
The
Public Health Disparities Geocoding Project Monograph 

Geocoding
and Monitoring US Socioeconomic Inequalities in Health: An introduction to using areabased socioeconomic measures 
WHY? 
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MORE 
HOW
TO 
TRY
IT OUT! 
TOOLS 

STEP
BY STEP COMPARISON 

Step
5: For each category of CT poverty, calculate the agestandardized incidence rate, using the year 2000 standard million. 

SAS
PROGRAMMING click here to download SAS program 

In order to do this:
d. Calculate the agestandardized incidence rate standardized to the year 2000 standard million, and the corresponding “gamma” confidence intervals for the direct standardized rates. 
1.
Agestandardized incidence rates For our project, we used five broad age categories to age standardize, in order to obtain more stable rates in each age stratum, particularly for outcomes with sparse data. If cases 
************************************************************* CREATE DATASET WITH STANDARD MILLION FOR AGE STANDARDIZATION (IN FIVE CATEGORIES) 014 1524 2544 4564 65+ *************************************************************; data stdrd ; input agecat y1940 y1970 y1980 y1990 y2000 ; cards
; RUN ;
DATA Step5a ; retain NMR DNM ; NMR=NMR+NUMER ; if last.CINDPOV
then DO ; DROP AREAKEY NUMER
DENOM ;
w_i=y2000/1000000 ; IR_i=NMR/DNM ; varpy_i=NMR/DNM**2 ; RUN ;
data Step5c ;
retain IRW VARPY VARPYW SUMWI WMAX CRNUM CRDEN ; if first.CINDPOV
then do ; IRW=IRW + (W_I*IR_I)
; if last.CINDPOV
then do ; LGAM gives the 95%
gamma interval using the formula given by Fay and Feuer. ***NOTE: FOR LGAM2
AND UGAM2, HAVE NOW PROGRAMMED OPTIONS FOR IRW=0 VARPYW=0 References: Anderson RN, Rosenberg
HM. Age standardization of death rates: implementation of the year 2000
standard. LGAM=(VARPYW/(2*IRW)) * CINV(0.025,((2*(IRW**2))/VARPYW)) ; IF IRW=0 AND VARPYW=0
THEN DO ; UGAM gives the 95%
gamma interval using the formula given by Fay and Feuer. ********************************; UGAM=((VARPYW +
(WMAX**2))/2*(IRW+WMAX)) * CINV(0.975,((2*((IRW + WMAX)**2))/(VARPYW +
(WMAX**2)))) ; ********************************

where
wj is the weight associated with category j
in the reference (standardizing) population (e.g. the population size or
the proportion of the total population). The estimated variance of the standardized
rate is given by: 

(When
the wj s are proportions, then 

and ). 

2.
Confidence
intervals for directly standardized rates Traditional confidence limits for the direct standardized rates are based on the normal distribution and require large cell counts. In our analyses, we found that they can also occasionally result in “impossible” lower limits that are less than zero. Because of this, we adopted an alternate method for calculating the confidence limits based on the inverse gamma function.2 This method assumes that the direct standardized rate is a linear combination of independent Poisson random variables. Assuming that this linear combination is also follows a Poisson distribution, the agestandardized rate E(X) = x follows a gamma distribution as follows: 

where
x is the agestandardized rate (IRst as estimated
above) and v is its variance, as described above. Converting this to the
gamma distribution in its standard form, i.e. where b=1, this yields 

which greatly simplifies calculations. Then the lower confidence limit for  
is given by  
and the upper confidence limit for  
is given by  
where


is a continuity correction necessitated by using a continuous distribution to estimate confidence limits for a discrete random variable. Increasing the number of events by 1 in an age stratum i results in a  
increase
in the agestandardized rate. If kj is constant for
all age intervals, then kj =k. However,
since the values for wj
and popj typically vary across age strata, it is unclear
what value of k to
use. A very conservative upper limit can be obtained by using the maximum
value of kj = km .However, following the recommendation of the NCHS, we used a close approximation that alleviates the need to calculate k m : 

To transform these intervals to obtain the desired confidence limits for X, we use  
and . 


This
work was funded by the National Institutes of Health (1RO1HD3686501)
via the National Institute of Child Health & Human Development (NICHD)
and the Office of Behavioral & Social Science Research (OBSSR). 

Copyright
© 2004 by the President and Fellows of Harvard College  The Public
Health Disparities Geocoding Project. 