## Section 1

Nominal mean *Campylobacter* culture confirmed cases reportable to
health department

# Overview for Sections 1 and 2 

The Centers for Disease Control and Prevention (CDC) obtained data for
the determination of the annual burden of *Campylobacter* infections
through active surveillance, surveys and case control studies. These
data sources will be described in detail in Sections 1 and 2.
Assumptions made in the risk assessment are presented in the sections
adjacent to the data points to which they apply and are listed
separately in Appendix B.

Section 1 explains the process of determining the estimated number of
reportable cases to the CDC's active surveillance system in the FoodNet
catchment area from the total number of culture confirmed cases reported
in a given year. It also details how the total number of
culture-confirmed cases is apportioned into confirmed cases of invasive
or enteric campylobacteriosis. The enteric cases are further apportioned
into those with bloody diarrhea and those without. These three distinct
categories of cases, confirmed cases with invasive disease and enteric
cases with and without bloody diarrhea, are required in the next step of
building the annual number of culture-confirmed *Campylobacter* cases in
the U.S.

Section 2 uses the estimated number of reportable cases in the
catchment, calculated in Section 1, to estimate the predicted total
number of *Campylobacter* cases in the U.S. Only a small number of cases
are reported in FoodNet surveillance, because only a small fraction of
persons with campylobacteriosis will progress along the medical care
path to the point of becoming a culture-confirmed case. The path
includes: seeking health care, having a specimen requested, submitting a
specimen when requested to do so, having the laboratory test for
*Campylobacter*, and having the laboratory that tests for
*Campylobacter* actually finding it. The probabilities of these events
occurring differ at points among the three distinct categories listed
above.

To illustrate the basic steps of the method used to determine the annual
burden of *Camplyobacter* illness, the calculations for 1999 are
described here using point estimates. Calculations for 1998 are similar.
The risk analysis calculations of the annual burden of
campylobacteriosis are described in Sections 1 and 2 and follow these
basic steps but incorporate confidence distributions in place of the
point estimates used for demonstration purposes in the pyramids below.
These pyramids are provided for demonstration purposes only and show
calculations of point estimates. Since the calculations in these
examples do not use the distributions as is done in the model the output
numbers will not exactly agree with the modeled values.

### Example -- Basic Steps in Calculation of total number of *Campylobacter* infections in the U.S. in 1999

The number of enteric culture-confirmed cases for the U.S. is calculated
by multiplying the number of enteric culture-confirmed cases in the
FoodNet sites for the year by the ratio of the U.S. population to the
FoodNet catchment size. There were 3,884 *Campylobacter*
culture-confirmed cases ascertained in FoodNet sites in 1999. Of these
cases, 51 were isolated from body sites considered invasive and 3,833
were from stool samples or were of unknown origin. For a FoodNet
population of 25,859,311 and a national population of 272,690,813 that
translates into approximately 40,419 culture-confirmed enteric
*Campylobacter* cases. Similarly, there are an estimated 538
culture-confirmed *Campylobacter* cases with invasive disease.
Therefore, the total number of culture-confirmed cases, combining those
with enteric disease and those with invasive disease, is the sum of
these two estimates: 40,419 + 538 or 40,957.

Of those culture confirmed cases in FoodNet in 1999, 46.5% came from
cases with bloody diarrhea (see Section 1.9). This means that 40,957 x
0.465= 19,045 cultures came from cases with bloody diarrhea, and 21,912
cultures came from cases without blood in the stool.

The way the number of culture-confirmed cases is built up to the total
number of cases is best illustrated by means of pyramids in the example
given below. The values of parameters in the pyramid that apply to

cases without bloody diarrhea are different from the values of
parameters in the pyramid for cases with bloody diarrhea. The pyramid
for *Campylobacter* cases without blood in the stool is as follows:

The calculation begins with the 21,912 cases one would have expected to
be confirmed if FoodNet active surveillance were extended over the
entire U.S. population. That number is divided by 0.75 to adjust for
losses in isolations due to stool handling procedures and lack of test
sensitivity, which are the cases that were tested but failed to yield a
positive result. This process of adjustment for the various steps along
the medical care path continues down the pyramid until the predicted
number of campylobacteriosis cases without blood in the stool in the
U.S. is attained at the bottom of the pyramid, 998,753 cases.

