Statistical Methods in Medical Research 4ed

206 Regression and correlation
discussed in §12.7. In that case, increasing the initial sample size may have a
smaller effect on the phenomenon of regression to the mean than would otherwise
be so.
Regression to the mean is not a problem when comparing treatments in a
randomized controlled trial since both treatment groups will be influenced
equally so that the difference will be unbiased, even though the mean improvements
of both treatments will include a regression to the mean effect. Another
approach is that after selecting patients by a screening test, a second pretreatment
value is obtained on admission into the study. This second value, and not
the screening value, is used as the initial value in the analysis (McDonald et al.,
1983). The extent to which this approach will be successful in eliminating
regression to the mean is dependent on the extent to which the second baseline
value is independent of the screening value (Senn, 1988).
Newell and Simpson (1990) and Beach and Baron (1998) summarize the
phenomenon of regression to the mean and provide additional references.
Example 7.2
Irwig et al. (1991) examined the effects of regression to the mean on the screening of
individuals to detect those with high levels of blood cholesterol. They considered three
hypothetical populations with the following mean values (all values quoted here and
below being in units of mmol/l): A, 5 2; B, 5 8; C, 6 4. These values are based on survey
data, as being characteristic of men under 35 years and women under 45 (A); men aged
35±74 and women aged 45±64 (B); and women aged 65 and older (C). The calculations are
based on the model described above, but with the assumption (again confirmed by
observations) that the log of the cholesterol level, rather than the level itself, is normally
distributed between and within subjects, with constant within-subject variance.
Standard guidelines would classify levels less than 5 2 as `desirable', levels between 5 2
and 6 1 as `borderline high', and those above 6 1 as `high'. Irwig et al. illustrate the effects
of regression to the mean in various ways. For instance, an individual in group B with a
single screening measurement of 9 0 would have an estimated true mean of 8 4 with 80%
confidence limits of 7 7 and 9 2. If the value of 9 0 was based on three measurements, the
estimated true level would be 8 8 (limits 8 3, 9 3)Ða less pronounced regression effect than
for single measurements.
An important concern is that individuals might be classified on the wrong side of a
threshold. For instance, an individual in group A with a screening measurement of
4 9 would have a probability of 0 26 of having a true mean above the threshold of 5 2.
For a screening measurement of 5 8 there is a probability of 0 10 that the true level is
below 5 2.
Other calculations are concerned with the assessment of an intervention intended to
lower blood cholesterol. Suppose that an intervention produces a mean reduction of 13%
(this figure being based on the results of a particular study). For an individual in group B
with three measurements before and one after the intervention, and a pre-intervention
mean of 7 8, an observed decrease of 25% corresponds to an estimated true decrease of
19%, while an observed decrease of 0% (no apparent change) corresponds to an estimated