selected. Each physician was asked a question concerning the frequency
with which an unnecessary transfusion was give because another physi-
cian suggested it. The same question was asked of a sample of 71 resi-
dents. The data are shown in Table E1.45.TABLE E1.45
Frequency of Unnecessary Transfusion
Very
Type of Frequently Frequently Occasionally Rarely
Physician (1/week) (1/two weeks) (1/month) (1/two months) Never
Attending 1 1 3 31 13
Resident 2 13 28 23 5(a) Choose ‘‘never’’ as the baseline and calculate the odds ratio asso-
ciated with each other frequency and ‘‘residency.’’
(b)Calculate the generalized odds and give your interpretation. Does
this result agree with those in part (a)?1.46 When a patient is diagnosed as having cancer of the prostate, an impor-
tant question in deciding on a treatment strategy is whether or not the
cancer has spread to the neighboring lymph nodes. The question is so
critical in prognosis and treatment that it is customary to operate on the
patient (i.e., perform a laparotomy) for the sole purpose of examining
the nodes and removing tissue samples to examine under the microscope
for evidence of cancer. However, certain variables that can be measured
without surgery are predictive of the nodal involvement; and the purpose
of the study presented here was to examine the data for 53 prostate can-
cer patients receiving surgery to determine which of five preoperative
variables are predictive of nodal involvement. Table E1.46 presents the
complete data set. For each of the 53 patients, there are two continuous
independent variables, age at diagnosis and level of serum acid phos-
phatase (100; called ‘‘acid’’), and three binary variables: x-ray reading,
pathology reading (grade) of a biopsy of the tumor obtained by needle
before surgery, and a rough measure of the size and location of the
tumor (stage) obtained by palpation with the fingers via the rectum. For
these three binary independent variables, a value of 1 signifies a positive
or more serious state and a 0 denotes a negative or less serious finding.
In addition, the sixth column presents the finding at surgery—the pri-
mary outcome of interest, which is binary, a value of 1 denoting nodal
involvement, and a value of 0 denoting no nodal involvement found at
surgery. In this exercise we investigate the e¤ects of the three binary
preoperative variables (x-ray, grade, and stage); the e¤ects of the two
continuous factors (age and acid phosphatase) will be studied in an
exercise in Chapter 2.
EXERCISES 55