Response to reviewer – Young-il Kim
We would like to thank you for your careful reading and helpful comments. We have
revised the manuscript accordingly by incorporating your comments.
1. Mathematical expressions in the manuscript seems ok
Thanks.
2. Author described “cut-off point for inclusion criteria seems to be based on
convenience or intuition, not mathematical rigor”
-- It is partially true, but most of clinical trial imported inclusion criteria from
similar referenced studies or pilot study. Author also needs to use pilot study
dataset or preliminary dataset to get idea about distribution of symptom severity.
As get more accurate information from preliminary data, the method introduced
by the manuscript might perform better. This would be same for conventional
method of sample size calculation based on t-test.
We think the statistical performance may be similar to the conventional method. But the
cost will be greatly reduced by our method. The conventional method does not take the
cost parameters into consideration.
3. 90% power is not typical required or desired power. Author might need to
show the proposed method also performed as good as at 80% power.
It would be much better to have an additional table show performance result at
80% power.
We provided results for 80% power as attachment here (on Page 3-6). Similar results
have been observed. In the discussion of the article, we noted this observation.
4. Mathematical relationship of x and z / a and b?
There is no explicit mathematical relationship between x and z or between a and b.
However a and b are constrained to produce optimal cost reduction.
5. Change notation for ?  is for conventional expression for type I error. It
might cause confusion to reader…
We have made the change.
6. Page 7, is this alpha1 = beta 1?
Thanks for your careful reading. We have corrected the typo.
7. Most of early stage of clinical trials is not rely on sample size calculation based
on t-test. Not sure about strength of application area…
We agree there are many other tests used in early stage of clinical trials. We are using
the t-test for illustration.
8. Significant sample size change by size of standard deviation and power.
Smaller standard deviation and less power require smaller sample size.
Depend on STD, drop to 80% power could make half cut of sample size required
at 90% power. In the case, cost saving effect may not significant while there are
many preliminary analysis required for sample size computation.
The absolute amount of cost saving may decrease with smaller sample sizes. However
in our new results for 80% power (see attached plots on the following pages), we still
observe very similar relative amount of cost saving as the 90% power case.
NEXT PAGE: Plots for 80% power.
Figure 1. Plots of total costs (A.) and sample size (B.) as a function of the symptom
severity threshold used for inclusion criteria. The vertical line indicates the optimum
threshold for minimum total cost. The treatment sample size (solid line in B.)
decreases as the symptom severity threshold increases, whereas the screening size
(dashed line in B.) is curvilinear as a function of the symptom severity threshold.
Figure 2. Plots of optimum total costs (A.) and optimum screening sample sizes (B.) as
a function of cost ratios of screening. The optimum total costs increase as the cost of
screening is weighted more heavily in comparison to the cost of intervention (in A.),
whereas the screening size decreases (in B.).
Figure 3. Plots of optimum total costs (A.) and sample sizes (B.) as a function of
screening severity threshold a. The solid vertical lines indicate the optimum screening
severity threshold for minimum total cost under the two stage procedure. The dashed
vertical line indicates the optimum screening severity threshold for minimum total cost
under the single stage procedure. In B., the gray solid line is the screening sample
size under the single stage procedure.
Figure 4. Plots of optimum total costs as a function of prescreening cost ratios (A.)
and of the correlation coefficient  (B.). The solid lines correspond to the two stage
screening procedure and the dashed line to the single stage procedure.