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Sample Size Considerations

Sample Size Considerations. A Carefully Planned Study is Crucial for Success An Important Aspect of Most Studies: Proper Sample Size Determination. Sample Size & Study Goals. Sample size estimation (SSE) should be related to the goals of the experiment.

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Sample Size Considerations

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  1. Sample Size Considerations A Carefully Planned Study is Crucial for Success An Important Aspect of Most Studies: Proper Sample Size Determination

  2. Sample Size & Study Goals Sample size estimation (SSE) should be related to the goals of the experiment. It should not be too small or too big LSU-HSC School of Public Health Biostatistics

  3. Sample Size & Study Goals Too small a study : • Scientifically - Cannot detect clinically important effects • Economically - waste resources without capability of producing useful results. • Ethically: Expose subjects to potentially harmful treatments without advancing knowledge LSU-HSC School of Public Health Biostatistics

  4. Sample Size & Study Goals Too large a study : • Scientifically - demonstrate scientifically (clinically) irrelevant, but statistically significant effects. • Economically - waste resources by using more than necessary. • Ethically: Expose unnecessary number of subjects to potentially harmful treatments or subjects denied potentially beneficial ones. LSU-HSC School of Public Health Biostatistics

  5. Components of Sample Size Sample size estimation should incorporate: • clinical or scientific effects of interest • Precision (error variance) • study design LSU-HSC School of Public Health Biostatistics

  6. Sample Size Considerations Power approach to sample estimation: - Specifying the hypothesis - Specifying a significance level - Specifying an effect size or clinical difference - Obtaining estimates of parameters (historical or pilot data) - Specifying a value of power

  7. Sample Size Example Comparison of Topical Anesthetics Used in Tooth Restoration A two-group parallel randomized double-blind study is planned in patients undergoing dental restoration. Each patient will be randomly assigned to receive either a new topical anesthetic or the standard topical anesthetic before dental restoration.

  8. Sample Size Example The sample sizes in each group will be equal. The primary outcome measure will be the number of minutes until complete numbness is achieved, which will be compared between the two groups. The research hypothesis is that the mean time to numbness in the restoration area will be significantly different for the two anesthetic groups.

  9. Sample Size Example Specifying the hypothesis test on the mean: vs

  10. Sample Size Example Specifying a significance level:  = 0.05 or 5% (Type I error rate)

  11. Sample Size Example Specifying a clinically meaningful difference:

  12. Sample Size Example Effect size: Where  is the common standard deviation between groups

  13. Sample Size Example Obtaining estimates of parameters (historical or pilot data)

  14. Sample Size Example From Pilot Data we obtain estimates: Test Group: Mean = 6.8 minutes S.D. = 1.64 n = 5 Standard Group: Mean = 8.2 minutes S.D. = 1.92 n = 5

  15. Sample Size Considerations Specifying a value of Power: 80% or 90%

  16. Sample Size Considerations Sample size per group for comparing means of two groups:

  17. Sample Size Considerations Sample size per group for comparing means of two groups:

  18. Sample Size Considerations Sample size per group for comparing means of two groups (80% Power):

  19. Sample Size Considerations Sample size per group for comparing means of two groups (90% Power):

  20. Sample Size Considerations Two group t-test of equal means (equal n's) Power 80% 90% Test significance level 0.05 0.05 1 or 2 sided test? 2 2 Difference in means 1.4 1.4 Common std deviation 1.78 1.78 Effect size 1.07 1.07 n per group 26 34

  21. Sample Size for Equivalence Trials One-sided equivalence testing • Non-inferiority Is test drug at least as good as the std?

  22. Sample Size for Equivalence Trials Two-sided equivalence testing • Bio-equivalence testing Is test drug neither better nor worse than the std? • Usually carried out as two-one-side CI’s. • If equivalence limit  is contained in both.

  23. Sample Size for Equivalence Trials

  24. Sample Size for Survival • Sample sizes based on hazard rates • =1/2 Parametric Models • Exponential • Weibull Non-parametric

  25. Sample Size for Survival Parametric Models Non-parametric (result in slightly larger sample sizes)

  26. Sample Size for Survival Unbalanced treatment allocation

  27. Account for Accrual Accrual models can be incorporated into sample size projections. Poisson distribution can be used as distribution for accrual times.

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