Introductory Biostatistics

Note: An SAS program would include the instruction

MODEL CASES = AGEGROUP CITY/DIST = POISSON
LINK = LOG OFFSET = LN TYPE3;

Specific and Sequencial Adjustments In type 3 analysis, or any other multiple
regression analysis, we test the significance of the e¤ect of each factoraddedto
the model containingall other factors; that is, to investigate theadditionalcon-
tribution of the factor to the explanation of the dependent variable. Sometimes,
however, we may be interested in a hierarchical or sequential adjustment. For
example, we have Poisson-distributed responseYand three covariates,X 1 ,X 2 ,
andX 3 ; we want to investigate the e¤ect ofX 1 onY(unadjusted), the e¤ect
ofX 2 added to the model containingX 1 , and the e¤ect ofX 3 added to the
model containingX 1 andX 2. This can be achieved using PROC GENMOD by
requesting atype 1 analysisoption.

Example 10.13 Refer to the data set on emergency service of Example 10.5
(Table 10.2). Type 3 analysis yields the results shown in Table 10.8 and type 1
analysis yields Table 10.9. The results for physician hours are identical because
it is adjusted for all other three covariates in both types of analysis. However,
the results for other covariates are very di¤erent. The e¤ect of residency is
marginally significant in type 1 analysis (p¼ 0 :0741, unadjusted) and is not
significant in type 3 analysis after adjusting for the other three covariates. Sim-
ilarly, the results for revenue are also di¤erent; in type 1 analysis it is adjusted
only for residency and gender (p¼ 0 :3997; the ordering of variables is specified
in the INPUT statement of the computer program), whereas in type 3 analysis
it is adjusted for all three other covariatesðp¼ 0 : 5781 Þ.
Note: An SAS program would include the instruction

MODEL CASES = RESIDENCY GENDER REVENUE HOURS/
DIST = POISSON LINK = LOG OFFSET = LN TYPE1 TYPE3;

TABLE 10.7

Source df LRw^2 pValue

Age group 7 2561.57 <0.0001

City 1 258.72 <0.0001

TABLE 10.8

Source df LRw^2 pValue

Residency 1 1.09 0.2959

Gender 1 0.82 0.3641

Revenue 1 0.31 0.5781

Hours 1 4.18 0.0409

POISSON REGRESSION MODEL 367