Introductory Biostatistics

L¼

YN

i¼ 1

expðbxiÞ

expðbxiÞþ

Pmi

j expðbxijÞ

from which we can obtain an estimate of the parameterb. The likelihood
function above has the same mathematical form as the overall partial likeli-
hood for the proportional hazards survival model with strata, one for each
matched set, and one event time for each (see Sections 11.3 and 11.4). This
enables us to adapt programs written for a proportional hazards model to
analyze epidemiologic matched studies as seen in subsequent examples. The
essential features of the adaptation are as follows:

1. Creating matched set numbers and using them as di¤erent levels of a
   stratification factor.


2. Assigning to each subject a number to be used in place of duration times.
   These numbers are chosen arbitrarily as long as the number assigned to
   a case is smaller than the number assigned to a control in the same
   matched set. This is possible because when there is only one event in each
   set, the numerical value for the time to event becomes irrelevant.

Measure of Association Similar to the case of the logistic model of Chapter 9,
expðbÞrepresents one of the following:

1. The odds ratio associated with an exposure ifXis binary (exposedX¼ 1
   versus unexposedX¼0); or

TABLE 11.14(Continued)

Matched
Set Case

Mother’s

Weight Hypertension Smoking

Uterine

Irritability

12 1 120 1 0 1
0 120 1 0 0
0 167 0 0 0
0 250 1 0 0
13 1 130 0 0 1
0 150 0 0 0
0 135 0 0 0
0 154 0 0 0
14 1 142 1 0 0
0 153 0 0 0
0 110 0 0 0
0 112 0 0 0
15 1 102 1 0 0
0 215 1 0 0
0 120 0 0 0
0 150 1 0 0

416 ANALYSIS OF SURVIVAL DATA