Download Determination of Sample Size

Determination of Sample Size
DR R.P. NERURKAR
Associate Professor
Dept. of Pharmacology
T.N. MEDICAL COLLEGE
B.Y.L NAIR HOSPITAL, MUMBAI
AYUSH Workshop
18th April 2006
Objectives
At the end of this session participants should be able to
• list the factors influencing the sample size
• appreciate importance of incorrect sample
size in research
• calculate the sample size using appropriate
formulae
Factors affecting sample size
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Size of population
Resources – subjects, financial, manpower
Method of Sampling- random, stratified
Degree of difference to be detected
Variability (S.D.) – pilot study, historical
Degree of Accuracy (or errors)
- Type I error (alpha) p<0.05
- Type II error (beta) less than 0.2 (20%)
- Power of the test : more than 0.8 (80%)
• Statistical Formulae
• Dropout rate, non-compliance to Rx
Correct () decisions and Types of
Errors (X) in hypothesis testing
CONCLUSION
hypothesis test
Difference exists
(H1)
TRUE Situation
Difference exists (H1) No Difference (H0)

(Power or 1-beta)
X
No Difference
Do not reject (H0)
Type II error or
Beta error
X
Type I error or
Alpha error

Approach to sample size determination
Determine the expected difference
Find out the Standard deviations of both groups
Set alpha error to be tolerated viz. P = 0.05
Decide the power of the study desired viz. 80%, beta error 0.2
Select the appropriate formula
Calculate the sample size using the formula
Give allowance for drop-out rate
Give allowance for non-compliance of treatment if possible
Incorrect sample size
will lead to
• Wrong conclusions
• Poor quality research (Errors)
– Type II error can be minimized by increasing the
sample size
• Waste of resources
• Loss of money
• Ethical problems
• Delay in completion
Formulae for Sample Size
Comparison of means (two groups)
(alpha=0.05, Beta=0.2, power 80%)
– Between group comparison (Unpaired)
n = 16 X (S.D./M1-M2)2
– Within group comparison (Paired)
n = 8 X (S.D.of differences/M1-M2)2
Formulae for Sample Size
Comparison of percentages (two groups)
(alpha=0.05, Beta=0.2, power 80%)
n = 8 X p1q1 + p2q2
(p1-p2)2
Formulae for Sample Size
Comparison of mean of one group only
(alpha=0.05, Beta=0.2, power 80%)
n = 8 X (S.D./M1-M0)2
THANK YOU
Are you ready for group tasks?
Group Task 1 - Question
The cure rate of disease is 20% with a known drug
treatment. It is claimed that yoga is better than the drug
and a trial is to be conducted find out the truth. It is
decided that a even 10% increase in cure rate would
be clinically important. The alpha and beta were set at
0.05 and 0.2. The results will be analysed using Chi
Square test. How many patients would be required for
the trial?
GROUP TASK 1 – Answer
• Aim – To see whether yoga is better than standard drug Rx
in curing the pt.
• Analysis type- comparison of percentage cure rate
• Parameters- cure rate 20% vs 30%
• No. of groups – 2
• p1=20 q1=80, p2=30 q2=70
• Set alpha=0.05, beta=0.2, Power=0.8
• Statistical formula to be used
n = p1q1 + p2q2 X 8
(p1-p2)2
Ans. 296
Group Task No. 2 - Question
The mean(+SD) hospital stay of patients after a
conventional surgical procedure (CP) is 12.3(+4.8) days.
A modified procedure(MP) is to be tried to reduce the
hospital stay. Two groups of patients will be undergoing
either CP or MP. Their hospital stay will be compared
using unpaired t test at p<0.05 with power of 80%. The
minimum clinically important difference in the duration
of hospital stay is expected to be 3. Calculate the sample
size for each group ?
GROUP TASK 2 - Answer
• Aim – To see whether modified procedure reduces the
hospital stay as compared to conventional proc
• Analysis type- comparison of mean, unpaired data
• Parameters- duration of hospital stay 12.3 vs 9.3
• No. of groups-2
Given M1=12.3, M2=9.3, SD= 4.8
• Set alpha=0.05, beta=0.2, Power=0.8
• Statistical formula to be used
n = 16 X (S.D./M1-M2)2
Ans 40.96
Group Task 3 - Question
The mean fruit juice consumption in the population is 5
oz./day. Dennison and colleagues wanted to know
whether mean juice consumption in 2 year old children is
different from 5 oz./day – either more or less by1 oz/day.
SD is 3 oz/day.
Calculate the sample size required ?
GROUP TASK 3 - Answer
• Aim – To see whether fruit juice consumption differs by 1
from the population (Normal standard) mean of 5oz./day
• Analysis type- comparison of mean, unpaired data
• Parameters- fruit juice/day 5 vs 6 or 4
• No. of groups-1
Given M1= 4 or 6, Mo=5, SD= 3
• Set alpha=0.05, beta=0.2, Power=0.8
• Statistical formula to be used
n = 8 X (S.D./M1-M0)2
Ans 72