their response to treatment. These could be related
to the subject demographic background, such as
age, sex and ethnic origin, genetic disposition or
other prognostic variables. The method of allocat-
ing subjects to treatment must make sure that the
resulting treatment groups are balanced with
respect to such factors. The most effective way to
achieve this is by randomization. That is, assign
each subject to a treatment group using a chance
mechanism. Of course, one could achieve the
desired balance by using a systematic, nonrandom
allocation scheme that will force the balance. Ran-
domization, however, has some important advan-
tages. Any nonrandom method inevitably involves
a decision by the individual making the allocation.
This potentially could result with the preference of
a certain type of subjects for one of the treatments
that may not be reflected as an imbalance in any
of the identified prognostic variables. Furthermore,
there might be some other variables which affect
the response to treatment and which are either
unrecognized as such at the time the study is
planned or are impossible to balance for logistical
reasons. A random allocation, at least in large
trials, can typically protect the investigator against
such problems.
To achieve a completely random allocation, one
could use a mechanism such as a simple toss of a
balanced coin or anything equivalent to it and
assign a subject to receive treatment A if the coin
lands on Heads (‘H’), say, and treatment B if the
outcome is Tails (‘T’). Although the result of a coin
toss is a perfect random sequence of ‘H’s and ‘T’s,
the number of ‘H’s in any finite sequence of coin
tosses is rarely equal to the number of ‘T’s. Thus,
the result of using a coin toss mechanism for treat-
ment allocation would typically result in an imbal-
ance among the treatment groups, an undesirable
statistical design property. The most common
method of randomization that will guarantee that
approximately equal number of subjects is allo-
cated to the different treatment groups is therando-
mized blocksmethod. Let us illustrate this for a trial
with three treatment groups: A, B and C. Blocks
containing the letters A, B and C in a random order,
with each letter repeated the same number of times,
are generated. Such a block of length 6 might look
like (B, B, A, C, C, A). The requirement that each
letterappears in theblockasfrequentlyasany ofthe
other two letters implies that the length of the block
must be a multiple of 3. Thus, for the case of three
treatment groups, the block size must be 3, 6, 9 and
soon. Thenumberofsuchrandomblocksgenerated
must be such that the number of letters in the
resulting string equals or exceeds the number of
subjects to be enrolled in the trial. Subjects are then
assigned sequentially to the treatment group corre-
sponding to the next unassigned letter in the rando-
mization string. Because each individual block
contains the same number of each of the letters,
the treatment assignment sequence obtained from
the randomized blocks method is not exactly a
sequence of random numbers. However, the
method has the advantage that it guarantees a max-
imum balance in the resulting sizes of the treatment
groups. In fact, the number of subjects allocated to
two treatment groupscannot differ by more than the
number of times each treatment is repeated within
the block.Bias and blinding
Statisticians routinely use data obtained from a
sample to estimate a parameter of interest. The
estimate is subject to variability inherited from
the data. Thus, using different and independent
samples would result in different values of the
estimate that are distributed around a mean value.
Biasis the difference between that mean value and
the quantity it intends to estimate. Thebias, then, is
a measure of the magnitude by which a statistical
estimation method is overestimating or underesti-
mating the parameter it is designed to estimate. We
refer to this type of bias asstatistical bias. Clinical
researchers often use the term ‘bias’ in a broader,
though less precise, fashion. They refer tobiasas
the effect of any factor, or combination of factors,
resulting in inferences, which lead systematically
to incorrect decisions about the treatment effect.
Although this usage has the appeal that it corre-
sponds to our intuitive understanding of the word
‘bias’, it cannot be quantified because of its impre-
cision. It is, nevertheless, useful in discussing pro-
blems that could result from a faulty design or
inadequate conduct of a trial.25.6 THE CONTROLLED CLINICAL TRIAL: BASIC DESIGN ELEMENTS 319