1 / 73

Sample Size and Power

Sample Size and Power. Steven R. Cummings, MD Director, S.F. Coordinating Center. The Secret of Long Life. Resveratrol In the skin of red grapes Makes mice Run faster Live longer. What I want to show. Consuming reservatrol prolongs healthy life. Sample Size Ingredients.

brianna-nixon
Télécharger la présentation

Sample Size and Power

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 and Power Steven R. Cummings, MD Director, S.F. Coordinating Center

  2. The Secret of Long Life • Resveratrol • In the skin of red grapes • Makes mice • Run faster • Live longer

  3. What I want to show • Consuming reservatrol prolongs healthy life

  4. Sample Size Ingredients • Testable hypothesis • Type of study • Statistical test • Type of variables • Effect size (and its variance) • Power and alpha

  5. Sample Size Ingredients • Testable hypothesis • Type of study • Statistical test • Type of variables • Effect size (and its variance) • Power and alpha

  6. My research question • I need to plan the study • My question is Does consuming reservatrol lead to a long and healthy life?

  7. What’s wrong with the question? • I need to plan the study • My question is Does consuming reservatrol lead to a long and healthy life?

  8. What’s wrong with the question? Does consuming resveratrol lead to a long and healthy life? • Vague • Must be measurable

  9. “Consuming resveratrol” • Most rigorous design: randomized placebo-controlled trial • Comparing red wine to placebo would be difficult • But resveratrol supplements are widely available

  10. Measurable (specific) outcome • “Consuming resevertrol” = taking resveratrol supplements vs. taking placebo • “Prolong healthy life” =

  11. Measurable (specific) outcome • “Consuming resevertrol” = taking resveratrol supplements vs. taking placebo • “Prolong healthy life” = reduces all-cause mortality Do people randomized to get a resveratrol supplement have a lower mortality rate than those who get a placebo?

  12. In whom? • Elderly men and women (≥70 years)

  13. The research hypothesis Men and women > age 70 years randomized to get a resveratrol supplement have a lower mortality rate than those who get a placebo.

  14. The research hypothesisThe ‘alternative’ hypothesis Men and women > age 70 years randomized to get a resveratrol supplement have a lower mortality rate than those who get a placebo. • Cannot be tested statistically • Statistical tests only reject null hypothesis - that there is no effect

  15. The Null Hypothesis Men and women > age 70 years randomized to receive a resveratrol supplement do not have lower mortality rate than those who receive placebo. • Can be rejected by statistical tests

  16. Ingredients for Sample Size  Testable hypothesis • Type of study • Statistical test • Type of variables • Effect size (and its variance) • Power and alpha

  17. Type of study • Descriptive • Only one variable / measurements • What proportion of centenarians take resveratrol supplements? • Confidence interval for proportions • What is the mean red wine intake of centenarians? • Confidence interval for the mean

  18. Sample size for a descriptive study For example: • “What proportion of centenarians (>100 years old) take resveratrol supplements?” • How much precision do you want? • Sample size is based on the width of the confidence interval (Table 6D and 6E) • I assume that 20% of centenarians take resveratrol • Conventional 95% C.I. • I want to be confident that the truth is within ±10% • Total width of the C.I. = 0.20

  19. Analytical studies • Analytical means a comparison • Cross-sectional • Mean red wine intake in centenarians vs. 60-80 year olds • Randomized trial • Elders who get resveratrol have lower mortality than those who get placebo

  20. Ingredients for Sample Size  Testable hypothesis  Type of study: analytical (RCT) • Statistical test • Type of variables • Effect size (and its variance) • Power and alpha

  21. This works for most study planning Type of statistical testsDepends on the types of variables

  22. The types of variables? Men and women > age 70 years randomized to receive a resveratrol supplement do not have lower mortality rate than those who receive placebo • Dichotomous: resveratrol or placebo • Continuous: mortality rate What’s wrong?

