model and the more specific the model assump-
tions, the more the final results of the analysis will
depend on it. Statisticians are advised to always
start the statistical analysis by performing certain
diagnostic procedures on the data to check to what
extent the model assumptions are supported by the
data. This process involves a certain level of sub-
jective judgment, and different statisticians may
reach different conclusions looking at the same
data. Statisticians have at their disposal certain
tools by which they can manipulate the data so as
to conform better to the model assumption. For
example, the distributions of measured pharmaco-
kinetic (PK) parameters is typically skewed. The
assumption of Normality of the distribution
implies that the distribution is symmetric. It turns
out that if one calculates the PK parameters using
the natural logarithms of the blood concentrations
rather than the raw measured concentrations, the
distributions of the estimated parameters are less
skewed. The choice of model is part of the study
design. It is, therefore, done before any data are
available. It is not uncommon that at the analysis
stage, it becomes evident that the model assump-
tions are grossly violated. It may become necessary
to use different methods that are not as dependent
on the model assumptions to analyze the data. This
should be done with great care so that spurious
patterns in the data would not lead the researcher
to reach wrong conclusions. Additionally, chan-
ging the analysis methods after an inspection of
the data could result in an introduction of bias if the
statistician is aware of the treatment assignments.
For this reason, it is prudent to perform these
diagnostic examinations of the data without reveal-
ing the treatment assignments. In blinded studies,
this means that these procedures are executed prior
to the breaking of the blind. The statistical guide-
lines issued by the International Conference on
Harmonization (ICH), which were adopted by
the Food and Drug Administration (FDA) and the
European regulatory authorities, address this issue
as follows:
The [statistical]plan should bereviewed and possibly
updated as a result of the blind review of the data...
and should be finalized before breaking the blind.
Formal records should be kept of when the statisticalanalysis plan was finalized as well as when the blind
was subsequently broken. If the blind review sug-
gests changes to the principal features stated in the
protocol, these should be documented in a protocol
amendment. (ICH, E9, 4.1)It is important to remember that the question is not
whether the statistical model is true or false. The
statistical model is a theoretical construct, and thus
it isalways false. The question is how well it
approximates the situation under study. Or, in the
words of a famous statistician, ‘All models are
wrong, but some are useful’.25.9 Statistical inference
Hypothesis testing revisited:
thep-value; powerIn Section 25.3 above, we discussed the concept of
the statistical test and defined some basic terms. In
this section, we take a closer look at this idea and
see, through an example, how this is actually done.
Let us look at the data presented in Table 25.4
earlier in the chapter. The graduate student who
generated the data did not, in fact, study 20 ran-
domly selected students. The purpose of her study
was to demonstrate that engaging in aerobic work-
out on a regular basis has a beneficial effect on the
cardiovascular system, including the slowing down
the heart rate. To do this, the researcher set out to
test thenull hypothesis(H 0 )thatthemean heart rate
of exercising students,mA, is the same as the mean
of the non-exercising students,mB. The alternative
hypothesis (H 1 ) is thatmA<mB. In order to test H 0
against H 1 , one would need to identify a variable
(or astatistic), the distribution of which is sensitive
to the difference between the heart rates of the
different groups. Such a statistic is the signal-to-
noise ratio,T¼XBXA
S:EðXBXAÞð 1 Þwhere the signal is the difference between the
sample mean of Group B,XB, and the sample
mean of Group A,XA, and the noise is the standard
error of the differenceXBXA.25.9 STATISTICAL INFERENCE 327