The above example illustrates well the idea
behind stratification. The study population is
usually quite heterogeneous. If one measures the
effect of treatment by calculating the overall mean
effect in the population, although this mean repre-
sents an estimate of the treatment effect in this
population, it might be associated with a large
measurement error which could make it difficult
to distinguish the signal from the background
noise. In other words, the overall mean may be
anestimate of the treatment effect, but an ineffi-
cient one. If one can identifya prioricertain sub-
groups, orstrata, in the study population which are
more homogeneous with respect to the efficacy
variable of interest in the trial, then by estimating
the effect within each of these strata and combining
these estimates one may increase substantially the
power of the analysis because the noise masking
the effect ofinterest is reduced. It is well known, for
example, that in multicenter trials, the measured
effect often differs between investigators. This
could be a result of the physician’s procedures,
his or her instruments, the method of evaluating
the subject’s response or a myriad of other reasons,
especially when the measurement has a great
degree of subjectivity. Sometimes the difference
is due to the characteristics of subject populations
from which the different investigators draw their
subjects. Whatever the reason, it is often common
practice to stratify the subjects by investigators. It
is also wise to identify important prognostic vari-
ables and design the trial so as to stratify according
to them. Examples of some common stratification
variables are sex, race, age, disease severity,
Karnofsky status score in cancer studies, disease
staging and so forth. When strata are identified, it is
recommended that the randomization process will
be done within the strata. This helps to equalize the
number of subjects in the various treatment groups
within each of the strata and balance them with
respect to the stratification variables. The draw-
back is that as the number of important prognostic
variables increases, the number of strata increases
by multiples, thus complicating the trial’s logistics.
For example, if onewants to stratify by sexand race
when sex has two categories (male and female) and
race has four (White, Black, Hispanic, other), the
number of strata is 8. Adding another variable with
three categories, such as disease severity at base-
line (mild, moderate, severe), will bring the num-
ber of strata to 24. If, in addition, investigator is a
stratification variable, then this would mean that
each data center performing the randomization
will have to manage 24 randomization tables for
each investigator, one for each stratum, which is
utterly impractical. For a study of moderate size of
100–500 subjects, a large number of strata may
mean that some strata may contain very small
number of subjects, which complicates the statis-
tical analysis and its interpretation.
Insummary, stratification is avery useful toolfor
noise reduction, but it has its limitations. Usually,
the one stratification variable used in multicenter
trial is the investigational site. More than one addi-
tional variable can introduce serious logistical and
methodological difficulties. If one is not concerned
about the investigator’s effect, then central rando-
mization procedures can be very useful in situa-
tions of complex stratification requirements.
Computerized central randomization procedures
are now available that make complex stratification
schemes possible.Blocking
Another common method employed to decrease
the background variability isblocking. Like strati-
fication, blocking involves the subdivision of the
subject population into homogeneous subgroups.
The experimenter defines block of subjects and
randomizes the subjects within each block to the
study treatments such that the same number of
subjects are assigned to each treatment within
each block. The blocks are defined so that the
intra-block variability is minimal. For example,
to determine whether a drug is carcinogenic, rats
of the same litter are randomized to receive several
doses of the drug or placebo. This way, effects due
to genetic variation are minimized.
To take advantage of the block design, the treat-
ments are compared within each block and then the
information is pooled across blocks. When the
‘within-block’ or ‘intra-block’ variability is sub-
stantially smaller than the ‘between-block’ or
‘inter-block’ variability, blocked designs could be322 CH25 STATISTICAL PRINCIPLES AND APPLICATION IN BIOPHARMACEUTICAL RESEARCH