The results above are di¤erent for two di¤erent choices ofX, and this causes
an obvious problem of choosing an appropriate measurement scale. Of course,
we assume alinear model, and one choice ofXwould fit better than the other
(there are methods for checking this assumption).
Note: An SAS program would include these instructions:
PROC PHREG DATA = CANCER;
MODEL WEEKS*DEATH(0) = WBC;
where CANCER is the name assigned to the data set, WEEKS is the variable
name for duration time, DEATH is the variable name for survival status, and
‘‘0’’ is the coding for censoring.
11.3.3 Tests of Association
The null hypothesis to be considered is
H 0 :b¼ 0The reason for interest in testing whether or notb¼0 is thatb¼0 implies that
there is no relation between survival timeTand the covariateXunder investi-
gation. For the case of a categorical covariate, the test based on the score sta-
tistic of Cox’s regression model is identical to the log-rank test of Section
11.2.2.
11.4 MULTIPLE REGRESSION AND CORRELATION
The e¤ect of some factor on survival time may be influenced by the presence of
other factors through e¤ect modifications (i.e., interactions). Therefore, to pro-
vide a more comprehensive prediction of the future of patients with respect to
duration, course, and outcome of a disease, it is very desirable to consider a
large number of factors and sort out which are most closely related to diagno-
sis. In this section we discuss a multivariate method for risk determination. This
method, multiple regression analysis, involves a linear combination of the
explanatory or independent variables; the variables must be quantitative with
particular numerical values for each patient. Information concerning possible
factors is usually obtained as a subsidiary aspect from clinical trials that were
designed to compare treatments. A covariate or prognostic patient characteris-
tic may be dichotomous, polytomous, or continuous (categorical factors will be
represented by dummy variables). Examples of dichotomous covariates are
gender, and presence/absence of certain comorbidity. Polytomous covariates
include race and di¤erent grades of symptoms; these can be covered by the use
ofdummy variables. Continuous covariates include patient age and blood pres-
sure. In many cases, data transformations (e.g., taking the logarithm) may be
desirable.
MULTIPLE REGRESSION AND CORRELATION 395