+ All Categories
Home > Documents > LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to...

LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to...

Date post: 15-Dec-2015
Category:
Upload: celeste-simpkin
View: 219 times
Download: 1 times
Share this document with a friend
Popular Tags:
56
LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD
Transcript
Page 1: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

1

Statistical Core Didactic

Introduction to

Biostatistics

Donald E. Mercante, PhD

Page 2: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

2

Randomized Experimental Designs

Page 3: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

3

Randomized Experimental Designs

•Three Design Principles:

• 1. Replication

• 2. Randomization

• 3. Blocking

Page 4: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 5: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 6: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

6

Randomized Experimental Designs

If you don’t replicate . . .

. . . You can’t estimate!

Page 7: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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 ...

Page 8: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

8

Randomized Experimental Designs

. . . Randomization

Page 9: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

9

Randomized Experimental Designs

2. Randomization

• leads to unbiased estimates of treatment effects

Page 10: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 11: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

11

Randomized Experimental Designs

Without randomization, we may need to adjust analysis by

• stratifying

• covariate adjustment

Page 12: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

12

Randomized Experimental Designs

3. Blocking

• Arranging subjects into similar groups to

• account for systematic differences

Page 13: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 14: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

14

Randomized Experimental Designs

•Blocking

• leads to increased sensitivity of

statistical tests by reducing expt’l

error.

Page 15: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

15

Randomized Experimental Designs

Blocking

•Result: More powerful statistical test

Page 16: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 17: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

17

Randomized Experimental Designs

Three Aspects of Any Statistical Design

• Treatment Design

• Sampling Design

• Error Control Design

Page 18: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 19: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 20: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 21: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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 ?

Page 22: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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?

Page 23: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 24: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

24

Randomized Experimental Designs

3. Error Control Design

Goal: Decrease experimental error

Page 25: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 26: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

26

Inferential Statistics

• Hypothesis Testing

• Confidence Intervals

Page 27: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

27

Hypothesis Testing

• Start with a research question

• Translate this into a testable hypothesis

Page 28: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 29: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 30: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

30

Errors in Hypothesis Testing

Reality Decision H0 True H0 False

Fail to Reject H0 Type II ()

Reject H0 Type I ()

Page 31: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 32: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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 -

Page 33: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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 ().

Page 34: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

34

Errors in Hypothesis Testing

Goal of Hypothesis Testing

– Simultaneously minimize chance of making either error

Page 35: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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 -

Page 36: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 37: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 38: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 39: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

39

Steps in Hypothesis Testing

test statistic

• For example, if our hypothesis is

• Test statistic might be:

N N0 1H : pop mean = 120 vs. H : pop mean 120

sample mean hypothesized mean

standard errort

Page 40: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 41: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 42: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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

Page 43: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

43

Hypothesis Testing

P-values

Generally, p<0.05 considered significant

Page 44: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

44

Hypothesis Testing

Page 45: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 46: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 47: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 48: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 49: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 50: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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.

Page 51: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

LSU-HSC School of Public Health Biostatistics

51

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.

Page 52: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

Interval Estimation

Statistics such as the sample mean, median, and variance are called

point estimates

-vary from sample to sample

-do not incorporate precision

Page 53: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

Interval Estimation

Take as an example the sample mean:

X ——————> (popn mean)

Or the sample variance:

S2 ——————> 2

(popn variance)

Estimates

Estimates

Page 54: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

Interval Estimation

Recall, a one-sample t-test on the population mean. The test statistic was

This can be rewritten to yield:

0xt

sn

Page 55: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

Interval Estimation

Confidence Interval for :

CC sx tn

The basic form of most CI :

Estimate ± Multiple of Std Error of the Estimate

Page 56: LSU-HSC School of Public Health Biostatistics 1 Statistical Core Didactic Introduction to Biostatistics Donald E. Mercante, PhD.

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)


Recommended