a. Estimate the approximate cumulative distribution function for CT poverty, based on the population denominator for each poverty stratum (summed up over age).

b. Calculate the expected cases in each CT poverty stratum, based on the age-standardized incidence rate.

c. Fit a Poisson log linear model, modeling the expected number of cases as a function of the approximate cumulative distribution of CT poverty, using the population denominator as an offset.

d. Exponentiate the beta term from this model to get the relative index of inequality.

5. Relative Index of Inequality (RII)
Comparisons of socioeconomic gradients based on categorical ABSM may be complicated by differences in the population distributions of area-based socioeconomic measures. For example, it may be expected that the classifications producing smaller groups at the margins would lead to larger incidence rate ratios, comparing the most deprived to the most affluent, because finer discrimination of extremes of socioeconomic position is achieved. The relative index of inequality (RII) has been proposed as a measure which explicitly addresses this problem.5-7 Assuming ordinality of the ABSM categories, the RII is calculated by regressing the incidence rate in each ABSM category on the total proportion of the population that is more deprived in the socioeconomic hierarchy.

In practice, this latter quantity is represented by the cumulative distribution function (cdf). We approximate the cdf for the jth level of a given ABSM by summing the proportion of the population represented by the categories ABSM1, …, ABSMj-1, and adding one-half the proportion of the population represented by the category ABSMj.

In order to compare RII meaningfully across groups with differing age composition, we developed an age-standardized RII, standardized to the year 2000 standard million, as follows. Let observedij be the observed number of cases in the ith age group and the jth category of ABSM, and popij be the population at risk in the corresponding category. First, we calculate the age-standardized rate IRst in each stratum j defined by ABSM, as described above. For each stratum j, we estimate the expected number of cases in stratum j, expectedj, by multiplying the age-standardized rate IRst by the population denominator,

if _N_=1 then do ;
dxden=0 ;
end ;

dxnum=dxden + (CRDEN/2) ;
dxden=dxden+CRDEN ;

DUMMY=1 ;
output Step7a ;
IF LASTOBS then output Step7b ;

data Step7c ;
merge Step7a (drop=dxden) Step7b (keep=DUMMY dxden) ;
BY DUMMY ;

dxpct=dxnum/dxden ;
wght=CRDEN/dxden ;

CRCNT=CRDEN*IRW ;
LOGDEN=LOG(CRDEN) ;

ods output ParameterEstimates=param ;
PROC GENMOD DATA=Step7c ;
MODEL CRCNT = DXPCT /OFFSET=LOGDEN LINK=LOG DIST=POI ;
RUN ;

data Step7d;
set param (where=(Parameter not in ("Intercept")));

if stderr ne 0 then do;
riiest=exp(estimate);
riilo95=exp(estimate-1.96*stderr);
riihi95=exp(estimate+1.96*stderr);
end;

proc print ;
where Parameter="dxpct" ;
var Parameter riiest riilo95 riihi95 ;
run ;