a. Starting with the data from Step 4, sum up over AREAKEY into strata defined by AGECAT and CT poverty.

b. Calculate (i) the total cases in each age stratum, over poverty; and (ii) the rate in the reference group of CT poverty.

c. Calculate stratum specific rates, rate ratios, and case fractions.

d. Calculate the age-stratum-specific population attributable fractions.

e. Calculate the grand total of all cases to use in calculating weights for all age strata.

f. Finally, calculate the aggregated population attributable fraction, using the age specific weights based on proportion of cases in each age stratum.

To calculate the age-standardized RIIst, we fit the following Poisson model for the expected cases:

Using the age-stratified numerators and denominators from Step 4, calculate the age-stratum specific population attributable risk fractions and aggregate population attributable risk fraction over all age strata following the method of Hanley8.

SOME NOTATION:

Assume that the dataset provided has stratum specific numbers of
cases (NUMER) and denominator (DENOM).

Subscript i as age, j as covariate (in this case, CINDPOV)

1. Sort data by AGECAT and CINDPOV.

2. Calculate the quantities
NUMERi+ = SUMj(NUMERij)
RATEiREF = rate in the reference group
and save them in a dataset.

3. Merge the quantities from (2) with the dataset and calculate

(a) rate RATEij=NUMERij/DENOMij
(b) case fractions CFij = NUMERij/NUMERi+
(c) rate ratio RRij = RATEij/RATEiREF

4. Calculate the (age)stratum-specific population attributable risk fraction

AFPi = CFi1 * (RRi1-1)/RRi1 + CFi2 * (RRi2-1)/RRi2 + ... CFij * (RRij-1)/RRij

5. Calculate the grand total of cases NUMER++ to use to calculate age-specific weights.

6. Determine age-stratum specific weights from the case distribution:

w_i = NUMERi+/NUMER++

and calculate the aggregated AFPagg = SUM(w_i * AFPi)

***********************************************************;

**********************************
STEP 8a SUM OVER AREAKEY INTO STRATA BY AGECAT AND CINDPOV
**********************************;

PROC SORT DATA=Step4 ;
BY AGECAT CINDPOV AREAKEY ;
RUN ;

DATA Step8a ;
SET Step4 (WHERE=(CINDPOV^=.)) ;
BY AGECAT CINDPOV ;

RETAIN NNN DDD ;

IF FIRST.CINDPOV THEN DO ;
NNN=0 ;
DDD=0 ;
END ;

NNN=NNN+NUMER ;
DDD=DDD+DENOM ;

IF LAST.CINDPOV THEN DO ;
OUTPUT ;
END ;

KEEP AGECAT CINDPOV NNN DDD ;

RUN ;

**********************************
STEP 8b: CALCULATE THE QUANTITIES

NUMERI+
RATEIREF

**********************************;

DATA Step8b ;
SET Step8a ;
BY AGECAT ;

RETAIN NIPLUS RATEIREF ;

IF FIRST.AGECAT THEN DO ;
NIPLUS=0 ;
END ;

NIPLUS=NIPLUS + NNN ;

IF CINDPOV=1 THEN DO ;
RATEIREF=NNN/DDD ;
END ;

IF LAST.AGECAT THEN DO ;
OUTPUT ;
END ;

KEEP AGECAT NIPLUS RATEIREF;

**********************************
STEP 8c: CALCULATE STRATUM SPECIFIC RATES, RATE RATIOS, AND CASE FRACTIONS
(a) rate RATEij=NUMERij/DENOMij
(b) case fractions CFij = NUMERij/NUMERi+
(c) rate ratio RRij = RATEij/RATEiREF

**********************************;

DATA Step8c ;
MERGE Step8a Step8b ;
BY AGECAT ;

RATEij=NNN/DDD ;

*******************************
NOTE: IF NIPLUS=0 THEN THERE ARE
NO CASES IN THIS AGE STRATUM AT ALL
SO SET CASE FRACTION TO ZERO
*******************************;
IF NIPLUS=0 THEN CFij=0 ;
ELSE CFij = NNN/NIPLUS ;

RRij = RATEIJ/RATEIREF ;
RUN ;

**********************************
STEP 8d: Calculate the (age)stratum-specific population attributable risk fraction
AFPi = CFi1 * (RRi1-1)/RRi1 + CFi2 * (RRi2-1)/RRi2 + ... CFij * (RRij-1)/RRij

**********************************;

DATA Step8d ;
SET Step8c ;
BY AGECAT ;

DUMMY=1 ;
RETAIN AFPI ;

IF FIRST.AGECAT THEN DO ;
AFPI=0 ;
END ;

*************************
NOTE: IF RRij=. because of an infinite risk ratio,
then (RR-1)/RR is basically equal to 1, so apply
the whole case fraction to the AFPI
*************************;
IF RRij in (.,0) THEN DO ;
AFPI=AFPI + CFij ;
END ;
ELSE DO ;
AFPI=AFPI + (CFij * (RRij-1)/RRij) ;
END ;

IF LAST.AGECAT THEN DO ;
OUTPUT ;
END ;

KEEP AGECAT NIPLUS AFPI DUMMY ;
RUN ;

**********************************
STEP 8e: CALCULATE THE GRAND TOTAL OF CASES TO USE IN CALCULATING WEIGHTS FOR EACH
AGE STRATUM

**********************************;

DATA Step8e ;
SET Step8d END=LASTOBS ;

RETAIN NPLUSPLUS ;
IF _N_=1 THEN DO ;
NPLUSPLUS=0 ;
END ;
NPLUSPLUS=NPLUSPLUS+NIPLUS ;
IF LASTOBS THEN OUTPUT ;

KEEP DUMMY NPLUSPLUS ;

**********************************
STEP 8f: CALCULATE THE AGGREGATED POPULATION ATTRIBUTABLE RISK
USING THE AGE SPECIFIC WEIGHTS.

Determine age-stratum specific weights from the case distribution:

w_i = NUMERi+/NUMER++

and alculate the aggregated AFPagg = SUM(w_i * AFPi)
**********************************;

DATA Step8f ;
MERGE Step8d END=LASTOBS Step8e ;
BY DUMMY ;

RETAIN AFPAGG ;

IF _N_=1 THEN DO ;
AFPAGG=0 ;
END ;

AFPAGG = AFPAGG + ((NIPLUS/NPLUSPLUS)*AFPi) ;

IF LASTOBS THEN DO ;

OUTPUT ;

END ;

RUN ;

proc print ;
var AFPAGG ;
run ;