[Non-bloody stool pyramid:]{.underline}

The pyramid for cases with bloody diarrhea contains the assumptions that
a larger percentage of persons with bloody diarrhea will seek care, will
be requested and will submit specimens when they are requested to do so
(Section 2.3). This pyramid begins with 19,045 cases with bloody stool.

[Bloody stool pyramid:]{.underline}

Finally, all cases of invasive campylobacteriosis were assumed to have
been reported, obviating the need to use calculations. Thus, the
estimated total burden of campylobacteriosis for 1999 is the sum of the
three values for cases without bloody diarrhea, with bloody diarrhea,
and with invasive disease. That is 998,753 + 310,106 + 538 = 1,309,387
cases.

This basic calculation makes use of point estimates derived from CDC
data. Sections 1 and 2 describe the data points with their inherent
uncertainty or confidence distributions that were used in modeling the
risk to provide an estimate of the total annual burden of
campylobacteriosis.

+--------+----------------------------------------+--------------------+
| **Sy   | **Description**                        | **Formula**        |
| mbol** |                                        |                    |
+--------+----------------------------------------+--------------------+
| n~US~  | U.S. population                        | Data               |
+--------+----------------------------------------+--------------------+
| n~FN~  | FoodNet catchment site total           | Data               |
|        | population                             |                    |
+--------+----------------------------------------+--------------------+
| o~ej~, | Expected observed enteric/invasive     | Data               |
| o~ij~  | disease by site {j}                    |                    |
+--------+----------------------------------------+--------------------+
| λ~e~   | Expected observed enteric/invasive     | = n~US~ / n~FN~    |
|        | disease in the U.S.                    | \*                 |
| λ~i~   |                                        | Σ~j~Gamma(o~ej~,1) |
|        |                                        |                    |
|        |                                        | = n~US~ / n~FN~    |
|        |                                        | \*                 |
|        |                                        | Σ~j~Gamma(o~ij~,1) |
+--------+----------------------------------------+--------------------+
| p~b~   | Proportion of culture confirmed        | Beta distribution  |
|        | enteric infections with bloody         | based on data      |
|        | diarrhea                               |                    |
+--------+----------------------------------------+--------------------+
| λ1~n~  | Nominal mean *Campylobacter* culture   | =λ~e~\*(1- p~b~)   |
|        | confirmed cases reportable to health   |                    |
| λ1~b~  | department (non-bloody, bloody and     | =λ~e~\* p~b~       |
|        | invasive and **total**)                |                    |
| λ1~i~  |                                        | =λ~i~              |
|        |                                        |                    |
| **λ    |                                        | =λ1~n~+λ1~b~+λ1~i~ |
| 1~T~** |                                        |                    |
+--------+----------------------------------------+--------------------+

### Parameter estimations

1.1 (n~us~) -- U.S. population

The numbers used in the calculation of FoodNet incidence rates for the
catchment areas and the size of the total U.S. population are obtained
from the U.S. Census Bureau post-census estimates. These post-census
estimates are calculated annually, based upon the most recent census
survey. More information about how these population estimates are
calculated is available from the U.S. Census Bureau (114) (available at
http://www.census.gov/).

For 1998, n~US~ = 270,248,003

For 1999, n~US~ = 272,690,813

[1.2]{.underline} (n~FN~) - [FoodNet Catchment site total
population]{.underline}

FoodNet is a sentinel surveillance network of Emerging Infections
Program Sites. FoodNet was initiated in 1996 in five sites (California,
Connecticut, Georgia, Minnesota, Oregon) to provide more accurate
national estimates of the burden of foodborne disease than was
previously available through passive surveillance (19). By 1998, the
FoodNet catchment area had expanded to include the states of Minnesota
(MN), Connecticut (CT), Oregon (OR), and selected counties in California
(CA), Georgia (GA), Maryland (MD), and New York (NY) (21). Expansion in
1999 included the entire state of Georgia and additional counties in New
York. The seven sites represented approximately 7.7%, and 9.5% of the
U.S. population in 1998 and 1999 respectively. Because FoodNet is an
active surveillance system, all clinical laboratories within the
catchment areas and outside the catchment area, if they receive
specimens from persons who reside within the catchment area, are
contacted by FoodNet representatives to identify culture-confirmed cases
of campylobacteriosis occurring among catchment area residents. Cases
are identified from laboratory reports collected for the previous month
or are collected more frequently, depending on laboratory volume. Active
surveillance is considered more accurate than passive surveillance
because it does not rely upon laboratories to provide reports of cases
to the surveillance system. Instead, the system contacts and collects
the information from the laboratories. FoodNet incidence rates are based
upon laboratory-confirmed cases of campylobacteriosis and are being used
to document the effectiveness of new food safety control measures.
FoodNet incidence rates of culture-confirmed campylobacteriosis
therefore include only those persons with campylobacteriosis who sought
care for their illness and had a specimen submitted that was tested for
and yielded the organism. FoodNet reporting limits case reports to a
single report per affected individual within any 12-month period. If
more than a single isolation of *Campylobacter* from a single individual
occurs from multiple specimens, only one, with priority given to the
most invasive isolation, is reported to FoodNet for incidence rate
estimates. While this sentinel surveillance system is not designed
specifically to be representative of the U.S. population, based on a
comparison of the demographic characteristics the disease incidence is
likely to be representative of the U.S. population. Although comparison
of risk factors is preferable to comparison of demographic
characteristics for extrapolating data, the data are not available to
make this comparison.

