Presentation on theme: "Determination of Sample Size"— Presentation transcript:
1 Determination of Sample Size DR R.P. NERURKARAssociate ProfessorDept. of PharmacologyGood afternoon everybody, the topic given to me in this post-prandial session is statistical pitfalls and the time given for me to put you in to deep sleep is only 30 minutes and I hope that at least some of you are awake to listen to me at the end of my talk which will be followed by discussion and demo of user friendly statistical software. (next slide)T.N. MEDICAL COLLEGEB.Y.L NAIR HOSPITAL, MUMBAIAYUSH Workshop18th April 2006
2 Objectives At the end of this session participants should be able to list the factors influencing the sample sizeappreciate importance of incorrect sample size in researchcalculate the sample size using appropriate formulae
3 Factors affecting sample size Size of populationResources – subjects, financial, manpowerMethod of Sampling- random, stratifiedDegree of difference to be detectedVariability (S.D.) – pilot study, historicalDegree 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 FormulaeDropout rate, non-compliance to RxWhat should be the sample size? Well, it depends upon many factors such as size of the population to whom the finding of study will be applied, Resources available such subjects under study (e.g. a rare disease such as pheochomocytoma) financial, manpower. In case of animal studies restrictions imposed by CPCSEA.Degree of accuracy (or error)- Generally type I or alpha error should be less than 0.05 or 5%. Type II or beta error should be less than 0.2 or 20% and the power of the test should be more than 0.8 or 80%.Next is variablity within or between the samples (Standard deviation- this can be obtained from pilot study or previous reported studies (historical). Degree of difference to be detected which may be clinically significant. Method of sampling whether randomised or stratified and well selected. And last is the statistical formulae. You have to decide only after taking into consideration all these points. (Next Slide)
4 Correct () decisions and Types of Errors (X) in hypothesis testing TRUE SituationDifference exists (H1)No Difference (H0)CONCLUSION hypothesis testXType I error orAlpha errorDifference exists (H1)(Power or 1-beta)No DifferenceDo not reject (H0)Type II error orBeta error
5 Approach to sample size determination Determine the expected differenceFind out the Standard deviations of both groupsSet alpha error to be tolerated viz. P = 0.05Decide the power of the study desired viz. 80%, beta error 0.2Select the appropriate formulaCalculate the sample size using the formulaGive allowance for drop-out rateGive allowance for non-compliance of treatment if possible
6 Incorrect sample size will lead to Wrong conclusionsPoor quality research (Errors)Type II error can be minimized by increasing the sample sizeWaste of resourcesLoss of moneyEthical problemsDelay in completion
7 Formulae for Sample Size Comparison of means (two groups) (alpha=0 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)2Within group comparison (Paired)n = 8 X (S.D.of differences/M1-M2)2
8 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
9 Formulae for Sample Size Comparison of mean of one group only (alpha=0 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
11 Group Task 1 - QuestionThe 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?
12 Analysis type- comparison of percentage cure rate GROUP TASK 1 – AnswerAim – To see whether yoga is better than standard drug Rx in curing the pt.Analysis type- comparison of percentage cure rateParameters- cure rate 20% vs 30%No. of groups – 2p1=20 q1=80, p2=30 q2=70Set alpha=0.05, beta=0.2, Power=0.8Statistical formula to be usedn = p1q1 + p2q2 X 8(p1-p2)2Ans. 296
13 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 ?
14 Analysis type- comparison of mean, unpaired data GROUP TASK 2 - AnswerAim – To see whether modified procedure reduces the hospital stay as compared to conventional procAnalysis type- comparison of mean, unpaired dataParameters- duration of hospital stay 12.3 vs 9.3No. of groups-2Given M1=12.3, M2=9.3, SD= 4.8Set alpha=0.05, beta=0.2, Power=0.8Statistical formula to be usedn = 16 X (S.D./M1-M2)2Ans 40.96
15 Group Task 3 - QuestionThe 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 ?
16 Analysis type- comparison of mean, unpaired data GROUP TASK 3 - AnswerAim – To see whether fruit juice consumption differs by 1 from the population (Normal standard) mean of 5oz./dayAnalysis type- comparison of mean, unpaired dataParameters- fruit juice/day 5 vs 6 or 4No. of groups-1Given M1= 4 or 6, Mo=5, SD= 3Set alpha=0.05, beta=0.2, Power=0.8Statistical formula to be usedn = 8 X (S.D./M1-M0)2Ans 72