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

ANALYSIS OF GROUPED DATA 153
relative risk for the highest consumption level may vary with age, but the chi-square of 10.33 on five
degrees of freedom does not quite attain nominal significance at p = 0.05, and considerable doubt exists
as to the true significance level because of the small numbers in some tables. There is no evident trend
in the relative risk with increasing age.
Expected values and covariances for the exposure frequencies of the cases within each stratum, calculated
according to formulae (4.35)-(4.37), are presented in Table 4.6. For example, in the second
stratum we have
and
The cumulated vector of expected exposures e. and covariance matrix V. are shown at the bottom of the
table.
The adjusted global test (4.41) df the null hypothesis is calculated from the total observed values shown
in Table 4.4 and the totals shown at the bottom of Table 4.6 as
where the 3 x 3 matrix is the inverse of the cumulated covariance matrix. To find the conservative
approximation to this we compute from (4.42)
(29-81.59)'
In calculating the adjusted single degree of freedom test for trend (4.43), we first find the denominator
terms