This example computes the excess event risk fraction that is attributable to a specific chemical exposure for workers in a factory.
Suppose that the Factory
data set contains the stratum-specific event information for exposure to a specific chemical agent. The variable Age
is the grouping variable that forms the strata. The variables Event_E
and Count_E
indicate the number of events and number of workers for workers with the specific chemical exposure, respectively. The variables
Event_NE
and Count_NE
indicate the number of events and number of workers for workers without the specific chemical exposure, respectively.
data Factory; input Age $ Event_E Count_E Event_NE Count_NE; datalines; 20-29 31 352 143 2626 30-39 57 486 392 4124 40-49 62 538 459 4662 50-59 50 455 337 3622 60-69 38 322 199 2155 70+ 9 68 35 414 ;
The following statements invoke the STDRATE procedure and compute the attributable risk and population attributable risk for the chemical exposure:
ods graphics on; proc stdrate data=Factory refdata=Factory method=indirect(af) stat=risk plots(stratum=horizontal) ; population event=Event_E total=Count_E; reference event=Event_NE total=Count_NE; strata Age / stats; run; ods graphics off;
The "Standardization Information" table in Output 95.3.1 displays the standardization information.
The STATS option in the STRATA statement requests that the "Indirectly Standardized Strata Statistics" table in Output 95.3.2 display the strata information and the expected number of events at each stratum. The Expected Events column shows the expected numbers of events when the stratum-specific risks in the reference data set are applied to the corresponding numbers of workers in the study data set.
Output 95.3.2: Strata Information (Indirect Standardization)
Indirectly Standardized Strata Statistics | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Stratum Index |
Age | Study Population | Reference Population | Expected Events |
||||||||
Observed Events |
Number of Observations | Crude Risk | Standard Error |
Number of Observations | Crude Risk |
|||||||
Value | Proportion | 95% Normal Confidence Limits |
Value | Proportion | ||||||||
1 | 20-29 | 31 | 352 | 0.1585 | 0.088068 | 0.015105 | 0.058463 | 0.117673 | 2626 | 0.1492 | 0.05446 | 19.1683 |
2 | 30-39 | 57 | 486 | 0.2188 | 0.117284 | 0.014595 | 0.088678 | 0.145890 | 4124 | 0.2343 | 0.09505 | 46.1959 |
3 | 40-49 | 62 | 538 | 0.2422 | 0.115242 | 0.013767 | 0.088260 | 0.142224 | 4662 | 0.2648 | 0.09846 | 52.9691 |
4 | 50-59 | 50 | 455 | 0.2049 | 0.109890 | 0.014662 | 0.081153 | 0.138627 | 3622 | 0.2058 | 0.09304 | 42.3343 |
5 | 60-69 | 38 | 322 | 0.1450 | 0.118012 | 0.017979 | 0.082774 | 0.153251 | 2155 | 0.1224 | 0.09234 | 29.7346 |
6 | 70+ | 9 | 68 | 0.0306 | 0.132353 | 0.041095 | 0.051809 | 0.212897 | 414 | 0.0235 | 0.08454 | 5.7488 |
With ODS Graphics enabled and the specified STAT=RISK option, the default PLOTS=RISK option displays the stratum-specific risk estimates in the study and reference populations, as shown in Output 95.3.3. The STRATUM=HORIZONTAL global option in the PLOTS option displays the strata information on the horizontal axis. The plot displays the stratum-specific risk estimates in the "Indirect Standardized Strata Statistics" table in Output 95.3.2. In addition, confidence limits for the risk estimates in the study population and the overall crude risks for the two populations are also displayed
The METHOD=INDIRECT option requests that the "Standardized Morbidity/Mortality Ratio" table in Output 95.3.4 display the SMR, its confidence limits, and the test for the null hypothesis .
The "Standardized Morbidity/Mortality Ratio" table shows that SMR=1.259, the confidence limits do not contain the null value SMR=1, and the null hypothesis of SMR=1 is rejected at level from the normal test.
The "Indirectly Standardized Risk Estimates" table in Output 95.3.5 displays the standardized risks and related statistics.
The AF suboption in the METHOD=INDIRECT option requests that the "Attributable Fraction Estimates" table display the attributable risk and population attributable risk, as shown in Output 95.3.6
The attributable risk fraction 0.206 indicates that of all events in the chemical exposure group are attributed to the chemical exposure, and the population attributable risk fraction 0.028 indicates that about of all events in the total population are attributed to the chemical exposure.
The Attributable fraction can also be computed by using Mantel-Haenszel method.
Suppose that the Factory1
data set contains the stratum-specific event information for exposure to a specific chemical agent. The variable Age
is the grouping variable that forms the strata, and the variable Exposure
identifies workers with chemical exposure. The variables Event
and Count
indicate the number of events and number of workers, respectively.
data Factory1; input Exposure $ Age $ Event Count; datalines; Yes 20-29 31 352 Yes 30-39 57 486 Yes 40-49 62 538 Yes 50-59 50 455 Yes 60-69 38 322 Yes 70+ 9 68 No 20-29 143 2626 No 30-39 392 4124 No 40-49 459 4662 No 50-59 337 3622 No 60-69 199 2155 No 70+ 35 414 ;
The following statements invoke the STDRATE procedure and compute the attributable risk and population attributable risk for the chemical exposure:
proc stdrate data=Factory1 method=mh(af) stat=risk effect ; population group(order=data exposed='Yes')=Exposure event=Event total=Count; strata Age; run;
The GROUP=EXPOSURE option specifies the variable Exposure
, whose values identify the various populations. The ORDER= suboption specifies the order in which the values of Exposure
are to be displayed, and the EXPOSED= option identifies the exposed group in the derivation of the attributable fraction.
The "Standardization Information" table in Output 95.3.7 displays the standardization information.
The "Mantel-Haenszel Standardized Risk Estimates" table in Output 95.3.8 displays the Mantel-Haenszel standardized risks and related statistics.
Output 95.3.8: Standardized Risk Estimates (Mantel-Haenszel Estimation)
Mantel-Haenszel Standardized Risk Estimates | |||||||||
---|---|---|---|---|---|---|---|---|---|
Exposure | Study Population | Mantel-Haenszel | Standardized Risk | ||||||
Observed Events |
Number of Observations |
Crude Risk |
Expected Events |
Weight | Estimate | Standard Error |
95% Normal Confidence Limits |
||
Yes | 247 | 2221 | 0.1112 | 219.122 | 1970.26 | 0.1112 | 0.00667 | 0.0981 | 0.1243 |
No | 1565 | 17603 | 0.0889 | 174.134 | 1970.26 | 0.0884 | 0.00214 | 0.0842 | 0.0926 |
The EFFECT option requests that the "Risk Effect Estimates" table display the risk ratio statistic for the two directly standardized risks, as shown in Output 95.3.9.
The AF suboption in the METHOD=MH option requests that the "Attributable Fraction Estimates" table display the attributable risk and population attributable risk, as shown in Output 95.3.10
Similar to the results of using the SMR estimates, the attributable risk fraction (0.205) indicates that of all events in the chemical exposure group are attributed to the chemical exposure, and the population attributable risk fraction (0.028) indicates that about of all events in the total population are attributed to the chemical exposure.