ered within five days of the case in the same hospital. The risk factors of inter-
est are the mother’s bleeding in this pregnancyðN¼no;Y¼yesÞand any
previous pregnancy loss by the mother ðN¼no;Y¼yesÞ. Response data
(bleeding, previous loss) are given in Table 11.13.
Example 11.11 For each of 15 low-birth-weight babies (the cases), we have
three matched controls (the number of controls per case need not be the same).
Four risk factors are under investigation: weight (in pounds) of the mother at
the last menstrual period, hypertension, smoking, and uterine irritability (Table
11.14); for the last three factors, a value of 1 indicates a yes and a value of 0
indicates a no. The mother’s age was used as the matching variable.
11.7.1 Simple Regression Analysis
In this section we discuss the basic ideas of simple regression analysis when
only one predictor or independent variable is available for predicting the binary
response of interest. We illustrate these for the more simple designs, in which
each matched set has one case and caseiis matched tomicontrols; the number
of controlsmivaries from case to case.
Likelihood Function In our framework, letxibe the covariate value for casei
andxijbe the covariate value the thejth control matched to casei. Then for
theith matched set, it was proven that the conditional probability of the out-
come observed (that the subject with covariate valuexibe the case) given that
we have one case per matched set is
expðbxiÞ
expðbxiÞþPmi
j expðbxijÞIf the sample consists ofNmatched sets, the conditional likelihood function is
the product of the terms above over theNmatched sets:
TABLE 11.13
Control Subject NumberSet Case 1 2 3 4
1 ðN;YÞðN;YÞðN;NÞðN;NÞðN;NÞ
2 ðN;YÞðN;YÞðN;NÞðN;NÞðN;NÞ
3 ðY;NÞðN;YÞðN;NÞðN;NÞðN;NÞ
4 ðY;YÞðN;NÞðN;NÞðN;NÞðN;NÞ
5 ðN;NÞðY;YÞðN;NÞðN;NÞðN;NÞ
6 ðY;YÞðN;NÞðN;NÞðN;NÞðN;NÞ
7 ðN;YÞðN;YÞðN;NÞðN;NÞðN;NÞ
8 ðN;YÞðN;NÞðN;NÞðN;NÞðN;NÞ
414 ANALYSIS OF SURVIVAL DATA