The comparison of FoodNet and U.S. populations by demographic
characteristics (sex, age, race, and rural-to-urban distribution),
indicated that the population distributions appeared to be similar
(Table 1.1). The exception may be the lower proportion of Hispanics
represented in FoodNet catchment areas compared to the U.S. population.
The demographic characteristics available for comparison are, in most
instances, only markers for other risk factors that influence the rates
of disease in populations. The ideal extrapolation of FoodNet incidence
rates to the U.S. population would require knowledge of the distribution
of risk factors that affect the rates of disease. However, many of these
risk factors are not well described. Some risk factors for
campylobacteriosis are age (the most susceptible are the very young and
elderly), immune status (the immunocompromised are most at risk), and
antibiotic therapy in the month prior to illness onset (74). Because the
comparison of demographic characteristics between the FoodNet and the
U.S. populations was similar, this indicates that the risk factors that
affect disease rates may also be distributed similarly. Therefore, the
rates of disease obtained from FoodNet are likely to be representative
of disease rates in the U.S.

Table 1.1. Comparison of the distribution of demographic characteristics
by FoodNet total catchment to U.S. population (1998)

+----------------------+-------------+---------------+----------------+
| Demographic          |             | FoodNet Total | U.S.           |
| Characteristic       |             |               | Population     |
|                      |             | Catchment     |                |
|                      |             | Area          |                |
+----------------------+-------------+---------------+----------------+
| Rural vs. Urban^1^   | Rural       | 4,076,398     | 61,656,386     |
|                      |             | (21.78)       | (24.80)        |
+----------------------+-------------+---------------+----------------+
|                      | Urban       | 14,637,400    | 187,053,487    |
|                      |             | (78.22)       | (75.20)        |
+----------------------+-------------+---------------+----------------+
| Age Distribution     | 0-\<1 year  | 280,015 (     | 3,776,389 (    |
|                      |             | 1.35)         | 1.40)          |
+----------------------+-------------+---------------+----------------+
|                      | 1-\<10      | 2,907,058     | 39,050,749     |
|                      | years       | (14.03)       | (14.45)        |
+----------------------+-------------+---------------+----------------+
|                      | 10-\<20     | 2,865,920     | 38,050,749     |
|                      | years       | (13.83)       | (14.29)        |
+----------------------+-------------+---------------+----------------+
|                      | 20-\<30     | 2,767,848     | 36,296,139     |
|                      | years       | (13.36)       | (13.43)        |
+----------------------+-------------+---------------+----------------+
|                      | 30-\<40     | 3,591,391     | 43,608,568     |
|                      | years       | (17.33)       | (16.13)        |
+----------------------+-------------+---------------+----------------+
|                      | 40-\<50     | 3,201,640     | 39,778,258     |
|                      | years       | (15.45)       | (14.72)        |
+----------------------+-------------+---------------+----------------+
|                      | 50-\<60     | 2,047,441 (   | 26,692,895 (   |
|                      | years       | 9.88)         | 9.88)          |
+----------------------+-------------+---------------+----------------+
|                      | 60+ years   | 3,062,669     | 42,472,248     |
|                      |             | (14.78)       | (15.71)        |
+----------------------+-------------+---------------+----------------+
| Sex                  | Male        | 10,148,135    | 132,046,334    |
|                      |             | (48.97)       | (48.85)        |
+----------------------+-------------+---------------+----------------+
|                      | Female      | 10,575,847    | 138,252,190    |
|                      |             | (51.03)       | (51.15)        |
+----------------------+-------------+---------------+----------------+
| Race                 | Native      | 126,418 (     | 2,000,000 (    |
|                      | American    | 0.61)         | 0.74)          |
+----------------------+-------------+---------------+----------------+
|                      | White       | 15,913,196    | 195,439,508    |
|                      |             | (76.79)       | (72.31)        |
+----------------------+-------------+---------------+----------------+
|                      | Black       | 2,534,928     | 32,717,955     |
|                      |             | (12.23)       | (12.10)        |
+----------------------+-------------+---------------+----------------+
|                      | Hispanic    | 1,147,715 (   | 30,250,255     |
|                      |             | 5.54)         | (11.19)        |
+----------------------+-------------+---------------+----------------+
|                      | Asian       | 1,001,725 (   | 9,890,223 (    |
|                      |             | 4.83)         | 3.66)          |
+----------------------+-------------+---------------+----------------+

