This
post creates and discusses confidence intervals for number of diabetics age 50
and over in 2005 and in 2015. The confidence
intervals were constructed with STATA using survey weights. The interpretation of these confidence
intervals requires an ad hoc adjustment for population growth.
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 (13.8 * 1.27) 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.
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