  23. The types of variables? Men and women > age 70 years randomized to receive a resveratrol supplement do not have lower mortality rate than those who receive placebo • Dichotomous: reseveratrol or placebo • Continuous: mortality rate • It is a proportion at certain times • For example, 3% at 1 year

  24. The appropriate test for this randomized trial for mortality

  25. Ingredients for Sample Size  Testable hypothesis  Type of study: analytical (RCT)  Statistical test  Type of variables • Effect size (and its variance) • Power and alpha

  26. Estimating the effect size For randomized trials, • Start with the expected rate in the placebo • Usually available from population or cohort studies • In this case, we know the mortality rates by age: • 3-4% per year*; for a 3 year study: 10% * ~ mean annual female/males @ 78 yrs

  27. Effect sizethe hardest part What should I assume for the effect of resveratrol on mortality?

  28. Effect sizethe hardest part Ways to choose an effect size: • What is likely, based on other data? • Do a pilot study • Estimate based on effect on biomarkers • What difference is important to detect? • “We don’t want to miss a __%_ difference” • What can we afford?

  29. The effect of resveratrol on mortality rate? • What is likely, based on other data? • Do a pilot study • Estimate based on effect on biomarkers • What difference is important to detect? • “We don’t want to miss a __%_ difference” • What can we afford?

  30. Resveratrol pronged survival of mice fed high calorie diet ~ 25% Baur, Nature 2006

  31. The effect of resveratrol on mortality rate? • What is likely, based on other data? • Pilot study? What endpoint? • No reliable markers for the effect on death • What difference is important to detect? • “We don’t want to miss a ____ difference” • What can we afford to find?

  32. The effect of resveratrol on mortality rate? • What is likely, based on other data? • Do a pilot study • Estimate based on biomarkers • What difference is important to detect? • “We don’t want to miss a _1%_ difference” • What can we afford? • 1%: too big & expensive • 5%: small and cheap

  33. The effect of resveratrol on mortality rate? • Finding a smaller effect is important to health • Allowing a larger effect is important for your budget

  34. Effect size Men and women > age 70 years randomized to receive a resveratrol supplement do not have lower mortality rate than those who receive placebo • It would be important to find (I don’t want to miss) a 20% decrease • Placebo rate: 10% • Resveratrol rate: 8%

  35. Ingredients for Sample Size  Testable hypothesis  Type of study: analytical (RCT)  Statistical test  Type of variables  Effect size (and its variance) • Power and alpha

  36. (alpha) The probability of finding a ‘significant’ result if nothing is going on

  37. I will need to convince people • Customarily, a result is ‘statistically significant’ if P<0.05 In other words, • Probability of a type I error = 5% • (alpha) = 0.05

  38. I will need to convince skeptics • Very small chance that a positive result is an error (alpha) = 0.01 P<0.01 • A smaller means larger sample size

  39. Two-sided vs. one-sided  • A 2-sided  assumes that the result could go either way • Recognizes that you have two chances of finding something that isn’t really there • Resveratrol decreases mortality • Resveratrol increases mortality • A 1-sided hypothesis reduces sample size (somewhat) • A one-sided  of 0.05 corresponds to a two-sided  of 0.10 • It assumes that the result could, plausibly, go only one way

  40. Two-sided vs. one-sided  • You may believe that your effect could only go one way! • Resveratrol is ‘natural.’ It could not increase mortality! • Be humble. • The history of research is filled with results that contradicted expectations • Vitamin D trial (JAMA 2010): • To everyone’s surprise, ~1500 IU of vitamin D/d increased the risk of falls and fractures in elderly women and men • A 1-sided test is almost never the best choice

  41. (beta) The probability of missing this effect size in this sample, if it is really true in the populations

  42. Power (1- ) The probability of finding this effect size in this sample, if it is really true in the population

  43. If it’s true, I don’t want to miss it • The chance of missing the effect () is “customarily” 20% In other words • Probability of a type II error = 0.20 •  (beta) = 0.20 • Power = 1- 0.80

  44. I really don’t want to miss it •  = .10 • Power (1- ) = 0.90 • Greater power requires a larger sample size

  45. We have all of the ingredients  Testable hypothesis  Type of study: analytical (RCT)  Statistical test: Chi-squared  Effect size 10% vs 8%  Power: 0.90; alpha: 0.20

  46. From Table 6B.2Comparing two proportions

  47. From Table 6B.2Comparing two proportions

  48. From Table 6B.2 • Sample size: 4,401 • Per group • Total: 8,802 • Does not include drop-outs • 20% drop-out: 11,002 total sample size!

  49. Alternatives • Tweak : one-sided • Almost never appropriate • Tweak the power: 0.80

More Related