Sample Size Sample Size DeterminationDeterminationIntroductionIntroductionn nIntegral part of vast majority of quantitative Integral part of vast majority of quantitative studiesstudiesn nImportant in ensuring validity, accuracy, Important in ensuring validity, accuracy, reliability 299:690-41978;299:690-4n nReviewed the power of 71 published RCTs which Reviewed the power of 71 published RCTs which had failed to detect a differencehad failed to detect a differencen nFound that 67 could have missed a 25% therapeutic Found that 67 could have missed a 25% therapeutic improvementimprovementn n50 could have missed a 50% improvement50 could have missed a 50% improvementIntroductionIntroductionn nThree main parts in its calculationThree main parts in its calculationn nEstimation (depends on a host of items)Estimation (depends on a host of items)n nJustification (in the light of budgetary or biological Justification (in the light of budgetary or biological considerations)considerations)n nAdjustments (accounting for potential dropouts or Adjustments (accounting for potential dropouts or effect of covariates)effect of covariates)IntroductionIntroductionn nConsequences of getting it wrongConsequences of getting it wrongn nScientificScientificn nEthicalEthicaln nEconomicalEconomicaln nProblems can be approached in two waysProblems can be approached in two waysn nPatients I need Patients I need approach: based on calculations of approach: based on calculations of sample size for a given power, significance, and sample size for a given power, significance, and clinically meaningful differenceclinically meaningful differencen nPatients I can get Patients I can get approach: based on calculations of approach: based on calculations of power for a given sample size the standard deviation of measured on the Beck scale; the standard deviation of this scale in a previous study was 7.7, and a difference this scale in a previous study was 7.7, and a difference of 5 points is considered to be of clinical importance. It of 5 points is considered to be of clinical importance. It is anticipated that around one third of patients may is anticipated that around one third of patients may drop out of treatment drop out of treatment Example: Comparing Two MeansExample: Comparing Two MeansRequired information Required information n nPrimary outcome variable = The Beck scale for Primary outcome variable = The Beck scale for suicidal ideation. A continuous variable summarized suicidal ideation. A continuous variable summarized by means. by means. n nStandard deviation = 7.7 points Standard deviation = 7.7 points n nSize of difference of clinical importance = 5 points Size of difference of clinical importance = 5 points n nSignificance level = 5% Significance level = 5% n nPower = 80% Power = 80% n nType of test = two-sidedType of test = two-sidedExample: Comparing Two MeansExample: Comparing Two MeansThe formula for the sample size for comparison of The formula for the sample size for comparison of 2 means (2-sided) is as follows 2 means (2-sided) is as follows n nn n = = A A + + B B2 x 2 x 2 x 2 x SDSD2 / 2 / DIFFDIFF2 2n nwhere where n n = the sample size required in each group = the sample size required in each group (double this for total sample). (double this for total sample). n nSDSD = standard deviation, of the primary outcome = standard deviation, of the primary outcome variable - here 7.7. variable - here 7.7. n nDIFFDIFF = size of difference of clinical importance - = size of difference of clinical importance - here 5.0.here 5.0.Example: Comparing Two MeansExample: Comparing Two Meansn nA A depends on desired significance level (see table) - here 1.96. depends on desired significance level (see table) - here 1.96. n nB B depends on desired power (see table) - here 1.28. depends on desired power (see table) - here 1.28. n nTable of values for A and B Table of values for A and B Significance level A 5% 1.96Significance level A 5% 1.96, 1% , 1% 2.58 2.58 Power BPower B 80% 0.84, 80% 0.84, 90% 1.2890% 1.28, 95% 1.64 Inserting the , 95% 1.64 Inserting the required information into the formula gives: required information into the formula gives: n nn n = 1.96 + 0.842 x 2 x 7.72 / 5.02 = = 1.96 + 0.842 x 2 x 7.72 / 5.02 = 3838 n nThis gives the number required in each of the trials two groups. This gives the number required in each of the trials two groups. Therefore the total sample size is double this, i.e. Therefore the total sample size is double this, i.e. 7676. . n nTo allow for the predicted dropout rate of around one third, the To allow for the predicted dropout rate of around one third, the sample size was increased to 60 in each group, a sample size was increased to 60 in each group, a total sample oftotal sample of 120120. . Example: Comparing Two MeansExample: Comparing Two MeansSuggested description of this sample size Suggested description of this sample size calculation cal