Principles and Practice of Pharmaceutical Medicine

The subject’s diastolic blood pressure is measured
twice: once prior to treatment when the subject is
free of any antihypertensive medication, and once
following the administration of treatment (experi-
mental drug or placebo). The change in diastolic
blood pressure between the two measurements is
the primary efficacy variable. The researcher
knows that for the drug to be sufficiently effica-
cious to justify further development, it must reduce
the subject’s diastolic blood pressure by at least 10
points. So, if we denote the mean decrease in
diastolic blood pressure for the drug group bymD
and the corresponding decrease for the placebo
groupbyP, then the null hypothesisthe researcher
is set to test is:

H 0 :D¼P;or H 0 :D
P¼ 0 ;

versus the alternative hypothesis

HA:D>P;or HA:D
P> 0 :

One particular alternative of interest is

H 10 :D¼Pþ 10 ;or H 10 :D
P¼ 10 :

In order to guarantee that the statistical test of H 0
will have a significance levelaand power not less
than 1
bat the alternative H
:D¼Pþ
,
each of the two treatment groups must have at least
Nsubjects, whereNis given by the formula:

N¼ 2 ðZ 1 
a= 2 þZ 1 
bÞ^2 ðs=
Þ^2 ð 5 Þ

sis the standard deviation of the raw measure-
ments (i.e. the decrease in diastolic blood pres-
sure). For simplicity, we assume that it is the
same for both treatment groups.Z 1
a= 2 andZ 1
b
are two constants depending onaandb, that can be
obtained from tables of the standard normal dis-
tribution. If in our case, we assume thats¼12,

¼10, a¼ 0 :05 and b¼ 0 :10, then
Z 1
a= 2 ¼ 1 :96, Z 1
b¼ 1 :28, and (5) yields
N¼ 30 :23. That is, a sample size of at least 31
subjects per group is required. Expression (5)
is specific to situations similar to our example.

In general, the sample size required is calculated

by a formula that looks like expression (6) below:

N¼Ca;bðs=
Þ^2 ð 6 Þ

whereCa,bis some constant depending onaandb.

There are a number of important observations

implied by Equation (6):

(a) The sample size is proportional tos^2 , the

measurements variance. That is, the more vari-

able the measurements, the larger must be the

sample size to enable one to distinguish the

effect of interest from the noise.

(b) The sample size is inversely proportional to


^2. That is, the smaller the effect of interest,

the larger must the sample size be to enable us

to separate it from the background noise.

(c) The sample size depends on the squares of the

parameterssand
; meaning that if we are

able to reduce the noise in the experiment by

half, the payoff is that the clinical trial will

require one-fourth of the number of subjects.

Similarly, if we wish to build in sufficient

power to detect half of the effect, the clinical

trial would have to enroll four times as many

subjects.

During the design phase of the trial, the statistician

will typically ask the clinical researcher questions

leading to the determination ofsand
. The

anticipated standard deviation is often very diffi-

cult to estimate, and the best way of arriving at a

useful number is to look for such an estimate either

in the published scientific literature or estimate it

from data obtained similar studies performed by

the pharmaceutical company. Underestimatings

can result in an underpowered study resulting with

unacceptable errors rates leading to ambiguities

and an inability to make reliable inferences. For

this reason, it is always preferable to overestimate

srather than underestimate it when information on

sis scanty. The value of
, the minimal clinically

important effect, is usually arrived at by the clin-

ician based on past clinical experience.

332 CH25 STATISTICAL PRINCIPLES AND APPLICATION IN BIOPHARMACEUTICAL RESEARCH