the set of all possible posttreatment minus pretreat-
ment blood pressure measurements) with standard
deviation of 10.5 would have a mean of 12.8 or
larger is less than 0.15% (or 15 in 10 000).
Although this outcome is not impossible, it is
highly unlikely. Thus, it is more prudent to con-
clude that the drugisefficacious and that the
observed mean of 12.8 is due to a systematic effect
caused by the drug rather than to chance.
The above example encapsulates many of the
ideas and concepts behind the theory of statistical
inference. The standard deviation quantifies how
widely a measurement is expected to deviate from
a theoretical typical value of the variable being
measured. In our example, the variable being mea-
sured is the change between pretreatment and post-
treatment in a patient’s diastolic blood pressure.
So, if the drug is ineffective, any change is due
entirely to chance and therefore one would expect
the change to be zero. This expected typical value
is theoretical. In reality, blood pressure is affected
by a variety of factors independent of the treatment
and therefore actual measurements will not neces-
sarily be zero. The standard deviation enables us to
calculate the probability that the measurements
will fall close or far away from zero. For example,
the probability is 95% that a measurement will fall
within2 S.D. That is, assuming the drug is inef-
fective and the standard deviation is 10.5, 95% of
patients treated with the drug should have a change
in their pretreatment and posttreatment diastolic
blood pressure between21 andþ21. This is a
fairly large range and indeed all but two of the
measurements in our example are within this
range. This observation does not contradict our
previous conclusion that the drug is effective.
This is because our conclusion that the drug is
effective was based on the mean of 10 measure-
ments rather than on a single measurement. The
mean change is also associated with experimental
error. If we calculate the mean change for another
set of 10 measurements obtained from different
patients, it is unlikely that the result will be 12.8.
However, the variability associated with a mean is
smaller than that of a single measurement. The
standard deviation associated with the mean is
called thestandard error of the mean(SEM) and
is smaller than the S.D. by a factor equal to the
square root of the number of measurements used
to calculate the mean. In our example, SEM¼
ð 10 : 5 =p
10 Þ¼ð 10 : 5 = 3 : 16 Þ¼ 3 :32. Thus, in our
experiment, the probability is 95% that themean
changewill fall between 6 :64 andþ 6 :64. The
mean of 12.8 is well outside that range. In fact,
ð 12 : 8 =SEMÞ¼ 3 :85. The probability of observed
sample mean to be as a distance of 3.85 SEMs or
more from the actual population mean is approxi-
mately 0.15 %.
To summarize, statistical methods are not
intended to establish a cause and effect relationship
between treatment and the response of anyindivi-
dualsubject; rather, it is to establish a cause and
effect relationship in the aggregate response (e.g.
the mean) of apopulationof subjects. The key to
this is the fact that by considering aggregates, one
can control the variability of a measured quantity.
By increasing the sample size, one can reduce the
standard error of the mean to a level that would
make it possible to determine whether a signal is
likely or unlikely to be due to chance and thus
decide whether a causal relationship is likely or
unlikely to exist.25.6 The Controlled Clinical Trial:
basic design elementsRandomization
The CCT is the scientific tool for demonstrating
causality. Two essential elements characterize the
CCT: (a) it contains a control group and an experi-
mental group, and (b) with the exception of treat-
ment, all other conditions and procedures to which
the subjects are exposed during the trial are con-
stant. These two characteristics of the CCT enable
the researcher to establish a causal relationship
between treatment and the outcome of the trial.
The tool for standardizing the trial is the study
protocol, the document defining the subjects eligi-
ble for inclusion in the study, the study procedures
and schedules.
A key element is the method of allocating sub-
jects to the treatment groups. Subjects may possess
a variety of characteristics that could influence318 CH25 STATISTICAL PRINCIPLES AND APPLICATION IN BIOPHARMACEUTICAL RESEARCH