130 CHAPTER 8 Contingency Tables
simply based on the treatment without regard to their status. Hospital
A follows the patients, and records the results after 2 years of follow -
up, hoping to see better survival under the new treatment. The results
are given in Table 8.2.
By examining the table, the results seem clear. There were 221
patients receiving the new treatment, and 221 the old. But the old treat-
ment appears better because 177 survived, compared with only 117
under the new treatment. The survival rate for patients under the old
treatment is 80.1%, and only 52.9% for the new treatment. This is puz-
zling to the investigators, because they thought that the new treatment
was better!
The investigators think about it, and now they say to themselves
“ maybe the greater survival in the old treatment group could be due to
an imbalance of terminally ill patients. ” Since terminally ill patients
are likely to die regardless of treatment, it is possible that the observed
difference is explained, because many more patients were terminally
ill in the new treatment group.
They decide to split the data into two groups and generate two 2 × 2
tables. Table 8.3 is the table for the terminal patients, and Table 8.4 for
the nonterminal patients.
Table 8.2
All Patients: Survival Versus Treatment
Treatment Survived 2 years Died within 2 years Total
New 117 104 221
Old 177 44 221
Total 294 148 442Table 8.3
Terminal Patients Only: Survival Versus
Treatment
Treatment Survived 2 years Died within 2 years Total
New 17 101 118
Old 2 36 38
Total 19 137 156