Sample size
Exercises
Type 1 diabetes
Here is some background information needed for the next exercise:
Early introduction to cow’s milk has been suggested as a possible risk factor for type 1 diabetes.
We want to study the association between exposure to cow’s milk (in supplements) before the
age of 6 months and type 1 diabetes before age 15 years. The risk of getting diabetes before the
age of 15 is approximately 0.5%. About 35% of infants in the population are exposed to cow’s
milk before the age of 6 months. We want to be able to detect a relative risk (or odds ratio) of 1.5
for the association. The incidence rate of type 1 diabetes is about 30 per 100 000 py, the
population of 0-15 year olds is about 900 000.
Exercise 1: Cohort versus traditional Case Control
Below are sample size calculations for the study of cow’s milk on type 1 diabetes (based on a
sample size calculator found at http://folk.uio.no/heins/Utilities/Utilities.html ). The first is a
cohort study, the second a traditional case control study.
Cohort study:
Values
40 000
0.5 %
35.0 %
1.50
95 %
80 %
Number of subjects, N=
Proportion with disease=
Proportion exposed=
Expected OR=
Confidence level:
Power:
Names
Diabetes
Cow-milk
Diabetes
Cow-milk
+
-
Proportion exposed=
Decimals=
2
2
+
-
89
111
13 911
25 889
200
44.6 %
39800
35.0 %
Proportion with disease
14 000
0.6 %
26 000
0.4 %
40000
0.5 %
35.0 %
OR=1.5, 95% CI=(1.01 , 2.24)
RR=1.5, 95% CI=(1.01 , 2.23)
Traditional case control study:
Cases:
Controls per case:
Proportion of cases exposed:
Proportion of controls exposed:
Expected OR:
Confidence level:
Power:
Values:
Names:
400 Diabetes
1.0
<- Choose one of the numbers to be
<- calculated by the program, and
<- write in values for the other two
The proportion of cases exposed
is calculated by the program
35.0 %
1.50
95 %
80 %
Diabetes
Cases
Controls
Cow-milk
+
-
sum
Proportion exposed=
Decimals=
2
Cow-milk
179
221
140
260
400
44.7 %
400
35.0 %
sum
319
481
800
39.8 %
OR=1.5, 95% CI=(1 , 2.25), power=80%
A case control study may be done with prevalent (existing) cases, or with incident (new) cases.
The latter is preferable from a theoretical point of view (no survival bias), but may take some
time. With an incidence of 30/100 000 new cases per year and a population of 900 000 youths we
will have 270 new cases of diabetes per year.
Questions:
Discuss pros and cons for the two designs.
1. Explain the results of the cohort sample size calculation in words
2. Explain the results of the case-control sample size calculation in words
3. Compare the number of subjects in the two designs.
4. Compare the durations of the studies. There will be 3 durations: cohort, case-control with
incident cases, and case-control with prevalent cases.