Tuesday, January 23, 2018

Evaluation of Confidence Intervals from Two Annual Surveys


 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 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.

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
--------------------------------------------------------------

.


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