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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 18 th April 2006

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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

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Factors affecting sample size 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< 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

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Correct ( ) decisions and Types of Errors (X) in hypothesis testing X X Difference exists (H 1 )No Difference (H 0 ) Difference exists (H 1 ) No Difference Do not reject (H 0 ) TRUE Situation CONCLUSION hypothesis test (Power or 1-beta) Type II error or Beta error Type I error or Alpha error

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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

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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

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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./M 1 -M 2 ) 2 –Within group comparison (Paired) n = 8 X (S.D.of differences/M 1 -M 2 ) 2

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Formulae for Sample Size Comparison of percentages (two groups) (alpha=0.05, Beta=0.2, power 80%) n = 8 X p 1 q 1 + p 2 q 2 (p 1 -p 2 ) 2

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Formulae for Sample Size Comparison of mean of one group only (alpha=0.05, Beta=0.2, power 80%) n = 8 X (S.D./M 1 -M 0 ) 2

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THANK YOU Are you ready for group tasks?

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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?

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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 GROUP TASK 1 – Answer Ans. 296

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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 ?

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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 GROUP TASK 2 - Answer Ans 40.96

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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 ?

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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./M 1 -M 0 ) 2 GROUP TASK 3 - Answer Ans 72

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