1 / 45

Sample Size Calculation

Sample Size Calculation. PD Dr. Rolf Lefering IFOM - Institut für Forschung in der Operativen Medizin Universität Witten/Herdecke Campus Köln-Merheim. sample size. uncertainty. Sample Size Calculation. costs & effort & time. Sample Size Calculation. Single study group

toya
Télécharger la présentation

Sample Size Calculation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sample Size Calculation PD Dr. Rolf Lefering IFOM - Institut für Forschung in der Operativen MedizinUniversität Witten/HerdeckeCampus Köln-Merheim

  2. sample size uncertainty Sample Size Calculation costs & effort & time

  3. Sample Size Calculation Single study group - continuous measurement - count of events Comparative trial (2 or more groups) - continuous measurement - count of events

  4. Confidence Interval Which true value is compatible with the observation? Confidence interval ... range where the true value lies with a high probability (usually 95%)

  5. Confidence Interval Example: 56 patients with open fractures, 9 developed an infection (16%) sample all patients with open fractures n=56 infection rate: 16% true value ???

  6. p * (100 - p) CI95 = P +/- 1,96 *  n Example:n = 56 p = 16% CI95 = 16 +/- 1,96 *  (16*84) / 56 =16 +/- 9,6 [ 6,4 - 25,6 ] Confidence Interval Formula for event rates n = sample size p = percentage

  7. Confidence Interval 95% confidence interval around a 20% incidence rate

  8. 1,65 für 90%1,96 für 95%2,58 für 99% Confidence Interval Formula for continuous variables Mean: M = meanSE = standard errorSD = standard deviationn = sample size CI95 = M  1,96 * SE Remember: SE = SD /n

  9. Sample Size Calculation Comparative trials

  10. „What is the sample size to show that early weight bearing therapy, as compared to standard therapy, is able to reduce the time until return to work from 10 weeks to 8 weeks, where time to work has a SD of 3 ?“ 36 cases per group ! „What is the sample size to show that early weight-bearing therapy is better ?“ „Which key should I press here now ?“

  11. Outcome Measures Survival Organ failure Hospital stay Recurrencerate Complications Sepsis Lab values Blood pressure Wound infection Beweglichkeit Wellbeing Inedpemdence,autonomy Pain Fear Depressionen Anxiety Social status Fatigue

  12. Select Outcome Measure • RelevanceDoes this endpoint convince the patient / the scientific community? • Reliability; measurabilityCould the outcome easily be measured, without much variation, also by different people? • Sensitivity Does the intervention lead to a significant change in the outcome measure? • RobustnessHow much is the endpoint influenced by other factors?

  13. Select Outcome Measure • Primary endpointMain hypothesis or core question; aim of the studyStatistics: confirmative • Secondary endpointsOther interesting questions, additional endpoints Statistics: explorative (could be confirmative in case of a large difference)Advantage: prospective selection in the study protocol • Retrospektively selected endpointsSelected when the trial is done, based on subgroup differencesStatistics: ONLY explorative !

  14. Sample Size Calculation Sample size Differenceto be detected Certainty - errorPower

  15. Statistical Testing A statistical test is a method (or tool) to decide whether an observed difference* is really present or just based on variation by chance * this is true for a test for difference which is the most frequently applied one in medicine

  16. Statistical Testing Test for difference„Intervention A is better than B“ Test for equivalence„Intervention A and B have the same effect“ Test for non- inferiority„Intervention A is not worse than B“

  17. Statistical Testing How a test procedure works 1. Want to show:there is a difference 2. Assume:there is NO difference between the groups; („equal effects“, null-hypothesis) 3. Try to disprove this assumption:- perform study / experiment- measure the difference 4.Calculate:the probability that such a difference could occur although the assumption („no difference“) was true = p-value

  18. Statistical Testing statistical test for difference: The p-valueis the probability for the case that the observed difference occured just by chance

  19. Statistical Testing statistical test for difference : pis the probability for„no difference“

  20. Statistical Testing „Germany and Spain areequally strong soccer teams !“ Game tonight: 6 : 0 für Germany trial n=6 Null hypothesis p-value says: How big is the chance that one of two equally strong teams scores 6 goals, and the other one none. statisticaltest: p = 0,031 Spain could still be equally strong as Germany, but the chance is small (3,1%)

  21. Statistical Testing small sample large sample small difference p=0,68 p=0,05 large difference p<0,001 p=0,05

  22. Statistical Testing The more cases are included, the better could „equality“ be disproved Example: drug A has a success rate of 80%, while drug B is better with a healing rate of 90% drug A drug Bsample size 80% 90% p-value 20 8/10 9/10 0,53 40 16/20 18/20 0,38 100 40/50 45/50 0,16 200 80/100 90/100 0,048 400 160/200 180/200 0,005 1000 400/500 450/500 <0,001

  23. Statistical Testing A „significant“ p-value ... does NOT prove the sizeof the difference, but only excludes equality!

