sample size and low prevalence values, the Poisson distribution
approximates the binomial variability distribution and is incorporated
in the model supporting the exposure assessment for live bovines
(\[Section IV.A. and Attachment 2\]) to represent variability around the
prevalence estimates generated here.

References

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(<http://www.oie.int/eng/normes/mcode/en_sommaire.htm>)

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Appendix 1. WinBUGS Code Used to Implement BBC Model

\# Calculate probabilities of infection in each year. Probability of
infection is assumed constant until the implementation of the feed ban
in 1997. The level of reduction in each of the 5 years after the
implementation of the ban is based on BSE incidence data from DEFRA
(2005) based on methods described in Schreuder et al. (1997). The
reductions only apply to first 5 years following the ban. After 5 years,
there is assumed no further reduction associated with the ban.

model{

\# Set prior

P \~ dbeta(1,1) #prevalence in Population in year of Canadian ban

P1991 \<- P

P1992 \<- P

P1993 \<- P

P1994 \<- P

P1995 \<- P

P1996 \<- P

P1997 \<- P

P1998 \<- P\*0.4223

P1999 \<- P\*0.2817

P2000 \<- P\*0.1285

P2001 \<- P\*0.1109

P2002 \<- P\*0.0824

P2003 \<- P\*0.0824 \# Set as conservatively high

P2004 \<- P\*0.0824

P2005 \<- P\*0.0824

\# Calculate expected infections for the number of points accumulated
for each year

L1991 \<- P1991\*24737

L1992 \<- P1992\*35814

L1993 \<- P1993\*61914

L1994 \<- P1994\*115950

L1995 \<- P1995\*183528

L1996 \<- P1996\*225473

L1997 \<- P1997\*217155

L1998 \<- P1998\*173111

L1999 \<- P1999\*142290

L2000 \<- P2000\*150111

L2001 \<- P2001\*128565

L2002 \<- P2002\*59090

L2003 \<- P2003\*13894

L2004 \<- P2004\*558

L2005 \<- P2005\*2170

\# Match Poisson(expected infections for points accumulated in year) to
observed infections

S1991 \~ dpois(L1991)

S1992 \~ dpois(L1992)

S1993 \~ dpois(L1993)

S1994 \~ dpois(L1994)

S1995 \~ dpois(L1995)

S1996 \~ dpois(L1996)

S1997 \~ dpois(L1997)

S1998 \~ dpois(L1998)

S1999 \~ dpois(L1999)

S2000 \~ dpois(L2000)

S2001 \~ dpois(L2001)

S2002 \~ dpois(L2002)

S2003 \~ dpois(L2003)

S2004 \~ dpois(L2004)

S2005 \~ dpois(L2005)

\# Sum \[Prevalence in each year \* number from each cohort expected to
remain standing in the 2005 Canadian population\]

InfectedNow \<- (0.0002 \* P1991 + 0.0005 \* P1992 + 0.001 \* P1993 +
0.0017 \* P1994 + 0.0042 \* P1995 + 0.0093 \* P1996 + 0.0186 \* P1997 +
0.0344 \* P1998 + 0.0667 \* P1999 + 0.131 \* P2000 + 0.2538 \* P2001 +
0.4659 \* P2002 + 0.6811 \* P2003 + 0.8002 \* P2004 + 0.8902 \* P2005)
\* 1194932

PrevNow \<- InfectedNow / 5979757

}

Data

\# A list of the observed BSE cases in each year

list(S1991 = 1, S1992 = 0, S1993 = 0, S1994 = 0, S1995 = 0, S1996 = 2,
S1997 = 2, S1998 = 1, S1999 = 0, S2000 = 2, S2001 = 0, S2002 = 1, S2003
= 0, S2004 = 0, S2005 =0)

Initial values

\# Two chains with different values for P to monitor convergence of the
estimates

list(P=0.1)

list(P=0.0001)

\# The output (node) is PrevNow