25.2 The statistical method:
making decisions under
conditions of uncertaintyThe scientific method runs into difficulties when
applied to the study of random phenomena. A
random phenomenonis one where the outcome
cannot be predicted with certainty from the experi-
mental conditions.One cannotguarantee the repeat
of a coin toss, no matter how hard one tries to keep
the conditions constant. Neither can one expect a
drug to produce an identical effect in the same
patient under identical conditions on separate
occasions. Such phenomena can be described
probabilistically. That is, one can assign numerical
values describing the likelihood,or probability,of
the possible outcomes. Because of the uncertainty,
an isolated failure of a drug to produce an expected
therapeutic effect does not prove that the drug is
non-efficacious. Similarly, an isolated successful
drug treatment outcome does not prove that the
drug is efficacious.
Unfortunately, it is impossible to design an
experiment that will totally disprove a theory
based on random phenomena. Various outcomes
may occur, some of which may be unlikely but not
impossible. Thus Popper’s falsifiability condition
does notapply. Thestatistical methodadvocated by
Fisher (1956) attempts to overcome this problem
by substituting ‘unlikely’ for ‘impossible’ but
otherwise follows the principles of the scientific
method. With this substitution, Fisher and others
proposed conceptual structures for testing theories
and scientific hypotheses under conditions of
uncertainty that are analogous to the scientific
method. However, these approaches, although
being very useful in practice, have raised a host
of conceptual issues that are the subject of ongoing
debates.
Let us illustrate the statistical method with an
example.
A pharmaceutical company has developed an
antihypertensive drug that is theorized to lower
diastolic blood pressure when given to subjects
with moderate to severe hypertension. If the dia-
stolic blood pressure were constant under given
conditions, then failure to lower diastolic pressure
by any amount in any human subject treated with
this drug under a constant set of conditions would
disprove the theory. In reality, the subject’s blood
pressure is a random phenomenon. It varies with or
without treatment. Thus, administering the drug to
one subject and measuring the resulting change in
blood pressure cannot be used to prove or disprove
the hypothesis that the drug has no efficacy. How
can one tell whether the difference in blood pres-
sure before and after treatment is due to the effect
of the drug or due to the natural randomness of
blood pressure? To answer this question, one must
(a) have knowledge of degree of the natural varia-
bility of diastolic blood pressure and (b) determine
whether the change in blood pressure is likely to
result from natural variability. Measuring variabil-
ity requires the study of more than one subject.
Thus, a statistical experiment always consists of
the study of groups of subjects rather than indivi-
dual ones.
A typical experiment might look like this: Sub-
jects are selected from a target population to parti-
cipate in the study. They are assigned to one of two
groups, A and B. Group A receives no treatment or
a placebo. Group B receives the test drug. A quan-
titative variable that is hypothesized to be affected
by the drug (e.g. diastolic blood pressure), the
efficacy variable, is measured in all subjects before
treatment and at some time point when the drug
effect should be measurable if the drug is effica-
cious. Mean change in the efficacy variable is
compared between the groups. If the difference
appears random, the drug is probably ineffective.
If the difference appears nonrandom, it is probably
due to the effect of the drug. The starting point for
the experimenter is the hypothesis that the drug is
ineffective. Thus, smaller the probability that the
observed difference is due to randomness, the more
confidence the experimenter has that the hypoth-
esis of no efficacy is incorrect.
The above example illustrates the basic steps in
statistical research methodology. (a) A scientific
question is posed (‘The drug effect is to reduce
blood pressure’). (b) An experiment is designed
that in the absence of randomness would yield
distinctly different outcomes (‘Treat one group of
subject with the supposedly active drug and
another with inert substance, or placebo’) and a314 CH25 STATISTICAL PRINCIPLES AND APPLICATION IN BIOPHARMACEUTICAL RESEARCH