  24. Statistical Testing p-value p-value small (0.05) chance alone is not sufficient to explain this difference there is a systematicdifferencenull-hypothesis is rejected “significant difference“ p-value large (>0.05) The observed difference is probably caused by chance only, or the sample size in not sufficient to exclude chance null-hypothesis in maintained “no difference”

  25. Statistical Testing Errors The decision - for a difference (significance, p  0.05) - or against it („equality“, not significant, p > 0.05) is not certain but only a probability (p-value). Therefore, errors are possible: Type 1 error:Decisionfor a difference although there is none => wrong finding Type 2 error:Decision for „equality“ although there is one => missedfinding

  26. Statistical Testing Errors Truth Test says ... no difference difference type 1 error C significant wrong finding a C not significant type 2 error missed finding b

  27. Statistical Testing type 1 error type 2 error “wrong finding“ „missed finding“ Fire detector wrong alarm no alarm in case of fire Court conviction of set a an innocent criminal free Clinical study difference difference was “significant” was missed by chance

  28. Power “What is the Power of the study ?” Type 2 error  probability to miss a difference Power = 1 -  probability to detect a difference Power depends on: - the magnitude of a difference- the sample size- the variation of the outcome measure- the significance level ()

  29. “Does the study have enough powerto detect a difference of size X ?” Power “What is the Power of the study ?” POWER is the probability to detect a certain difference X with the given sample size n as significant (at level ).

  30. Power When to perform power calculations? 1.Planning phase – sample size calculation:if the assumed difference really exists, what risk would I take to miss this difference ? 2.Final analysis – in case of a non-significant result:what size of difference could be rejected with the present data ?

  31. Power Example Clinical trial: Laparoscopic versus open appendectomy Endpoint: Maximum post-operative pain intensity (VAS 0-100 points) Patients: 30 cases per group Results: lap.: 28 (SD 18) open: 32 (SD 17) p = 0.38 not significant ! What is the power of the study ???

  32. Sample Size Calculation Sample size Differenceto be detected Certainty - errorPower

  33. Sample Size Calculation Sample size Differenceto be detected  = 0.05 = 0.20  error Risk to find a difference by chance  error Risk to miss a real difference

  34. Sample Size Calculation Sample size PT& PC or Difference& SD  = 0.05 = 0.20 Event rates: Percentages in the treatment and the control group Continuous measures: difference of means and standard deviation

  35. Sample Size Calculation Continuous Endpoints • SD unknown • if the variation (standard deviation) is not known,the expected advantage could be expressed as • „effect size“ • which is the difference in units of the (unknown) SD • Example: • pain values are at least 1 SD below the control group (effect size = 1.0) • the difference will be at least half a SD (effect size = 0.5)

  36. Sample Size Calculation Continuous Endpoints • Test with non-parametric rank statistics • non-normal distribution, or non-metric values • Mann-Whitney U-test; Wilcoxon test • Use t-Test for sample size calculation • and add 10% of cases

  37. Sample Size Calculation Guess … How many patients are needed to show that a new intervention is able to reduce the complication rate from 20% to 14% ? (=0.05; =0.20, i.e. 80% power)

  38. Sample Size Calculation Dupont WD, Plummer WD Power and Sample Size Calculations: A Review and Computer Program Contr. Clin. Trials (1990) 11:116-128 http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/PowerSampleSize

  39. Sample Size Calculation

  40. Multiple Testing • Mehr als eine Versuchs-/Therapiegruppe • Mehrere Zielgrößen • Mehrere Follow-Up Zeitpunkte • Zwischenauswertungen • Subgruppen-Analysen Multiple testing increases the risk of arbitrary significant results Overall statistical error in 8 tests at the 0.05 level: α = 1 - 0.95 8 = 1 - 0,66 = 0.34

  41. Multiple Testing • correct at least 1 error • 1 test (with 5% error) 95% 5% • 2 tests (with 5% error each) 90,25% 9,75% • 3 tests • 4 tests • 5 tests • ….. 90,25% 4,75% 0,25% 4,75%

  42. Multiple Testing • correct at least 1 error • 1 test (with 5% error) 95% 5% • 2 tests (with 5% error each) 90,2% 9,8% • 3 tests 85,7% 14,3% • 4 tests 81,5% 18,5% • 5 tests 77,4% 22,6% • …..

  43. Multiple Testing What could you do? • Select ONE primary and multiple secondary questions • Combination of endpoints multiple complications  „Negative event“ multiple time points  AUC, maximum value, time to normal multiple endpoints  sum score acc. to O‘Brian • Adjustment of p-values, i.e. each endpoint is tested with a „stronger“ αlevel e.g. Bonferroni: k tests at level α / k (5 tests at the 1% level, instead of 1 Test at 5% level) • A priori ordered hypothesespredefine the order of tests (each at 5% level)

  44. Interim Analysis • Fixed sample size end of trial • Sequential design after each case • Group sequential design after each step • Adaptive design after each step

  45. Interim Analysis aus: TR Flemming, DP Harrington, PC O‘BrianDesign of group sequential tests. Contr. Clin Trials (1984) 5: 348-361

More Related