^1^1990 U.S. Census Estimates

ASSUMPTION: An extrapolation from FoodNet catchment populations to the
U.S. population at large assumes that the FoodNet catchment populations
will, in aggregate, be reasonably representative of the U.S. population
(Table 1.1).

DISCUSSION: Although the incidence rates varied by site, from
6.8/100,000 in Maryland to 32.2/100,000 in California in 1999 (22), the
overall rate of *Campylobacter* isolation is likely to reflect isolation
rates in the U.S. population. Comparisons of demographic characteristics
between the FoodNet sites and the U.S. population show similar
distributions of sex, age, race and rural/urban distributions (Table
1.1).

In addition to demonstrating similarity in population composition, an
evaluation of potential exposure is important. In a 1994-5 United States
Department of Agriculture, Food Safety Inspection Service, survey, 88%
of chicken carcasses were reported to carry *Campylobacter* at slaughter
(Table 1.2)(104). Another estimate, of *Campylobacter* carriage on
retail chicken products was demonstrated at a level of 88% in a
Minnesota survey of chicken products in 1997 (92).

Sporadic cases of *Campylobacter* account for approximately 99% of all
*Campylobacter* cases. Epidemiologic investigations of sporadic
infections have indicated that chicken is the most common source of
human infections (3, 92, 95). The frequency of chicken consumption was
evaluated to assess exposure to this risk factor in the U.S. population.
The National Chicken Council provided a chicken consumption survey,
conducted by Bruskin Goldring Research in June 1999 (18). The survey
utilized computer-assisted telephone interviewing and evaluated the
frequency of chicken consumption at home or away from home by sex, age,
income and region. The sample consisted of 1,019 completed interviews of
males and females, at least 18 years of age, in approximately equal
numbers. The selection of interviewees was based upon a computer-based
random-digit dialing sample of all households with telephones in the
continental U.S. There was equal probability of selection for each
household with a telephone, including listed and unlisted numbers. Each
number was subject to an original and at least four follow-up attempts
to complete the interviews. Findings, at a 5% significance level,
indicated that there was no difference in frequency of chicken
consumption at home or away from home by sex. Frequency of chicken
consumption at home or away from home was slightly greater for younger
respondents 18-24 years of age (mean=8.3 times per month, p\<0.05)
compared to other age groups (range of means=6.6-7.6 times per month,
p\<0.05). Respondents from the Northeast (mean=8.2 times per month,
p\<0.05), consumed chicken at home more frequently compared to other
parts of the country (range of means=6.1-7.5 times per month, p\<0.05),
but when eating chicken away from home all regions were similar. The
proportion of people rarely or never consuming chicken was low and did
not vary significantly by sex, age, income or region of the U.S. at a 5%
significance level (18).

