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Statistical Core Didactic

Statistical Core Didactic. Introduction to Biostatistics Donald E. Mercante, PhD. Randomized Experimental Designs. Randomized Experimental Designs. Three Design Principles: 1. Replication 2. Randomization 3. Blocking. Randomized Experimental Designs. 1. Replication

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Statistical Core Didactic

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  1. Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD LSU-HSC School of Public Health Biostatistics

  2. Randomized Experimental Designs LSU-HSC School of Public Health Biostatistics

  3. Randomized Experimental Designs • Three Design Principles: • 1. Replication • 2. Randomization • 3. Blocking LSU-HSC School of Public Health Biostatistics

  4. Randomized Experimental Designs 1. Replication • Allows estimation of experimental error, against which, differences in trts are judged. LSU-HSC School of Public Health Biostatistics

  5. Randomized Experimental Designs Replication • Allows estimation of expt’l error, against which, differences in trts are judged. Experimental Error: • Measure of random variability. • Inherent variability between subjects treated alike. LSU-HSC School of Public Health Biostatistics

  6. Randomized Experimental Designs If you don’treplicate . . . . . . You can’t estimate! LSU-HSC School of Public Health Biostatistics

  7. Randomized Experimental Designs To ensure the validity of our estimates of expt’l error and treatment effects we rely on ... LSU-HSC School of Public Health Biostatistics

  8. Randomized Experimental Designs . . . Randomization LSU-HSC School of Public Health Biostatistics

  9. Randomized Experimental Designs 2. Randomization • leads to unbiased estimates of treatment effects LSU-HSC School of Public Health Biostatistics

  10. Randomized Experimental Designs Randomization • leads to unbiased estimates of treatment effects • i.e., estimates free from systematic differences due to uncontrolled variables LSU-HSC School of Public Health Biostatistics

  11. Randomized Experimental Designs Without randomization, we may need to adjust analysis by • stratifying • covariate adjustment LSU-HSC School of Public Health Biostatistics

  12. Randomized Experimental Designs 3. Blocking • Arranging subjects into similar groups to • account for systematic differences LSU-HSC School of Public Health Biostatistics

  13. Randomized Experimental Designs Blocking • Arranging subjects into similar groups (i.e., blocks) to account for systematic differences - e.g., clinic site, gender, or age. LSU-HSC School of Public Health Biostatistics

  14. Randomized Experimental Designs • Blocking • leads to increased sensitivity of statistical tests by reducing expt’l error. LSU-HSC School of Public Health Biostatistics

  15. Randomized Experimental Designs Blocking • Result: More powerful statistical test LSU-HSC School of Public Health Biostatistics

  16. Randomized Experimental Designs Summary: • Replication – allows us to estimate Expt’l Error • Randomization – ensures unbiased estimates of treatment effects • Blocking – increases power of statistical tests LSU-HSC School of Public Health Biostatistics

  17. Randomized Experimental Designs Three Aspects of Any Statistical Design • Treatment Design • Sampling Design • Error Control Design LSU-HSC School of Public Health Biostatistics

  18. Randomized Experimental Designs 1. Treatment Design • How many factors • How many levels per factor • Range of the levels • Qualitative vs quantitative factors LSU-HSC School of Public Health Biostatistics

  19. Randomized Experimental Designs One Factor Design Examples • Comparison of multiple bonding agents • Comparison of dental implant techniques • Comparing various dose levels to achieve numbness LSU-HSC School of Public Health Biostatistics

  20. Randomized Experimental Designs Multi-Factor Design Examples: • Factorial or crossed effects • Bonding agent and restorative compound • Type of perio procedure and dose of antibiotic • Nested or hierarchical effects • Surface disinfection procedures within clinic type LSU-HSC School of Public Health Biostatistics

  21. Randomized Experimental Designs 2. Sampling or Observation Design Is observational unit = experimental unit ? or, is there subsampling of EU ? LSU-HSC School of Public Health Biostatistics

  22. Randomized Experimental Designs Sampling or Observation Design For example, • Is one measurement taken per mouth, or are multiple sites measured? • Is one blood pressure reading obtained or are multiple blood pressure readings taken? LSU-HSC School of Public Health Biostatistics

  23. Randomized Experimental Designs 3. Error Control Design • concerned with actual arrangement of the expt’l units • How treatments are assigned to eu’s LSU-HSC School of Public Health Biostatistics

  24. Randomized Experimental Designs 3. Error Control Design Goal: Decrease experimental error LSU-HSC School of Public Health Biostatistics

  25. Randomized Experimental Designs 3. Error Control Design Examples: • CRD – Completely Randomized Design • RCB – Randomized Complete Block Design • Split-mouth designs (whole & incomplete block) • Cross-Over Design LSU-HSC School of Public Health Biostatistics

