Epidemiology

Lesson 4 Practice Examples Key

1. In country A, the mortality rate from unintentional injuries for last year is 36/100,000 people. In country B, the mortality rate from unintentional injuries for the same year is 42/100,000 people.

a. Calculate the RR for death due to unintentional injuries in country B as compared to country A. Show your work, please.

RR crude = (42/100,000) / (36/100,000) = 1.17

b. State what your RR means.

This means that the risk of death due to unintentional injuries are 1.17 times greater (or 17% greater) in Country B as compared to Country A

c. What are some of the potential explanations for your findings?

One could speculate many things to explain the difference: unsafe roads, high risk-taking behaviors, inadequate emergency response system, etc. However, what I want you to think about here is that we really don’t KNOW what this increased risk of death means. It could possibly be a result of some other factor – such as age. There could be a lot more teens in country B….

2.Four hundred people were stranded in a shelter during a recent hurricane. Relief workers brought sandwiches – 200 chicken salad and 200 peanut butter and jelly -- to the shelter for people to eat. That evening, 183 people were stricken with diarrhea. Of those, 141 had eaten chicken salad; the rest had peanut butter and jelly. Each person ate one sandwich.

The first step is to set up your epi matrix:

	D+ (diarrhea)	D- (no diarrhea)	Total
E+ (chicken salad)	141	200-141=59	200
E- (peanut butter and jelly)	183-141=42	200-42=158	200
Total	183	400-183=217	400

a. How much more or less likely were people who ate chicken salad to get diarrhea as compared to those who ate peanut butter and jelly?

This question is asking us to calculate what? (I’m pausing to let you answer) If you said RR, you are correct. The first step in doing this, therefore, is to calculate the incidence in the exposed.

IE+ = a/(a+b) = 141/(141+59) = 141/200=.705

Next, calculate the incidence among the unexposed

IE- = c/(c+d) = 42/(42+158) = 42/200 = .21

Now we can calculate RR by comparing IE+ to IE-

RR = IE+/IE- = .705/.21 = 3.36

My interpretation is this: People who ate the chicken salad were 3.36 times more likely to have diarrhea than those who ate peanut butter and jelly.

b. How many cases per 100 could be attributed to the chicken salad?

Here, we are calculating absolute risk: AR = IE+ - IE- = .705 - .21 = .495

Because I asked for “per 100” we will multiply this by 100, which equals 49.5, and interpret our finding as such: 49.5 per 100 cases of diarrhea were attributable to chicken salad.

c. What percentage of diarrhea cases would be eliminated if we did away with the chicken salad?

Here we need to calculate the attributable proportion (AR%).

AR% = AR/IE+ = .495/.705 = .702

Note: AR% can also be calculated as such:

AR% = (RR-1)/RR = (3.36 – 1)/3.36 = 2.36/3.36 = .702

Pretty cool, eh? Anyway, my interpretation would be: If we served only peanut butter and jelly, we would eliminate 70.2% of the diarrhea among people in the shelter.

d. How many cases of diarrhea per 100 in the population could be prevented if chicken salad was not served?

Here we are looking at PAR. Recall that PAR is an absolute measure that looks at the proportion of disease that can be prevented if that exposure were eliminated.

PAR = I total – IE-

Where I total = (a+c) / (a + b + c + d)

So, PAR = [(141+42) / (143 + 59 + 42 + 158 )] – [42 / (42 + 158)

= (183 / 400) - .21

= .458 - .21

= .248

Because we want to report this as per 100, we then multiply by 100 giving us the answer of 24.8 per 100 and interpret this to mean that 24.8 of the 70.5* cases of diarrhea per 100 could be eliminated by not serving chicken salad.

*this is the IE+ multiplied by 100 to get a per 100 measure

e. What percentage of diarrhea in the population could be prevented if chicken salad was not served?

Here you are being asked to compute and interpret the PAR%. We can do this the easy way by taking PAR and dividing it by the I total that we just computed:

PAR% = .248 / .458 = .541

Multiply by 100 to get the % and we get PAR% = 54.1%

Now we interpret by saying 54.1% of diarrhea in this population could be eliminated by not serving chicken salad.

3. In State A, the mortality rate from breast cancer for last year was 110/100,000 people. In State B, the mortality rate from breast cancer for the same year was 143/100,000 people.

a. Calculate the RR for death due to breast cancer in State B as compared to State A. Show your work, please.

RR crude = (143/100,000) / (110/100,000) = 0.00143/ 0.0011= 1.3

b. State what your RR means.