Table 1.2. Percent isolation of *Campylobacter* and level of
contamination

+-------------+-----------+------+------+--------------+------+-----+
| Food Animal | Source    | No.  | Per  | Conc         | Yea  | Ref |
|             |           | Sam  | cent | entration^1^ | r^2^ |     |
|             |           | pled |      |              |      |     |
|             |           |      | Posi | MPN/cm^2^    |      |     |
|             |           |      | tive |              |      |     |
+-------------+-----------+------+------+--------------+------+-----+
| # Cattle    | Carcass   | 2064 | 4    | 0.1 ( CI     | 19   | 106 |
|             |           |      |      | NA)^3^       | 92-3 |     |
| Sla         | (Strs^4^  | 2109 | 10   |              |      | 105 |
| ughterhouse | &         |      |      | 0.1 (CI 0.1- | 19   |     |
|             | Heifers)  | 562  | 0    | 0.2)         | 93-4 | 107 |
| Sla         |           |      |      |              |      |     |
| ughterhouse | Carcass   |      |      | NA           | 19   |     |
|             |           |      |      |              | 93-4 |     |
| Sla         | (Cows &   |      |      |              |      |     |
| ughterhouse | Bulls)    |      |      |              |      |     |
|             |           |      |      |              |      |     |
|             | Ground    |      |      |              |      |     |
|             | Beef^5^   |      |      |              |      |     |
+-------------+-----------+------+------+--------------+------+-----+
| **Swine**   | Carcasses | 2    | 32   | 0.1 (CI      | 19   | 108 |
|             |           | ,112 |      | 0.08-0.13)   | 95-6 |     |
| Sla         |           |      |      |              |      |     |
| ughterhouse |           |      |      |              |      |     |
+-------------+-----------+------+------+--------------+------+-----+
| **Broiler   | Carcasses | 1297 | 88   | 4.4 (CI      | 19   | 104 |
| Chickens**  |           |      |      | 3.8-5.1)     | 94-5 |     |
|             | Grd.      | 283  | 60   |              |      | 109 |
| Sla         | C         |      |      | 4.8 (CI      | 1995 |     |
| ughterhouse | hicken^6^ |      |      | 4.0-5.7)     |      |     |
|             |           |      |      |              |      |     |
| Processing  |           |      |      |              |      |     |
| Plant       |           |      |      |              |      |     |
+-------------+-----------+------+------+--------------+------+-----+
| # Turkeys   | Carcasses | 1221 | 90   | 0.18 (CI     | 19   | 111 |
|             |           |      |      | 0.16-0.20)   | 96-7 |     |
| Sla         | Ground    | 295  | 25   |              |      | 110 |
| ughterhouse | Turkey^7^ |      |      | 2.8 (CI      | 1995 |     |
|             |           |      |      | 0.42-18.52)  |      |     |
| Sla         |           |      |      |              |      |     |
| ughterhouse |           |      |      |              |      |     |
+-------------+-----------+------+------+--------------+------+-----+

^1^MPN-Most Probable Number indicates most likely level of
contamination, not actual level because enrichment steps were required
to isolate *Campylobacter*. Carcass units are MPN/cm^2^ and ground
product units are MPN/g.

^2^ These studies are nationally representative and well designed, more
recently conducted surveys were not available.

^3^ Strs=Steers, CI- 95% Confidence Interval

^4^ Not applicable

^5^ Sampling period omitted sampling between March through August

^6^ Grd=Ground, Sampling period omitted collection between June through
September.

^7^Sampling period omitted collection between March through and
September.

ASSUMPTION: The incidence rates for culture-confirmed *Campylobacter*
infections in the FoodNet catchment are representative of incidence
rates for culture-confirmed *Campylobacter* infections in the U. S.

For 1998, n~FN~ = 20,723,982

For 1999, n~FN~ = 25,859,311

1.3 (o~ej~ ~,~ o~ij~) --Expected observable FoodNet enteric/invasive
disease by site {j}

Culture-confirmed cases of campylobacteriosis represent only a fraction
of all *Campylobacter* illnesses. The majority of persons with
*Campylobacter* illnesses do not seek care and most patients who do seek
care are not asked and do not submit specimens for culture (70).

(o~ej~) -- Expected o*bserved FoodNet **enteric** cases of Campylobacter
by site*

FoodNet reported the number of laboratory-confirmed isolations from
stools submitted by persons ill and visiting a health care provider. A
FoodNet case is defined as an isolation of *Campylobacter* from a
catchment area resident without an isolation in the preceding 12 months.

Table 1.3 Total number of enteric cases of *Campylobacter* by FoodNet
site, 1998 and 1999

  ------- ------- ------- ------- ------- ------- ------- ------- -------
  Year    CA^1^   CT      GA      MD      MN      NY      OR      Total

  1998    780     595     460     240     998     221     691     3985

  1999    685     553     715     156     782     356     586     3833
  ------- ------- ------- ------- ------- ------- ------- ------- -------

^1^CA-California, CT-Connecticut, GA-Georgia, MD-Maryland, MN-Minnesota,
NY-New York, OR-Oregon

For 1998, the total number of enteric cases of *Campylobacter* was 3985.
For 1999, the total number observed was 3833. Uncertainty distributions
for the numbers of expected observable reportable cases, o~ej~, where j
is the index for site, were modeled as Gamma distributions with
o****~ej~, the actual observed number of enteric cases of
*Campylobacter*, as input. This was done for the data for each year.

o~ej~ = Gamma(o****~ej~ , 1).

