Power Calculation for the Increase in MEC Incentive (Jan 2022)

Response rate incentive increase power calculation
To perform a power calculation to estimate the required sample size to detect a change in the
exam response rate (among persons who were interviewed), we need to determine:
1) what the expected number of interviewed persons will be in each stand. We used the
average number of interviewed participants age 16+ years from the first 4 stands in
2021. This was approximately 250 people interviewed per stand (1,014, divided by 4).
2) the expected change in response rate. For an increase from $85 to $125, it is reasonable
to expect that we could observe a 5% increase in response rate. As we discussed last
week, we wouldn’t expect an increase in incentive to be the sole intervention needed.
The overall exam response rate for the first four stands in 2021 was 75%. We can
reasonably expect the higher incentive to increase the exam response rate to 80%.
Sample sizes and response rate for ages 16 years and above for the first 4 stands in 2021

Adults 16+ years
Interviewed
Examined
Exam response
rate

Total
1,014
757
75%

Stand 428
227
179
79%

Stand 429
278
207
75%

Stand 430
282
212
75%

Stand 431
228
159
70%

In the table below, the statistical power for each additional stand completed is shown in the
right column. For the first stand in which the exam incentive is raised to $125 and the expected
250 adults age 16+ are interviewed, the statistical power to detect a 5% difference in the exam
response rate (an increase from 75% to 80%) is only 37%. In the last row, after five stands are
visited (a cumulative total of 1,250 interviewed people), the statistical power reaches 81%. A
statistical power of 80% is the conventional target. In sum, for the assumptions used, NHANES
would need to visit five stands to detect a 5% increase in the exam response rate.
Statistical power calculation
Cumulative Response rate
Expected
Cumulative Statistical
# of stands first 4 stands Response rate sample size
Power
1
75%
80%
250
37%
2
75%
80%
500
58%
3
75%
80%
750
70%
4
75%
80%
1000
77%
5
75%
80%
1250
81%
However, field experience could vary:
-- If a greater number of people are interviewed (e.g., higher interview response rates), fewer
number of stands will be needed to detect a 5% increase in response rates.
-- Conversely, if interview response rates are lower and fewer adults per stand are interviewed,
a greater number of stands will be needed.
-- If the impact of the incentive is greater (higher than a 5% increase) it will take fewer stands to
detect a change in exam response rates.