1. Part 3: Weighting Estimation Samples Frank Porell
Data and Methodology
Part 3: Weighting Estimation Samples
Frank Porell

2. The Use of Weights in the Estimation of Medicare and BRFSS indicators
Medicare and BRFSS indicators are aggregate measures for geographic communities estimated from individual person-level data
Unbiased estimates of indicators require that the estimation sample of individuals be representative of the residents of those communities.
Relative inflation weights are applied to the cases of individual persons in community estimation samples so that the weighted age-sex population mix of each estimation sample matches the actual “target” age-sex distribution of older persons in each community.

3. The Use of Weights in the Estimation of Medicare and BRFSS indicators
Why might the age-sex distribution of community estimation samples differ from the actual age-sex distributions of populations in those communities?.
BRFSS samples are not selected to be representative of communities, there is no reason to expect that BRFSS respondents in a community will be representative of their community population.
Even though the CMS MBSF contains 100% of NH aged Medicare beneficiaries, the age-sex mix of community estimation samples may not match their actual Medicare age-sex distribution. This is because some beneficiaries are excluded from the estimation sample because of inadequate claims surveillance periods for the application of chronic disease algorithms. For example, there are no Medicare claims for Medicare Advantage enrollees.

4. The Use of Weights in the Estimation of Medicare and BRFSS indicators
Why do we weight individual cases based on age and sex?
BRFSS and Medicare indicators are measures of health status or health behaviors.
Age and sex are the two most important factors associated with differences in health and mortality rates among persons.
On average, older persons are not as healthy as their younger counterparts. Prevalence rates of most chronic diseases increase with age.
There are also gender differences in health and health behaviors. Women exhibit a greater propensity to make physician visits than men do. Men may be more likely to engage in poor health behaviors (e.g.,excessive drinking, smoking).

5. The Use of Weights in the Estimation of Medicare and BRFSS indicators
If an estimation sample is older, on average, than the community, then estimated prevalence rates for many chronic diseases in that community will too high relative to the actual prevalence rates.
If an estimation sample has disproportionately more men
than the community, estimates of smoking rates for the
community will be too high.
The purpose of inflation weights is to adjust estimates to reduce such potential biases due to differences between the age-sex population mix of estimation samples and communities.
We now present a simple hypothetical example to illustrate how inflation weights work.

6. The Use of Inflation Weights in the Estimation of Medicare and BRFSS indicators
Example: Classify persons in sample and community by sex and by two age groups (males: 60-74, 75+; females: 60-74, 75+). The proportions of the four groups for sample and the
community are shown below:
Sample
Community
60-74 yrs
75+ yrs
60-74yrs
Male
0.35
0.10
0.25
0.05
Female
0.15
0.40
Men (0.35>0.25), Men 75+ (0.10>0.05), and Women 75+ (0.40>0.35) are over-represented in estimation sample relative to community. Women are under-represented (0.15<0.35) in the estimation sample.

7. Sample prevalence rate
Unadjusted Prevalence Rate Estimates based on Unrepresentative Sample Data
Below left are hypothetical prevalence rates estimated for the four population subgroups with the community estimation sample. The right table shows the proportions of the four population subgroups in the estimation sample.
Sample prevalence rate
Sample proportions
60-74 yrs
75+yrs
60-74yrs
Male
25%
40%
0.35
0.10
Female
15%
20%
0.15
0.40
The unadjusted prevalence rate for the community is derived by multiplying the prevalence rate of each population subgroup by its proportion in the estimation sample. This yields an overall prevalence rate of 23%.

8. The Use of Weights in the Estimation of Medicare and BRFSS indicators
Unadjusted weighted indicator estimate= (25%*0.35) + (40%*0.10) + (15%*0.15) + (20%*0.40) =23%
The unadjusted prevalence rate estimate is upward biased because the age-sex distribution of the sample does not match that of the community. The three population subgroups with the highest prevalence rates are over-represented in the sample.

9. The Use of Weights in the Estimation of Medicare and BRFSS indicators
We can’t add or subtract individuals in the 4 subgroups of the estimation sample. We can apply inflation weights that give less weight to respondents in population categories that are over-represented and more weight to respondents in under-represented categories.
Sample
Community
60-74 yrs
75+yrs
60-74yrs
Male
0.35
0.10
0.25
0.50
Female
0.15
0.40
Taking the ratio of the community proportions to their respective proportion in the estimation sample yields the inflation weights shown at right
0.71
0.50
2.33
0.88

10. The Use of Weights in the Estimation of Medicare and BRFSS indicators
We can use the inflation weights to adjust the overall prevalence rate to reflect the actual age-sex mix of the community. The sample proportions are inflated or deflated so they match the community proportions. The lower adjusted estimate of 20.5% reflects the community population mix.
Adjusted weighted indicator estimate = (25%*0.71*0.35) + (40%*0.50*0.10) + (15%*2.33*0.15) + (20%*0.88*0.40) =20.5%

11. The End