(o~ij~) -- *Expected Observable FoodNet **invasive** cases of
Campylobacter by site*

Invasive *Campylobacter* infections were ascertained in FoodNet as an
isolation of *Campylobacter* from blood, cerebrospinal fluid (CSF), or
other normally sterile site. Invasive isolations represent approximately
1.0% of all culture-confirmed *Campylobacter* cases and the vast
majority are bloodborne infections (19, 20, 21, 95).

DISCUSSION: It is not precisely known the completeness of ascertainment
of invasive *Campylobacter* infections. However, because persons with
invasive *Campylobacter* infections will be moderately to severely ill,
it is likely that most of these patients will seek care and the cases
reported.

Little is known about the completeness of ascertainment of invasive
campylobacteriosis. We do not know the frequency with which laboratories
are requested to test blood, CSF or other sterile specimens for
*Campylobacter,* and we do not know the sensitivity of the diagnostic
tests used for isolation from blood and other sterile sites. The lack of
this information may result in an underestimate of actual invasive
disease rates. However, an increase in isolation of specimens classified
as invasive is unlikely to have much impact on the overall number of
cases of campylobacteriosis in the U.S. because the currently
ascertained proportion of invasive cases is approximately 1.0% of all
confirmed cases, and most cases are likely to seek care.

ASSUMPTION: All invasive campylobacteriosis cases seek care, have a
specimen collected that yields *Campylobacter*, and are ascertained by
FoodNet.

DATA GAP: Data are not available describing rates or cases of invasive
disease seeking care, requests for diagnostic tests, and the sensitivity
of diagnostic procedures, such as blood culture.

##### Table 1.4 Total number of invasive cases of *Campylobacter* by FoodNet Site, 1998 and 1999

  ------- ------- ------- ------- ------- ------- ------- ------- -------
  Year    CA^1^   CT      GA      MD      MN      NY      OR      Total

  1998    10      8       9       8       6       0       2       43

  1999    11      11      8       10      3       2       6       51
  ------- ------- ------- ------- ------- ------- ------- ------- -------

^1^CA-California, CT-Connecticut, GA-Georgia, MD-Maryland, MN-Minnesota,
NY-New York, OR-Oregon

For 1998, the total number of observed invasive cases of *Campylobacter*
was 43. For 1999, the total number was 51. Uncertainty distributions for
the expected numbers of observable reportable cases, o~ij~, where j is
the index for site, were modeled as Gamma distributions with o****~ij~,
the actual observed number of invasive cases of *Campylobacter*, as
input[^1]. This was done for the data for each year.

o~ij~ = Gamma(o****~ij~ , 1).

[1.4]{.underline} (λ~e~) and (λ~i~) - [Expected observed]{.underline}
[enteric/invasive disease in U.S.]{.underline}

The number of enteric and invasive infections in the FoodNet catchment
sites that are observed is affected by random chance. The true measure
of the health burden is the mean number of observations we would see if
we were able to repeat each year many times. The confirmed cases of
*Campylobacter* are rare events when compared to the population size, so
it is reasonable to assume that the frequency of confirmed cases is a
Poisson process. In this case, the mean number of observations are the
Poisson means *λ~i~* and *λ~e~* for invasive and enteric infections
respectively.

(λ~e~ and λ~e~) *Nominal mean **enteric** and **invasive** Campylobacter
culture confirmed infections reportable to health department*

The FoodNet sites cover only (n~FN~ / n~US~) of the population, so
estimates of the mean number of cases that would apply to the population
are calculated by dividing the sum of the modeled FoodNet mean
observable cases by this fraction. That is,

$$\lambda_{e} = \frac{n_{\text{US}}}{n_{\text{FN}}}\sum_{j}^{}\text{Gamma}\left( o_{\text{ej}} \right)$$

and

$\lambda_{i} = \frac{n_{\text{US}}}{n_{\text{FN}}}\sum_{j}^{}\text{Gamma}\left( o_{\text{ij}} \right)$.

