Sample size calculation

1. 12/1/2016
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Sample Size Calculation
Dr.S.Manikandan
Department of Pharmacology
JIPMER
Large Sample
• Waste of money, time and resources
• Exposes many people to harm – unethical
•Small difference may show up as significant
Small Sample
Results are not valid
Hence we need adequate number (sample size) that can
represent the population
Why Calculate Sample Size?
To find out whether rice is cooked :
1. How many grains do you really need to test?
2. If we mix four or more varieties of rice (Basmathi, IR 20 etc)
how many grains do we need to test?
Learning Point:
If the difference is large, we need a small sample size.
If the variation is large, we need a larger sample
What other factors affect sample size?
Minimum important difference
Standard deviation
Type I error (P value)
Type II error
Study design
Drop out
Patient compliance
How to find out minimum important difference (MID)?
The minimum difference that is clinically or practically
important
Essentially obtained from the previous studies.
What if there are no previous studies?
Repeat literature search with all possible keywords. Still if
there are no studies, do a pilot.
Learning Point
The researcher has to provide these values and it should be supported with a
reference. The statistician cannot fix these values.

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MID of which parameter should be considered
for analysis?
The primary parameter is always used for sample size
calculation.
Where can I get the S.D?
From the literature or pilot study.
What should be the power of the study?
Advisable to keep at 90% during calculation. Should never
be below 80%.
How to report sample size calculation
in protocol / paper?
The sample size was calculated for a minimum expected
difference in blood sugar of 25 mg/dl and standard deviation of
18.5. (Provide ref of the study from which you got these values)
For a power of 90%, significance level 5%, noncompliance of
20% and 10% attrition, we required a sample size of 146. The
sample size was calculated by PS software ver 3.0.
Post hoc Power Analysis
Power analysis – converse of sample size calculation.
If study concludes that there is no difference between
groups, the it is mandatory to calculate power and show
that study is adequately powered to pick the difference.
Take Home Message
Sample size calculation is mandatory for all studies.
Minimum important difference, standard deviation, P value,
power (80%), dropout rate and compliance of patient are
required.
If study concludes that there is no significant difference,
then power should be calculated.
Individual Task
Freely downloadable from
http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/PowerSampleSize
Developed by Dupont & Plummer, Department of Biostatistics,
Vanderbilt University

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Problem - 1
A new antihypertensive jipolol is compared with atenolol for its efficacy
in a randomised, double blind trial. Phase II clinical trials have shown
a difference of 5 mm Hg fall in mean B.P between the two groups. The
standard deviation of mean B.P is found to be 10 mm Hg. How many
patients will be required at 80% power, significance of 5%, non-
compliance of 20% and a dropout rate of 10%.
Problem – 1 Answer
From software: 128
Allowance for noncompliance (20% of 128): 26
Allowance for drop outs (10% of 154): 16
So total sample size required = 170
Problem - 2
The mean(SD) hospital stay of patients after a conventional surgical
procedure (CP) as reported in literature is 12.3(4.8) days. A modified
procedure(MP) is to be tried to reduce the stay. A few researchers
have tried this procedure and found that it reduced hospital stay by 3
more days when compared to CP. You want to design a study to
compare CP and MP. The hospital stay will be compared using
unpaired t test at p<0.05 with power of 90%. Calculate the total
sample size.
Problem – 2 Answer
From software: 110
Allowance for drop outs (10% of 110): 11
So total sample size required = 122
Problem - 3
A study Is primarily designed to determine whether caspofungin is
as effective as amphotericin B for the treatment of invasive
candidiasis, with efficacy measured in terms of overall response at
the end of intravenous therapy. It is known that amphotericin B
produces a response rate of 70%. It was expected that
caspofungin has a response rate of at least 50%. At 80% power,
10% attrition and 5% significance, what would be the required
sample size?
Problem – 3 Answer
From software: 206
Allowance for noncompliance (20% of 206): 42
Allowance for drop outs (10% of 248): 25
So total sample size required = 274

4. 12/1/2016
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Problem - 4
The cure rate of pharmacotherapy for a disease is 20%. Yoga is
reported to have a beneficial effect in this condition. A few studies
report that the cure rate for yoga is 30%. If you want to design
such a study at 80% power, 10% attrition and 5% significance,
what would be the required sample size?
Problem – 4 Answer
From software: 626
Allowance for noncompliance (20% of 626): 125
Allowance for drop outs (10% of 751): 75
So total sample size required = 826
Problem - 5
Chemotherapy is found to increase the survival of patients with a
solid tumor by 10 months. A study has reported that surgical
excision followed by chemotherapy can increase the survival by 8
more months compared to chemotherapy alone. A researcher
aims to conduct a study to compare the survival by these two
methods. The study is designed to have an enrolment period of 6
months and a follow-up for 3 years. At 80% power, 20% attrition
and 5% significance, what would be the required sample size?
Problem – 5 Answer
From software: 106
Allowance for drop outs (20% of 106): 22
So total sample size required = 128
Problem - 6
Few case reports implicate the use of an anaesthetic agent in the
causation of myocardial infarction. An investigator wants to conduct
a case control study to find out the association. He did a preliminary
review of case sheets in his hospital and found that around 30% of
operated cases receive this drug. As there are no similar previous
case control studies, he proposes that people who receive this drug
are at least three times greater risk for infarction. At 80% power and
5% significance, what would be the required sample size?
Problem – 6 Answer
From software: 124

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Concluding Remarks
Sample size calculation is not like
a wizard giving you some magic
number.
It is science and can be performed
easily by every researcher.
Problem - 7
A survey conducted in Goa has estimated that 20% of people in
age group 18 to 25 years who are admitted with head injury had
consumed alcohol. A similar survey is planned in Pondicherry.
With 95% confidence interval and a precision of 5%, What should
the sample size for the survey?
Problem – 7 Answer
From software: 246
Always give allowance for nonresponders.
Problem - 8
A researcher wants to compare a new diagnostic test with the
gold standard. The sensitivity of the gold standard is 85%. The
new test is found to have a sensitivity of 95%. At 80% power
and 5% significance, what would be the required sample size?
Problem – 8 Answer
From software: 140