This means that the risk of death due to breast cancer is 1.3 times greater (or 30% greater) in State B as compared to State A

c. What are some of the potential explanations for your findings?

One could speculate many things to explain the difference: family history, hormone replacement therapy, age etc. However, what I want you to think about here is that we really don’t KNOW what this increased risk of death means. It could possibly be a result of some other factor – such as age. There could be a lot more women in State B who are at the specific range of age….

4. 500 people attended in a conference held in convention center. They were served by two different sandwiches – 200 ham sandwiches and 300 chicken sandwiches. That evening, 162 people were diagnosed with diarrhea. Of those, 148 had eaten ham sandwiches; the rest had chicken sandwiches. Each person ate one sandwich.

First we need to set up our table and fill in the missing data. The known data are in bold.

	D+ (diarrhea)	D- (no diarrhea)	Total
E+ (ham sandwiches)	148	200-148= 52	200
E- (Chicken sandwiche)	162-148= 14	300-14= 286	300
Total	162	500-162= 338	500

a. How much more or less likely were people who ate ham sandwich to get diarrhea as compared to those who ate chicken sandwich?

This is asking us to calculate what? (I’m pausing to let you answer) If you said RR, you are correct. The first step in doing this, therefore, is to calculate the incidence in the exposed.

IE+ = a/(a+b) = 148/(148+52) = 148/200=.74

Next, the incidence among the unexposed

IE- = c/(c+d) = 14/(14+286) = 14/300 = .047

Now we can calculate RR

RR = IE+/IE- = .74/. 047 = 15.7

My interpretation is this: People who ate the ham sandwich were 15.7 times more likely to have diarrhea than those who ate chicken sandwiches.

b. How many cases per 100 could be attributed to the ham sandwich?

AR = IE+ - IE- =. 74- 0.047= 0.693

Because I asked for “per 100” we will multiply this by 100, which equals 69.3 and interpret our finding as such: 69.3 per 100 cases of diarrhea were attributable to ham sandwiches.

c. What percentage of diarrhea cases would be eliminated if we did away with the ham sandwich?

Here we need to calculate the attributable proportion (AR%).

AR% = AR/IE+ = 0.693/.74 = 0.93

Note: AR% can also be calculated as such:

AR% = (RR-1)/RR = (15.7 – 1)/15.7= 14.7/15.7= 0.93

My interpretation is: If we served only chicken sandwiches, we would eliminate 93% of the diarrhea among people in the shelter.

d. How many cases of diarrhea per 100 in the population could be prevented if ham sandwich was not served?

Here we are looking at PAR. Recall that PAR is an absolute measure that looks at the proportion of disease that can be prevented if that exposure were eliminated.

PAR = I total – IE-

Where I total = (a+c) / (a + b + c + d)

So,

PAR = [(148+14) / (148 + 14 + 52 + 286)] – [14 / (14 + 286)]

= (162/ 500) – 0.05

= 0.324- 0.05

= .274

Because we want to report this as a per 100, we then multiply by 100 giving us the answer of 27.4 per 100 and interpret this to mean that 27.4 of the 74 cases of diarrhea per 100 could be eliminated by not serving chicken salad.

*this is the IE+ multiplied by 100 to get a per 100 measure

e. What percentage of diarrhea in the population could be prevented if ham sandwich was not served?

Here you are being asked to compute and interpret the PAR%. We can do this the easy way by taking PAR and dividing it by the I total that we just computed:

PAR% = .274 / .324 = .84

Multiply by 100 to get the % and we get PAR% = 84 %

Now we interpret by saying 84% of diarrhea in this population could be eliminated by not serving ham sandwich.

5. In city A, the mortality rate from heart disease for last year was 110/100,000 people. In city B, the mortality rate from heart disease for the same year was 154/100,000 people.

a. Calculate the RR for death due to heart disease in city B as compared to city A. Show your work, please.

RR crude = (154/100,000) / (110/100,000) = 0.00154/ 0.0011= 1.4

b. State what your RR means.

This means that the risk of death due to heart disease is 1.4 times greater (or 40% greater) in City B as compared to City A

c. What are some of the potential explanations for your findings?

One could speculate many things to explain the difference: smoking, high risk-taking behaviors, inadequate physical activity, etc. However, what I want you to think about here is that we really don’t KNOW what this increased risk of death means. It could possibly be a result of some other factor – such as age. There could be a lot more elderly in city B….