Transcript Oral Biology 201 - Louisiana State University School of

Statistical Core Didactic
Introduction to
Biostatistics
Donald E. Mercante, PhD
LSU-HSC School of Public Health
Biostatistics
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Randomized Experimental Designs
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Biostatistics
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Randomized Experimental Designs
• Three Design Principles:
•
1. Replication
•
2. Randomization
•
3. Blocking
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Biostatistics
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Randomized Experimental Designs
1. Replication
• Allows estimation of experimental error,
against which, differences in trts are
judged.
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Biostatistics
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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.
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Biostatistics
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Randomized Experimental Designs
If you don’t replicate . . .
. . . You can’t estimate!
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Biostatistics
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Randomized Experimental Designs
To ensure the validity of our estimates of
expt’l error and treatment effects we rely
on ...
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Biostatistics
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Randomized Experimental Designs
...
Randomization
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Biostatistics
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Randomized Experimental Designs
2. Randomization
•
leads to unbiased estimates of
treatment effects
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Biostatistics
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Randomized Experimental Designs
Randomization
• leads to unbiased estimates of
treatment effects
• i.e., estimates free from systematic
differences due to uncontrolled variables
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Biostatistics
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Randomized Experimental Designs
Without randomization, we may
need to adjust analysis by
• stratifying
• covariate adjustment
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Biostatistics
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Randomized Experimental Designs
3. Blocking
• Arranging subjects into similar groups to
• account for systematic differences
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Biostatistics
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Randomized Experimental Designs
Blocking
• Arranging subjects into similar groups
(i.e., blocks) to account for systematic
differences
- e.g., clinic site, gender, or age.
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Biostatistics
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Randomized Experimental Designs
• Blocking
• leads to increased sensitivity of statistical
tests by reducing expt’l error.
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Biostatistics
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Randomized Experimental Designs
Blocking
• Result: More powerful statistical test
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Biostatistics
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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
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Biostatistics
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Randomized Experimental Designs
Three Aspects of Any Statistical Design
• Treatment Design
• Sampling Design
• Error Control Design
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Biostatistics
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Randomized Experimental Designs
1. Treatment Design
• How many factors
• How many levels per factor
• Range of the levels
• Qualitative vs quantitative factors
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Biostatistics
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Randomized Experimental Designs
One Factor Design Examples
– Comparison of multiple bonding agents
– Comparison of dental implant techniques
– Comparing various dose levels to achieve
numbness
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Biostatistics
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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
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Biostatistics
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Randomized Experimental Designs
2. Sampling or Observation Design
Is observational unit = experimental unit ?
or,
is there subsampling of EU ?
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Biostatistics
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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?
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Biostatistics
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Randomized Experimental Designs
3. Error Control Design
• concerned with actual arrangement of
the expt’l units
• How treatments are assigned to eu’s
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Biostatistics
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Randomized Experimental Designs
3. Error Control Design
Goal:
Decrease experimental error
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Biostatistics
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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
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Biostatistics
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Inferential Statistics
•
Hypothesis Testing
•
Confidence Intervals
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Biostatistics
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Hypothesis Testing
• Start with a research question
• Translate this into a testable hypothesis
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Biostatistics
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Hypothesis Testing
Specifying hypotheses:
• H0: “null” or no effect hypothesis
• H1: “research” or “alternative” hypothesis
Note: Only the null is tested.
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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
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Errors in Hypothesis Testing
Reality 
 Decision
H0 True
H0 False
Fail to Reject H0

Type II ()
Type I ()

Reject H0
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Biostatistics
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Errors in Hypothesis Testing
• Type I Error
– Rejecting a true null hypothesis
• Type II Error
– Failing to reject a false null hypothesis
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Biostatistics
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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 - 
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Biostatistics
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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 ().
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Biostatistics
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Errors in Hypothesis Testing
Goal of Hypothesis Testing
– Simultaneously minimize chance of making either error
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Biostatistics
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Errors in Hypothesis Testing
Indirect Control of β
• Power
– Ability to detect a false null hypothesis
POWER = 1 - 
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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
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Biostatistics
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Steps in Hypothesis Testing
test statistic
Summary of sample evidence relevant to
determining whether the null or the alternative
hypothesis is more likely true.
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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.
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Biostatistics
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Steps in Hypothesis Testing
test statistic
• For example, if our hypothesis is
H0 : popN mean = 120 vs. H1 : popN mean  120
• Test statistic might be:
sample mean  hypothesized mean
t
standard error
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Biostatistics
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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
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Biostatistics
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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.
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Biostatistics
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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
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Biostatistics
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Hypothesis Testing
P-values
 Generally, p<0.05 considered significant
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Biostatistics
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Hypothesis Testing
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Biostatistics
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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.
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Biostatistics
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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.
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Biostatistics
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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.
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Biostatistics
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Hypothesis Testing
Test Statistic:
The mean change in SBP (pre – post) divided by the
standard error of the differences.
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Biostatistics
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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.
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Biostatistics
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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.
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Biostatistics
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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.
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Biostatistics
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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:
S2
Estimates
——————> 2
(popn variance)
Interval Estimation
Recall, a one-sample t-test on the
population mean. The test statistic was
x  0
t
s
n
This can be rewritten to yield:
Interval Estimation
Confidence Interval for :
x
 tCC s
n
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)