3. general considerations for the analysis of case-control ... - IARC

ANALYSIS OF MATCHED DATA
Case
Exposed
Unexposed
Number of controls exposed
0 1 2 3 4 Total
156
7 18' 17 16
7
The total number of exposed cases in the paired sets is 3 + 17 + 16 + 15 = 51. According to (5.17), we
find the MLE by equating this figure to its expected value,
The solution I) = 7.95, obtained by numerical means, is almost identical to that calculated from the
unmatched data (Table 5.1). It may be compared with the M-H estimate, determined from (5.18) as
The chi-square statistic (5.19) for testing H, is
which is of course highly significant (p < 0.000001).
To obtain approximate 95% confidence limits for y2 we solve the equations (5.20)
and
this requiring numerical methods, and obtain yl, = 3.3 and yl, = 19.9. It is considerably easier to calculate
the variance of log I) using (5.20),
where we have inserted the MLE I$ = 7.95. Consequently approximate 95% limits on log yp are
log(7.95) + 1 .96m, or 1.249-2.899, corresponding to limits on yl of 3.5-18.1. Finally, the test-based
procedure centred about the MLE gives
ylL,ylU = 7.95-
+ 1 .96lW6)