  26. Inferential Statistics • Hypothesis Testing • Confidence Intervals LSU-HSC School of Public Health Biostatistics

  27. Hypothesis Testing • Start with a research question • Translate this into a testable hypothesis LSU-HSC School of Public Health Biostatistics

  28. Hypothesis Testing Specifying hypotheses: • H0: “null” or no effect hypothesis • H1: “research” or “alternative” hypothesis Note:Only the null is tested. LSU-HSC School of Public Health Biostatistics

  29. Errors in Hypothesis Testing When testing hypotheses, the chance of making a mistake always exists. Two kinds of errors can be made: • Type I Error • Type II Error LSU-HSC School of Public Health Biostatistics

  30. Errors in Hypothesis Testing LSU-HSC School of Public Health Biostatistics

  31. Errors in Hypothesis Testing • Type I Error • Rejecting a true null hypothesis • Type II Error • Failing to reject a false null hypothesis LSU-HSC School of Public Health Biostatistics

  32. Errors in Hypothesis Testing • Type I Error • Experimenter controls or explicitly sets this error rate -  • Type II Error • We have no direct control over this error rate -  LSU-HSC School of Public Health Biostatistics

  33. Randomized Experimental Designs When constructing an hypothesis: Since you have direct control over Type I error rate, put what you think is likely to happen in the alternative. Then, you are more likely to reject H0, since you know the risk level (). LSU-HSC School of Public Health Biostatistics

  34. Errors in Hypothesis Testing Goal of Hypothesis Testing • Simultaneously minimize chance of making either error LSU-HSC School of Public Health Biostatistics

  35. Errors in Hypothesis TestingIndirect Control of β • Power • Ability to detect a false null hypothesis POWER = 1 -  LSU-HSC School of Public Health Biostatistics

  36. Steps in Hypothesis Testing General framework: • Specify null & alternative hypotheses • Specify test statistic and -level • State rejection rule (RR) • Compute test statistic and compare to RR • State conclusion LSU-HSC School of Public Health Biostatistics

  37. Steps in Hypothesis Testing test statistic Summary of sample evidence relevant to determining whether the null or the alternative hypothesis is more likely true. LSU-HSC School of Public Health Biostatistics

  38. Steps in Hypothesis Testing test statistic When testing hypotheses about means, test statistics usually take the form of a standardize difference between the sample and hypothesized means. LSU-HSC School of Public Health Biostatistics

  39. Steps in Hypothesis Testing test statistic • For example, if our hypothesis is • Test statistic might be: LSU-HSC School of Public Health Biostatistics

  40. Steps in Hypothesis Testing Rejection Rule (RR) : Rule to base an “Accept” or “Reject” null hypothesis decision. For example, Reject H0 if |t| > 95th percentile of t-distribution LSU-HSC School of Public Health Biostatistics

  41. Hypothesis Testing P-values Probability of obtaining a result (i.e., test statistic) at least as extreme as that observed, given the null is true. LSU-HSC School of Public Health Biostatistics

  42. Hypothesis Testing P-values • Probability of obtaining a result at least as extreme given the null is true. • P-values are probabilities • 0 <p< 1 <-- valid range • Computed from distribution of the test statistic LSU-HSC School of Public Health Biostatistics

  43. Hypothesis Testing P-values • Generally, p<0.05 considered significant LSU-HSC School of Public Health Biostatistics

  44. Hypothesis Testing LSU-HSC School of Public Health Biostatistics

  45. Hypothesis Testing Example Suppose we wish to study the effect on blood pressure of an exercise regimen consisting of walking 30 minutes twice a day. Let the outcome of interest be resting systolic BP. Our research hypothesis is that following the exercise regimen will result in a reduction of systolic BP. LSU-HSC School of Public Health Biostatistics

  46. Hypothesis Testing Study Design #1:Take baseline SBP (before treatment) and at the end of the therapy period. Primary analysis variable = difference in SBP between the baseline and final measurements. LSU-HSC School of Public Health Biostatistics

  47. Hypothesis Testing Null Hypothesis: The mean change in SBP (pre – post) is equal to zero. Alternative Hypothesis: The mean change in SBP (pre – post) is different from zero. LSU-HSC School of Public Health Biostatistics

  48. Hypothesis Testing Test Statistic: The mean change in SBP (pre – post) divided by the standard error of the differences. LSU-HSC School of Public Health Biostatistics

  49. Hypothesis Testing Study Design #2:Randomly assign patients to control and experimental treatments. Take baseline SBP (before treatment) and at the end of the therapy period (post-treatment). Primary analysis variable = difference in SBP between the baseline and final measurements in each group. LSU-HSC School of Public Health Biostatistics

  50. Hypothesis Testing Null Hypothesis: The mean change in SBP (pre – post) is equal in both groups. Alternative Hypothesis: The mean change in SBP (pre – post) is different between the groups. LSU-HSC School of Public Health Biostatistics

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