Part I: Experimental Design Chapters 1 and 2

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Part I Experimental DesignChapters 1 and 2
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Medical Epidemic Context Polio
1916 - 56 killed many hundreds of thousands
Salk vaccine created
Option A
vaccinate a whole number of children measure
the incidence of polio for the year compare
rate of incidence versus prior years evaluate
the effect of the treatment
Potential Outcomes
rate increases, decreases, stays the
same vaccine has a negative, positive, no effect
Problems
epidemic disease rate varies naturally from
year to year 1952 60,000 cases versus 30,000 in
1953 (no tx) parental consent needed for
treatment differences? confounds results
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Medical Epidemic Context Polio
1916 - 56 killed many hundreds of thousands
Salk vaccine created
Option B
divide children into 2 groups as similar as
possible one group gets the vaccination, the
other does not compare the incidence of polio
between the groups evaluate the effect of the
treatment
Different types of Options

• B1 NFIP targeted the at risk kids (grades 1 -
  3) treatment group consenters, control group
  non-consenters

Problems with B1
BUT introduces bias high income parents
more likely to consent high income kids are
more likely to contract polio volunteerism and
SES confounds the conclusions
4
Medical Epidemic Context Polio
Option B2
NFIP targeted the at risk kids (grades 1 -
3) treatment group all grade 2
consenters control group all grades 1 and 3
children
Problems with B2
introduces same bias as before high
income parents more likely to consent high
income kids are more likely to contract polio
AND contagious disease rate of incidence in
grades may vary volunteerism, SES, contagion
confounds the conclusions
critical issue control and treatment groups
must be AS SIMILAR AS POSSIBLE prior to
the intervention
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Medical Epidemic Context Polio
Option B3
targeted the at risk kids (grades 1 -
3) treatment control groups from the
consenters no-consenters formed third group
Problems with B3
moral and ethical issues who gets/does not get
the vaccine human judgment versus chance/random
process
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Salk Vaccine Trial Results
B3 Study Size Rate Treatment 200,000
28 Control 200,000 71 No Consent 350,000
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B2 Study Size
Rate Grade 2 (vaccine) 225,000 25 Grades 1,
3 (Control ) 725,000 54 Grade 2 (No
Consent ) 125,000 44
71 per 100,000 to 28 per 100,000
54 per 100,000 to 25 per 100,000
bias volunteerism SES contagion
no bias

• RCDB study randomized controlled double blind
• reduces bias - controls the influence of chance
  error
• confounding biases NFIP results

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Chapter 1 Review of Concepts

• Comparison as the method for answering questions
• treatment group versus control group
• treatment control group except for the
  treatment
• Random assignment - avoids bias
• over time/with enough subjects, the laws of
  chance ensure that the groups are equivalent
• Confounds uncontrolled variables that effect
  the results
• bias results - exert a systematic influence
• 4. Blind subjects do not know which group they
  are in (placebos)
• 5. Double-blind - neither do the experimenters
• 6. Control 3 uses control subject/group co
  ntrolled experiment

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Generalization and Comparison

• Issue of generalization of results
• NFIP interested in extrapolating their results
  beyond just the children in their study
• Broader question of interest is whether the
  vaccine will prevent polio in all children!!
  
• Comparison forms the basis for inferential
  conclusions
• do results say anything about the population of
  interest?
• Implicit in this approach
• samples versus populations
• sample statistics versus population parameters
• Issue of representativeness is crucial

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Representativeness

• Does my new wonder drug improve the mental health
  of schizophrenics??
• Population all schizophrenics in the USA

Samples issue of how selected and their
representativeness!!
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Controlled Experiments versus Observational
Studies

• random assignment

• pre-existing groups

• control/manipulate

• little/less/no control

• control and measure

• observe and measure

• can examine causation

• correlational only

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Causation versus correlation

