## Friday, May 24, 2019

### Confidence Interval for Number of 50+ Diabetics

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 non-diabetics in the 50-and-over population for 2005 and 2015.

What would have been the estimated number of 50-and-over 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 Non-Diabetics 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 50-and-over population.

Analysis:  The 50-and-over 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)= a2 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 50-and-over diabetics based on the 2005 confidence interval adjusted for population growth is 17.5 (13.8 * 1.27) million.

The actual number of 50-and-over 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
--------------------------------------------------------------