The validity of the regression models was examined in several
ways (18). First, the influence of each separate observation (ie,
trial or trial arm) on the estimated regression coefficients was
assessed with the use of Cook’s distance to detect possible outliers.
Our initial analysis showed that there were 1 or 2 observations
with Cook’s distance > 0.3 that caused nonnormality of the
residuals. Excluding these observations did not change our conclusions
but resulted in normally distributed variables as indicated
by the Shapiro-Wilk test (18) and narrower confidence intervals,
a measure of the variability in dietary response between studies.
Therefore, we decided to exclude from the final analysis observations
with Cook’s distances > 0.3. Another source of errors in
regression statistics can be collinearity—ie, correlations between
supposedly independent variables (in this case, the various fatty
acids). Collinearity can be quantitated as tolerance. For all models
used, the tolerance for each fatty acid was ≥ 0.22, which indicated
that relation between the independent variables did not lead
to inappropriate estimates of the regression coefficients. Finally,
visual inspection of plots did not suggest a relation between residuals
and predicted values or between residuals and the independent
variables. This suggests that the differences between observed
and predicted values (ie, the residuals) did not depend on the
absolute serum lipid or lipoprotein of a trial or on the absolute
intake of a particular fatty acid or class of fatty acids. All statistical
analyses were carried out with PROC REG software, version 6
(19). Each study was represented by a dummy variable (the intrinsic
concentration). The use of a random-effects model, which is
frequently used in meta-analyses to correct for error within a
study, was not possible, because it requires standard errors of
treatment differences within studies, which generally were not
given. Therefore, we could not differentiate within-study and
between-study variability. However, the estimates of the regression
coefficients in the present analysis would have been comparable
with those of a random-effects analysis.