This problem involves two covariates: age and location; both are categori-
cal. Using seven dummy variables to represent the eight age groups (with 85þ
being the baseline) and one for location (with Minneapolis–St. Paul as the
baseline, we obtain the results in Table 10.6. These results indicate a clear
upward trend of skin cancer incidence with age, and with Minneapolis–St. Paul
as the baseline, the relative risk associated with Dallas–Ft. Worth is
RR¼expð 0 : 8043 Þ
¼ 2 : 235an increase of more than twofold for this southern metropolitan area.
Note: An SAS program would include the instruction
INPUT AGEGROUP CITY $ POP CASES;
LN = LOG(POP);
MODEL CASES = AGEGROUP CITY/DIST = POISSON
LINK = LOG OFFSET = LN;
Contribution of a Group of Variables This testing procedure addresses the
more general problem of assessing the additional contribution of two or more
factors to the prediction of the response over and above that made by other
variables already in the regression model. In other words, the null hypothesis is
of the form
H 0 :b 1 ¼b 2 ¼¼bm¼ 0To test such a null hypothesis, one can perform a likelihood ratio chi-square
test, withmdf,
w^2 LR¼ 2 ½lnLðbb^;allX’sÞlnLðbb^;all otherX’s withX’s under
investigation deletedÞTABLE 10.6
Variable Coe‰cient Standard Error zStatistic pValue
Intercept 5.4797 0.1037 52.842 <0.0001
Age 15–24 6.1782 0.4577 13.498 <0.0001
Age 25–34 3.5480 0.1675 21.182 <0.0001
Age 35–44 2.3308 0.1275 18.281 <0.0001
Age 45–54 1.5830 0.1138 13.910 <0.0001
Age 55–64 1.0909 0.1109 9.837 <0.0001
Age 65–74 0.5328 0.1086 4.906 <0.0001
Age 75–84 0.1196 0.1109 1.078 0.2809
Dallas–Ft. Worth 0.8043 0.0522 15.408 <0.0001
POISSON REGRESSION MODEL 365