Statistical Core Didactic Introduction to Biostatistics Donald E

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

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

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

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

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 5

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

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 7

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

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

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 10

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

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

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 13

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

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

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 16

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

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 18

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 19

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 20

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 21

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 22

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 23

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

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 25

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

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

Hypothesis Testing Specifying hypotheses: • H 0: “null” or no effect hypothesis • H 1: “research” or “alternative” hypothesis Note: Only the null is tested. LSU-HSC School of Public Health Biostatistics 28

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 29

Errors in Hypothesis Testing Reality Decision H 0 True H 0 False Fail to Reject H 0 Type II ( ) Type I ( ) Reject H 0 LSU-HSC School of Public Health Biostatistics 30

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 31

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 32

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 H 0, since you know the risk level ( ). LSU-HSC School of Public Health Biostatistics 33

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

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

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 36

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 37

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 38

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

Steps in Hypothesis Testing Rejection Rule (RR) : Rule to base an “Accept” or “Reject” null hypothesis decision. For example, Reject H 0 if |t| > 95 th percentile of t-distribution LSU-HSC School of Public Health Biostatistics 40

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 41

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 42

Hypothesis Testing P-values · Generally, p<0. 05 considered significant LSU-HSC School of Public Health Biostatistics 43

Hypothesis Testing LSU-HSC School of Public Health Biostatistics 44

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 45

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

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 47

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 48

Hypothesis Testing Study Design #2: Randomly assign patients to control and experimental treatments. Take baseline SBP (before treatment) and at the end of 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 49

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 50

Hypothesis Testing Test Statistic: The difference in mean change in SBP (pre – post) between the two groups divided by the standard error of the differences. LSU-HSC School of Public Health Biostatistics 51

Interval Estimation Statistics such as the sample mean, median, and variance are called point estimates -vary from sample to sample -do not incorporate precision

Interval Estimation Take as an example the sample mean: Estimates X ——————> (popn mean) Or the sample variance: S 2 Estimates ——————> 2 (popn variance)

Interval Estimation Recall, a one-sample t-test on the population mean. The test statistic was This can be rewritten to yield:

Interval Estimation Confidence Interval for : The basic form of most CI : Estimate ± Multiple of Std Error of the Estimate

Interval Estimation Example: Standing SBP Mean = 140. 8, S. D. = 9. 5, N = 12 95% CI for : 140. 8 ± 2. 201 (9. 5/sqrt(12)) 140. 8 ± 6. 036 (134. 8, 146. 8)