Confidence Intervals for Number of Diabetics
in 2005 and 2015
Question: Below are the confidence intervals for
number of diabetics and nondiabetics in the 50andover population for 2005
and 2015.
What would have been the
estimated number of 50andover diabetics in 2015 if the only factor that had
changed was the size of the population?
Can we reject the hypothesis that
the only factor impacting the number of diabetics in this age group is
population change?
Diabetics and NonDiabetics 2005 & 2015 (000 Omitted)


2005 Medical Expenditures Panel Survey


Total

Std. Error

LB of 95% CI

UB of 95% CI


Not Diabetic

76,900

2,015

72,900

80,900

Diabetes

12,900

465

11,900

13,800

2015 Medical Expenditures Panel Survey


Total

Std Error

LB of 95% CI

UB of 95% CI


Not Diabetic

93,600

2,672

88,300

98,900

Diabetes

20,300

683

18,900

21,600

Source 2005 and 2015 Medical
Expenditure Panel Survey. Figures in thousands of people for the 50andover population.
Analysis: The 50andover population grew by 27 percent
between 2005 and 2015. This means the
center, lower bound and upper bound of a 95 percent confidence interval
adjusted for population growth is 27 percent higher than the actual 2005
confidence interval.
How do I know this? Var(ax)= a^{2} Var(X) so the
STD(aX) =a* STD(x). The standard error
is the standard deviation divided by sample size with some adjustments for the
MEPS sample design.
The upper bound for the
number of 50andover diabetics based on the 2005 confidence interval adjusted
for population growth is 17.5 million.
The actual number of 50andover
diabetics in 2015 is 21.6 million.
Factors other than population
growth have apparently contributed to the increases in the number of people
with diabetes.
Authors Note: This post makes a somewhat arcane point on
how to adjust confidence intervals from two surveys for population growth. A more interesting article on diabetes and
obesity, which motivated this short post, can be found here.
Appendix:
The STATA CODE USED for this Post:
use
"/Users/davidbernstein1/Desktop/OneDrive/Documents/meps2005/H181v2.dta"
. use
"/Users/davidbernstein1/Desktop/OneDrive/Documents/meps2005/H181v2.dta"
. svyset varpsu
[pweight=PERWT15F], strata(varstr) vce(linearized) singleunit(missing)
pweight: PERWT15F
VCE: linearized
Single unit: missing
Strata 1: varstr
SU 1: varpsu
FPC 1: <zero>
. svy linearized, subpop(if age50p==1)
: total diabetes
(running total on estimation
sample)
Survey: Total estimation
Number of strata = 165
Number of obs = 35427
Number of PSUs =
369 Population size =
321423251
Subpop. no.
obs = 10544
Subpop.
size = 113873967
Design df =
204

 Linearized
 Total
Std. Err. [95% Conf. Interval]
+
diabetes 
2.03e+07 683199.4 1.89e+07 2.16e+07

. svy linearized, subpop(if
age50p==1) : total not_diabetes
(running total on estimation
sample)
Survey: Total estimation
Number of strata = 165
Number of obs = 35427
Number of PSUs =
369 Population size =
321423251
Subpop. no. obs =
10544
Subpop.
size = 113873967
Design df =
204


Linearized
 Total
Std. Err. [95% Conf. Interval]
+
not_diabetes  9.36e+07
2672184 8.83e+07 9.89e+07

.
No comments:
Post a Comment