probability that the statistical test would be signifi-
cant if the effect of the drug is to reduce the
diastolic blood pressure by 10 mmHg on average.
It is desirable that a statistical test should have as
smallaandb(i.e. low type I error and high power)
as possible with regard to alternatives of interest.
The perfect test would havea¼b¼0. However,
as we will see, this is not possible in practice due to
the fact that all experimental measurements
involve errors. If, in our example, the clinician
estimates that the drug should lower diastolic
blood pressure by an average of about 10 mmHg,
the statistician would wantato be small, say
0.05, and 1bto be large, say0.95, for the
alternativeE¼10. Can the statistician design a
study such that the test would have any desirablea
andb? Generally, yes, by selecting an appropriate
sample size; that is, by including a sufficient num-
ber of subjects in the study. Once the sample size is
fixed, the relationship betweenaandbis deter-
mined. A reduction inamust be compensated by
an increase inb, andvice versa. For a given study
design, the only way to decreaseaandbsimulta-
neously is by increasing the sample size. We will
discuss this topic in greater detail in Section 25.10.
25.4 Causality
The ultimate goal of clinical research is to establish
causality – to determine efficacy outcomes that are
due to the drug and to measure their magnitude and
to identify adverse effects caused by the drug.
How does one know whether an effect A (e.g.
giving a particular drug at a particular dose) causes
an event B (e.g. diastolic blood pressure is
reduced)? Two conditions must be satisfied. First,
A must precede B. Second, whenever A occurs, B
must occur too. These, of course, are not sufficient,
as both A and B could be caused by an effect C. In
addition, therefore, a theory is required that links A
to B. This requirement is the Achilles Heel of
‘causality’, as all theories are necessarily tentative.
In an experimental science such as pharmaceutical
research, the second condition can be established
by conducting an experiment both when effect A is
absent and when effect A is present, whereas all
other conditions remain unchanged. If B requires
the presence of A, then one can conclude that A
causes B. However, if B is present regardless of A,
then no causality is proven.
In studying drug effects in humans, the con-
trolled clinical trial is the preferred method to
establish causality. In its simplest form, a con-
trolled clinical trial is an experiment in human
subjects in which some subjects are treated with
an investigational drug and some are not, whereas
all other conditions remain the same for the two
treatment groups. In this way, differences in clin-
ical outcomes can be attributed to the investiga-
tional drug [Controlled Clinical Trials (CCT) will
be discussed in greater detail in Section 25.6
below].25.5 Variability – the source of
uncertaintyVirtually no drug has an identical response in all
patients. For example, an effective antibiotic will
almost certainly be ineffective in some patients,
possibly because such patients are infected with a
resistant strain or have a deficient immune
response. Variability in response introduces uncer-
tainty in establishing cause and effect. The fact that
administering a drug to a given subject has not
resulted with the desired therapeutic effect does
not necessarily imply that the drug in ineffective.
Causality in the strict sense discussed in the pre-
vious section can no longer be established when
outcome of an experiment is subject to variability.
However, one can still talk about causality in a
probabilisticsense by modifying the requirement
that ‘whenever A is present Bmustbe present too’
necessary for the establishment of causality, to ‘the
probabilitythat B will occur isgreaterin the pre-
sence of A than when A is not present’.
Another issue is that when the measurement of
efficacy is variable, it is impossible to determine
what part of the measured outcome is due to the
effect of the drug and what part is due to variability
unrelated to the drug effect. The size of a drug
effect is called the ‘signal’, whereas the variability
associated with it is referred to as the ‘noise’.316 CH25 STATISTICAL PRINCIPLES AND APPLICATION IN BIOPHARMACEUTICAL RESEARCH