The Public Health Disparities
Geocoding Project Monograph

Geocoding and Monitoring US Socioeconomic Inequalities in Health:
An introduction to using area-based socioeconomic measures
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Case Example
U.S. Census Tract Poverty Data

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STEP BY STEP COMPARISON
A step by step comparison of each task of the Case Example, the relevant section of Analytic Methods, and sample SAS code
(click here for a pdf version of all 8 steps)
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Step 6:
Estimate the age-standardized incidence rate ratio comparing the age standardized rates in each poverty stratum to the rate in the least impoverished poverty stratum (0-4.9%).  
CASE EXAMPLE
ANALYTIC METHODS
SAS PROGRAMMING
click here to download SAS program
Calculate the 95% confidence limits on the incidence rate ratio.

3. Confidence intervals for IRst=0
When the observed rate is zero (i.e. there were zero cases), the gamma method is unable to produce confidence limits for the direct standardized rates. In this situation, we adopt the following convention for the confidence limit. The lower limit is simply set to zero. For the upper limit, we assume that the number of cases (i.e. the count) follows a Poisson distribution, and use the formula for the “exact” upper confidence limit of a Poisson random variable3:

DATA Step6 ;
SET Step5c ;

RETAIN IRREF VARPYREF ;

IF _N_=1 THEN DO ;
IRREF=IRW ;
VARPYREF=VARPYW ;
END ;

************************************
Incidence rate difference
************************************;
IRD=IRW - IRREF ;
VARIRD=VARPYW + VARPYREF ;

L_IRD=IRD - (1.96 * SQRT(VARIRD)) ;
U_IRD=IRD + (1.96 * SQRT(VARIRD)) ;

************************************
Incidence rate ratio
************************************;
IRR=IRW/IRREF ;
VARIRR=(VARPYW/(IRW**2)) + (VARPYREF/(IRREF**2)) ;

L_IRR=EXP(LOG(IRR) - (1.96 * SQRT(VARIRR))) ;
U_IRR=EXP(LOG(IRR) + (1.96 * SQRT(VARIRR))) ;

RUN ;


proc print ;
var Cindpov IRD L_IRD U_IRD IRR L_IRR U_IRR ;
RUN ;

where y is the count, i.e. zero. When =0.05 (i.e. for a 95% confidence limit) this simplifies to
3.689.
We can then divide this upper limit on the count by the population denominator to give the upper limit on the rate.

4. Age-standardized incidence rate ratio
Two commonly used measures for comparing incidence rates from two different groups are the incidence rate difference (IRD) and the incidence rate ratio (IRR). The incidence rate difference compares the rates on the absolute scale, and summarizes the excess rate comparing the larger to the smaller rate. The incidence rate ratio compares the rates on a relative scale, summarizing the size of one rate relative to the other rate.

To compare two age-standardized incidence rates on the absolute scale, the age-standardized incidence rate difference (IRDst) is the rate in one group minus the rate in the other, i.e. IRst1 - IRst0. The variance of this age-standardized incidence rate difference is simply the sum of the estimated variance of the two age-standardized rates4,

To compare age-standardized rates from two different groups or regions on the relative scale, the age-standardized incidence rate ratio (IRRst) is simply IRst1/IRst0. Confidence intervals can be calculated using the variance estimator4:
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This work was funded by the National Institutes of Health (1RO1HD36865-01) 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.