PU650 Unit 5 Attack Rate Calculation Example

Two Hundred Twelve Enrolled, One Hundred Sixty-Four Went: A Unit 5 Attack Rate Calculation Narrowing a Composite Day Camp's Roster to the Children Who Could Have Met the Exposure

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Purdue University Global

PU650: Infectious Disease Epidemiology

Unit 5 Attack Rate Calculation

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[Date]

Dunmore County, the camp, its roster and its survey are composite; the formulas, the interval method and the research cited are real.

The Cohort

The camp enrolled 212 children aged 5 to 12. In the week of July 6, 164 went on a day outing to Harlan Park, which has a playground, a picnic shelter and a splash pad with recirculated water; 48 stayed at the recreation center. On July 15 and 16, investigators reached the parents of all 212 by phone with a structured questionnaire. An ill camper met the Unit 3 clinical criteria with onset from July 7 to July 20. Fifty-two campers were ill.

Every Rate, With Its Numerator and Denominator

1. Whole roster, the wrong rate. 52 ill over 212 enrolled, 24.5 percent. Denominator: everyone enrolled. Reason it is wrong: 48 of these children never left the recreation center that week and could not have met anything at the park, so mixing them in understates the risk of those exposed and hides the comparison that matters.

2. Went on the outing. 49 ill over 164, 29.9 percent. Denominator: children present at Harlan Park.

3. Stayed at the center. 3 ill over 48, 6.2 percent. Denominator: children who did not go.

4. Risk ratio, outing versus center: 29.9 divided by 6.25, 4.8; 95 percent confidence interval 1.6 to 14.7.

5. Played in the splash pad, among outing children. 47 ill over 138, 34.1 percent.

6. Stayed dry, among outing children. 2 ill over 26, 7.7 percent.

7. Risk ratio, played versus dry: 4.4, 95 percent confidence interval 1.2 to 17.1.

8. Swallowed water, among splash pad players. 38 ill over 81, 46.9 percent.

9. Did not swallow water, among splash pad players. 9 ill over 57, 15.8 percent.

10. Risk ratio, swallowed versus did not: 3.0, 95 percent confidence interval 1.6 to 5.7.

11. Household secondary attack rate. 9 secondary cases over 180 household contacts, 5.0 percent.

Each step narrows the denominator to the children who could have met the next exposure, and the rate rises at every step.

The Arithmetic, One Line per Rate

Attack rate equals ill people divided by people at risk during the period, times 100. For row 2, 49 divided by 164 is 0.299. For row 3, 3 divided by 48 is 0.0625. The risk ratio is 0.299 divided by 0.0625, 4.78. The confidence interval for a risk ratio is calculated on the log scale. The standard error of the log risk ratio is the square root of one over 49, minus one over 164, plus one over 3, minus one over 48, which is the square root of 0.327, or 0.572. The log of 4.78 is 1.565. Adding and subtracting 1.96 times 0.572 gives 0.444 and 2.686, and the antilogs are 1.56 and 14.67. Rows 7 and 10 follow the same steps. The household rate: the 52 ill campers lived with 189 other people. Nine of those relatives had also been at Harlan Park during the outing week as volunteers or on a separate family visit, and they are removed, because a relative exposed at the same source is a co-primary case, not a secondary one. That leaves 180 contacts at risk only through the camper, and 9 of them became ill with onset more than three days after the camper's onset.

What the Denominators Show

The three steps, from the outing, to the splash pad, to swallowed water, move the attack rate from 29.9 to 34.1 to 46.9 percent. A rising rate as exposure becomes more specific is a dose-response pattern, and it points at the water rather than at the park in general. Swallowing recreational water is the classic route for this parasite, which survives chlorine levels that kill most bacteria within minutes (Shields et al., 2008). The three children ill among those who stayed at the center deserve a sentence. Two had siblings who went on the outing, and their onsets came after their siblings', which makes them likely household secondary cases rather than evidence of exposure at the center. The third has no known link.

Confidence Intervals, Read Honestly

The intervals are wide, especially for rows 4 and 7, because the comparison groups are small: 48 children at the center and 26 who stayed dry, with only 3 and 2 cases. A risk ratio of 4.8 with an interval from 1.6 to 14.7 says that the outing was clearly associated with illness and that the size of that association is uncertain. The analysis does not claim a precise multiplier and reports every interval beside its ratio. With small cells like these, an exact method would be a reasonable check, and the conclusion would not change because all three intervals exclude one.

Why These Are Called Attack Rates

Strictly, these are proportions, cumulative incidence over a short and defined period, not rates with person-time in the denominator. Outbreak epidemiology calls them attack rates by convention, and the analysis keeps the term while noting what it means (Centers for Disease Control and Prevention [CDC], 2012).

What the Table Hands the Investigation

The camp cohort points to the splash pad and to swallowed water within it. It does not show that the pad caused the community cases outside the camp, which is the next unit's work. Camps, child care groups and their households are also where this parasite spreads person to person, and contact with infected people in child care settings was among the main exposures in national outbreak reports, so the household rate is a reason to give exclusion and hand-washing advice to camp families now (Gharpure et al., 2019).

References

Centers for Disease Control and Prevention. (2012). Principles of epidemiology in public health practice: An introduction to applied epidemiology and biostatistics (3rd ed.). U.S. Department of Health and Human Services.

Gharpure, R., Perez, A., Miller, A. D., Wikswo, M. E., Silver, R., & Hlavsa, M. C. (2019). Cryptosporidiosis outbreaks: United States, 2009-2017. Morbidity and Mortality Weekly Report, 68(25), 568-572. https://doi.org/10.15585/mmwr.mm6825a3

Shields, J. M., Hill, V. R., Arrowood, M. J., & Beach, M. J. (2008). Inactivation of Cryptosporidium parvum under chlorinated recreational water conditions. Journal of Water and Health, 6(4), 513-520. https://doi.org/10.2166/wh.2008.068