Principles and Practice of Pharmaceutical Medicine

not considered to be of material importance. Let
us illustrate this with the following example:
Suppose one is interested in determining whether
two antihypertensive drugs are equivalent in their
effect on diastolic blood pressure after four weeks
of treatment. Let mAand mBdenote the mean
change from the pretreatment baseline for patients
treated with drug A and drug B, respectively. Let

¼mA
mB. Blood pressure varies from mea-
surement to measurement, even when the mea-
surements are taken within minutes from each
other so that measurements within 3 mmHg
are not considered to be clinically different.
Therefore, as long as the two means are within
3 mmHg, the two drugs are considered as hav-
ing equivalent effectiveness. A trial to establish
whether the two drugs are equivalent must be then
designed so that a confidence interval for
with
confidence level of 0.90 or higher (or another
level considered by the researcher to be adequate)
will have width not exceeding 6 mmHg. When the
trial is concluded, the confidence interval is con-
structed. If it is entirely contained within the
intervalð
3 ;þ 3 Þ, the two drugs are considered
equivalent. Otherwise, they are not. It is possible
to design a trial so that a desired confidence
interval of a given confidence level will have a
desired width. The width of a confidence interval
for a parameter is the estimate’s precision.It
depends on (a) the confidence level, (b) the inher-
ent variability of the data and (c) the sample size.
The inherent variability of the data can be con-
trolled only to a limited degree. For a fixed sam-
ple size, the width of the confidence interval is
determined by the confidence level. As we have
seen in the previous example, the researcher can
increase the precision of his estimate only by
lowering the confidence level associated with
the confidence interval andvice versa. The only
way to guarantee an acceptable level of confi-
dence and precision is to include sufficiently
large number of subjects in the trial. In our exam-
ple, if the interval’s width is larger that 6 mmHg,
the trial could never establish equivalence
because the criterion for this cannot be met. How-
ever, it could establish the lack of equivalence if
the entire confidence interval is either lager than 3
or smaller than
3.

To summarize, when estimating the magnitude

of a parameter is an important objective of a trial,

thought must be given at the design stage to what

levels of confidence and precision are considered

acceptable and make sure that the trial is designed

to enroll sufficient number of subjects to accom-

modate these requirements. There are no hard and

fast rules about what levels of confidence are con-

sidered acceptable. However, rarely do researchers

go below 80%, and more typically, they require a

confidence level of 90% or higher. The desired

level of precision depends entirely on the particular

situation.

25.10 Study design: determining

the sample size

We have already seen through a number of exam-

ples the interplay between sample size, variability

and the performance of the statistical procedures

employed to analyze the data. The sample size

determines the amount of information that will be

available at the end of the trial. Therefore, the

determination of an adequate sample size is one

of the most important aspects of the trial design. A

trial accumulating inadequate amount of informa-

tion is hopelessly flawed, as it will not enable the

researcher to answer the questions the trial is

intended to answer.

The determination of the sample size is inti-

mately related to the trial objectives, the inferences

the researcher wants to be able to make and the

error probabilities in the case of hypotheses testing

or the confidence and precision in the case of

estimation that the researcher is willing to tolerate.

The following example illustrates the process of

determining the required sample size for a clinical

trial.

Suppose one wishes to conduct a trial to test the

efficacy of a new antihypertensive drug. The clin-

ical research physician plans to enroll a certain

number of subjects with mild to moderate hyper-

tension and randomize them to receive either the

experimental drug or placebo. The primary effi-

cacy variable is the decrease in the diastolic blood

pressure as compared to a pretreatment baseline.

25.10 STUDY DESIGN: DETERMINING THE SAMPLE SIZE 331