[1.5]{.underline} (p~b~) - [Proportion of culture confirmed enteric
infections with bloody diarrhea]{.underline}

The proportion of culture-confirmed enteric infections with patients
reporting bloody diarrhea was calculated from the *Campylobacter* Case
Control study for each FoodNet site (CA=18.2% (2/11), CT=40.2% (70/174),
GA=53.6% (15/28), MD=47.6% (10/21), MN=49.1% (113/230), NY=50.8%
(32/63), OR=54.6% (6/11) and weighted by catchment site population (18).
The estimate weighted by catchment population was 46.2%, and the crude
estimate was 46.1%. See Table 1.5.

Table 1.5. Catchment populations and cases reporting blood in their
stools. (*Campylobacte*r Case Control Study)

+------+----------+-------------+-------------------+-----------------+
| Site | C        | Weighting   | Number for whom   | Number who had  |
|      | atchment | Fraction    | response was      | bloody diarrhea |
| j    | po       |             | known             |                 |
|      | pulation | W~j~        |                   | B~j~            |
|      |          |             | A~j~              |                 |
+------+----------+-------------+-------------------+-----------------+
| CA   | 2        | 0.103556    | 11                | 2               |
|      | ,146,096 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+
| CT   | 3        | 0.157985    | 174               | 70              |
|      | ,274,069 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+
| GA   | 3        | 0.18076     | 28                | 15              |
|      | ,746,059 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+
| MD   | 2        | 0.117945    | 21                | 10              |
|      | ,444,280 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+
| MN   | 4        | 0.228017    | 230               | 113             |
|      | ,725,419 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+
| NY   | 1        | 0.053372    | 63                | 32              |
|      | ,106,085 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+
| OR   | 3        | 0.158366    | 11                | 6               |
|      | ,281,974 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+
| T    | 20       | 1           | 538               | 248             |
| otal | ,723,982 |             |                   |                 |
+------+----------+-------------+-------------------+-----------------+

The FoodNet data for reporting blood in the stool was used as follows to
determine an estimate for p~b~:

$$p_{b} = \sum_{j}^{}{W_{j} \ast \text{Beta}(B_{j} + 1,A_{j} - B_{j} + 1)}$$

where W~j~ is the weight for site j (site j size divided by total
catchment size), B~j~ is the site-specific number of cases reporting
bloody diarrhea and A~j~ is the site-specific number of cases providing
a response to whether blood had been observed in their stools. The Beta
distribution is used here to describe the uncertainty about a
proportion, as explained in Appendix A. Each of the summed Beta
distributions is approximately normally distributed because there are
reasonably large samples (94) and because the Beta distributions are
centered at values near 0.5 (i.e. B~j~/A~j~ are approximately 0.5). The
distribution of p~b~ can thus be approximated by first replacing each
Beta distribution with a Normal:

$$\text{Beta}(B_{j} + 1,A_{j} - B_{j} + 1) \approx \text{Normal}(\mu_{j},\sigma_{j})$$

where

$\mu_{j} = \frac{B_{j} + 1}{A_{j} + 2}$ and
$\sigma_{j} = \sqrt{\frac{(B_{j} + 1)(A_{j} - B_{j} + 1)}{(A_{j} + 2)^{2}(A_{j} + 3)}}$

and then noting the identity:

$$p_{b} \approx \sum_{j}^{}{W_{j} \ast \text{Normal}(\mu_{j},\sigma_{j}}) = \text{Normal}\left( \sum_{j}^{}{W_{j}\mu_{j},}\sqrt{\sum_{j}^{}\left( W_{j}\sigma_{j} \right)^{2}} \right)$$

[1.6]{.underline} (λ1~n~, λ1~b~, λ1~i~ ) - [Nominal mean number of
*Campylobacter* culture confirmed enteric infections in the FoodNet
catchment area with self reported bloody and non-bloody diarrhea and the
nominal mean number of culture confirmed invasive infections in the
catchment reportable to health department]{.underline}

These enteric infection parameters are calculated by multiplying the
nominal observed mean enteric infections in the population by the
probabilities a case will report visible blood in the diarrhea p~b~ and
(1-p~b~) the probability of reporting no visible blood in the diarrhea
respectively. The number of invasive cases is not subdivided, thus:

λ1~b~ = λ~e~\* p~b~

λ1~n~ = λ~e~ \*(1- p~b~)

λ1~i~ = λ~i~

In mathematical terms, λ1~b~ and λ1~n~ are the mean values (intensities)
of Poisson distributions and p~b~ has been interpreted as the
probability that an individual contracting campylobacteriosis will
report visibly bloody stools. An alternative interpretation of p~b~
would be the predictably constant fraction of the population contracting
campylobacteriosis that would report visibly bloody stools because of
some mechanism. The approach used in this model allows for greater
variability in the observable incidence of bloody diarrhea and,
therefore, produces greater uncertainty in our estimates of the mean
incidence.

