Continuous Data, Power 50%
An essential part of clinical studies is the
question, how many subjects need to be studied in order to answer
the studies’ objectives. As an example, we will use an intended
study that has an expected mean effect of 5, and a standard
deviation (SD) of 15.
What required sample size do we need to obtain a
significant result, or, in other words, a p-value of at least 0.05.
A.
16,
B.
36,
C.
64,
D.
100.
A suitable equation to assess this question can
be constructed as follows.
With a study’s t-value of 2.0 SEM-units, a
significant p-value of 0.05 will be obtained. This should not be
difficult for you to understand when you think of the 95%
confidence interval of study being between – and + 2 SEM-units
(Chap.
5).
We assume
From the above equation it can be derived that
Answer B is correct.
You are testing here whether a result of 5 is
significantly different from a result of 0. Often two groups of
data are compared and the standard deviations of the two groups
have to be pooled (see page 25). As stated above, with a t-value of
2.0 SEMs a significant result of p = 0.05 is obtained. However,
the power of this study is only 50%, indicating that you will have
50% chance of an insignificant result the next time you perform a
similar study.
Continuous Data, Power 80%
What is the required sample size of a study with
an expected mean result of 5, and SD of 15, and that should have a
p-value of at least 0.05 and a power of at least 80% (power index
= (zα + zβ)2 = 7.8).
A.
140,
B.
70,
C.
280,
D.
420.
An adequate equation is the following.
If you wish to have a power in your study of 80%
instead of 50%, you will need a larger sample size. With a power of
only 50% your required sample size was only 36.
Continuous Data, Power 80%, 2 Groups
What is the required sample size of a study with
two groups and a mean difference of 5 and SDs of 15 per Group, and
that will have a p-value of at least 0.05 and a power of at least
80%. (Power index = (zα + zβ)2
= 7.8).
A.
140,
B.
70,
C.
280,
D.
420.
The suitable equation is given underneath.
The required sample size is 140 patients per
group. And so, with two groups you will need considerably larger
samples than you do with 1 group.
Binary Data, Power 80%
What is the required sample size of a study in
which you expect an event in 10% of the patients and wish to have a
power of 80%.
10% events means a proportion of events of
0.1.
The standard deviation (SD) of this proportion is
defined by the equation
![$$ \surd [\rm{proportion}\times (1-\rm{proportion})]=\surd (0.1\times 0.9).$$](A216868_1_En_8_Chapter_Eque_8.gif)
The suitable formula is given.
We conclude that with 10% events you will need
about 71 patients in order to obtain a significant number of events
for a power of 80% in your study.
Binary Data, Power 80%, 2 Groups
What is the required sample size of a study of
two groups in which you expect.
A difference in events between the two groups of
10%, and in which you wish to have a power of 80%.
10% difference in events means a difference in
proportions of events of 0.10.
Let us assume that in Group one 10% will have an
event and in Group two 20%. The standard deviations per group can
be calculated.
![$$\begin{array}{llll}\hbox{For group 1}:\hbox{SD}=\surd [\text{proportion}\times (1-\hbox{proportion})]&=\surd (0.1\times 0.9)=\mathrm{0.3.}\\ \text{For group 2}:\text{SD}=\surd [\text{proportion}\times (1-\text{proportion})]&=\surd (0.2\times 0.8)=0.4\\\hbox{The pooled standard deviation of both groups}&=\surd ({\text{SD}}_{1}+{\text{SD}}_{2})\\ &=\surd ({0.3}^{2}+{0.4}^{2})\\ &=\surd 0.25=0.5\end{array}$$](A216868_1_En_8_Chapter_Equg_8.gif)
The adequate equation is underneath.
Obviously, with a difference of 10% events
between two groups we will need about 195 patients per group in
order to demonstrate a significant difference with a power of
80%.