STATISTICAL METHODS
The association between individual dietary
factors and CRC rates was examined first by
calculating simple (Pearson) correlation coeYcients.
CRC rates were used, rather than data
for cancers of the colon and rectum separately,
because fuller data were available for the
former. CRC rates were taken as the combined
rates for men and women as these were highly correlated with one another (r= 0.95) and also
because food supply data were available per
capita rather than separately for men and
women. Because the various dietary factors
were correlated with each other, the partial
correlation coeYcients (PCC) were also calculated.
These coeYcients measure the correlation
for each dietary factor after controlling for
the others. This procedure is similar to that
used by Armstrong and Doll3 in their study of
environmental factors, mostly dietary, and
cancer.
We then examined the association between
the dietary factors and CRC using stepwise
regression. This procedure starts by selecting
the model in which each individual factor fits
the data best. A second factor is selected for
inclusion in the model, in combination with the
first, as the one in which the model of the two
terms again produces the best fit. This
procedure is continued until the addition of no
other factor produces a significant (p<0.05)
improvement in fit.
Stepwise regression can be problematic as
the selection of variables can depend on the
criteria used for inclusion. The selection of
variables was therefore also carried out using a
backward elimination procedure. The model
was prepared containing terms for all of the
dietary factors. Each factor, in turn, was eliminated
from the model and the goodness of fit of
the resulting model examined. After each step the factor that produced the least change to the
goodness of fit of the model was eliminated. In
similar fashion, the factors were eliminated in
turn until none of the remaining factors could
be eliminated from the model without a significant
reduction in the goodness of fit of the
model.
We analysed the data using the stepwise procedures
outlined above for all the dietary
factors excluding olive oil to facilitate comparison
with other studies, few of which included
olive oil. We then added olive oil to the list of
dietary factors and repeated the analysis. The
fits of the various models were assessed by
determining the percentage of variation explained
by each model. To enable the fits of
these models to be compared, we adjusted
these percentages to allow for the diVerent
number of factors included in the models.1
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