[1.7]{.underline} **(λ1~T~**) - [Nominal total mean number of
*Campylobacter* culture confirmed cases reportable to health department
in the FoodNet catchment area]{.underline}

The total number of reportable cases is the sum of the reportable cases
of the three types, enteric non-bloody, enteric bloody, and invasive.
The parameter for the nominal total mean is modeled as the sum of the
parameters for numbers of reportable cases of the three types.

**λ1~T~** =λ1~n~+λ1~b~ +λ1~i~.

**λ1~T~** was modeled for 1998 and for 1999. The results are displayed
here.

  -------------- ----------------- ---------------- -------------- ----------------
  **Year**       **Model output**  **5^th^**        **Mean**       **95^th^**
                                   **percentile**                  **percentile**

  **1998**       **λ1~T~**         51,160           52,533         53,912

  **1999**       **λ1~T~**         39,879           40,957         42,044

  **Difference                                      -11,576        
  (99-98)**                                                        
  -------------- ----------------- ---------------- -------------- ----------------

**Section 1 Summary**

The model predicts that in 1999 there was a mean estimate of 21,630
reportable cases of campylobacteriosis with non-bloody diarrhea with a
5^th^ percentile estimate of 19,393 and a 95^th^ percentile estimate of
23,913 in the FoodNet catchment area. In 1999 there was a mean estimate
of 18,789 reportable cases with bloody diarrhea with a 5^th^ percentile
estimate of 16,570 and a 95^th^ percentile estimate of 21,071 and a mean
estimate of 538 confirmed invasive disease cases with a 5^th^ percentile
estimate of 420 and a 95^th^ percentile estimate of 668 in the
catchment. Relative contributions of the various components of the model
to the total model uncertainty will be presented in Section 5,
Sensitivity Analysis. The total sum of non-bloody, bloody and invasive
cases and their distributions are shown in the table above.

Table 1.6. 1998 and 1999 FoodNet active surveillance for *Campylobacter*
from culture confirmed cases

+---------+---------+---------+---------+---------+---------+---------+
| Site    | Ca      |         | ####    |         | ####    |         |
|         | tchment |         |  Enteri |         | Invasiv |         |
|         | Pop     |         | c Cases |         | e Cases |         |
|         | ulation |         |         |         |         |         |
|         |         |         |         |         |         |         |
|         | E       |         |         |         |         |         |
|         | stimate |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
|         | 1998    | 1999    | 1998    | 1999    | 1998    | 1999    |
+---------+---------+---------+---------+---------+---------+---------+
| #       | 2,      | 2,      | 780     | 685     | 10      | 11      |
| #### CA | 146,096 | 162,359 |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| CT      | 3,      | 3,      | 595     | 553     | 8       | 11      |
|         | 274,069 | 282,031 |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| GA      | 3,      | 7,      | 460     | 715     | 9       | 8       |
|         | 746,059 | 788,240 |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| MD      | 2,      | 2,      | 240     | 156     | 8       | 10      |
|         | 444,280 | 450,566 |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| MN      | 4,      | 4,      | 998     | 782     | 6       | 3       |
|         | 725,419 | 775,508 |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| NY      | 1,      | 2,      | 221     | 356     | 0       | 2       |
|         | 106,085 | 084,453 |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| OR      | 3,      | 3,      | 691     | 586     | 2       | 6       |
|         | 281,974 | 316,154 |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| Totals  | 20,     | 25,     | 3985    | 3833    | 43      | 51      |
| for     | 723,982 | 859,311 |         |         |         |         |
| Ca      |         |         |         |         |         |         |
| tchment |         |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+

[^1]: One exception occurred for NY in 1998 where there were no reported
    invasive cases. The uncertainty distribution for o~ij~ in that case
    was taken to be --ln(Beta(2,1) because a Gamma(0,1) model is not
    possible.