• causation does not equal correlation
• smokers versus non-smokers diseases are
  found to be more common among smokers strong
  association between smoking and
  disease explanation smoking causes
  disease BUT not the only possible cause
  some hidden confounding factor - groups
  may differ along some dimension other than
  smoking
• evaluating observational studies how were
  the comparison groups selected how similar are
  they?
• confounding factors can be controlled for
  statistically comparing smaller and more
  homogenous groups male smokers versus male
  non-smokers female smokers (50-59) vs female
  non-smokers (50-59)
• confounds can enter controlled experiments

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Confounding in RCDB experiments

• Clofibrate drug trial middle aged men with heart
  trouble clofibrate treatment group 1,103 20
  died control group 2,789 21
  died
• Results suggested no effect for clofibrate
• Possible reason for the lack of effect
  non-adherence in the Clofibrate group

• Clofibrate group results
• adherers 15 died non-adherers 25 died
• Suggests that Clofibrate works

• Control group results
• adherers 15 died non-adherers 28 died
• Suggests it does not work!!

• Issue adherence vs non-adherence
• self selection/pre-existing
• are adherers different from non-adherers in other
  ways - if so, similar results should be seen in
  the control group

• Conclusions
• Clofibrate does not work
• Adherers differ from non-adherers on other
  variables

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Controlling for confounding in observational
studies

• Berkeley graduate admissions 8,442 m applied
  44 4,321 f applied 35
• Examine major by major - identify those that
  discriminate

Men Major app A 825 62B 560 63C
325 37D 417 33E 191 28F 373
6 Total 2691 44
Women app 108 82
25 68593 34375 35393 24341 7 1835 30
By major no evidence for discrimination some
favor men, some women In each major s admitted
for males and females are about equal Why then
the 44 to 30 difference?

• Reason
• A and B are easy to get into gt50 of the men
  applied here
• C to F more difficult to get into gt90 of the
  females applied here
• Effect choice of major confounded by the effect
  due to gender

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Controlling for confounding in observational
studies
Men Major app A 825 62B 560 63C
325 37D 417 33E 191 28F 373
6 Total 2691 44
Women app 108 82
25 68593 34375 35393 24341 7 1835 30
The major effect is confounded with the gender
effect thus the two groups (men vs women
treatment vs control) differ systematically along
some other dimension (in this case, choice of
major) - not just the treatment (in this case,
gender)
The overall averages indicate the presence of a
gender difference The major averages show little
gender difference Overall male average total
males admitted/total males applied Weighted
average admission rate for each
gender controls for the effects of
major weights the total number of applicants
(both genders) per major
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Controlling for confounding in observational
studies
Men Major app A 825 62B 560 63C
325 37D 417 33E 191 28F 373
6 Total 2691 44
Women app 108 82
25 68593 34375 35393 24341 7 1835 30
Male weighted average (.62)933
(.63)585 (.37)918 (.33)792 (.28)584
(.06)714 39
Total app 933585918792584
714 4526
Weighted average admission rate for each
gender controls for the effects of
major weights the total number of applicants
(both genders) per major The weighted averages
thus are as follows males 39 female
s 43 and control for the confounding
factor of choice of major
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Chapter 2 Review of Concepts

• Observational studies subjects not
  assigned to groups study naturally formed
  groups (gender, smoking etc)
• Observational studies establish
  correlation (association) - and NOT causation
• Confounding variables third
  variable/factor along which the treatment and
  control group differ systematically
• Confounding variables can be controlled
  for compare groups that are relatively
  homogenous with regard to the factor of interest

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Definitions
Variables
a characteristic which varies from person to
person in a study
examples age gender of
siblings marital status height ethnicity
Quantitative
Qualitative
measured by numbers years feet and inches
described by a word/phrase married/single male/fem
ale
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Definitions
Variables
Quantitative
Qualitative
Continuous differences can be arbitrarily small
(infinite of possible values) e.g. age yr,
mth, day, hr, minute, sec.
Discrete variables differ by fixed
amounts (separate indivisible categories)
e.g. family size
Endpoint conventions
need to decide
center between values
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Scales of Measurement

• data collection measuring observations
• categorizing events/assigning s to
  characterize the event size

Interval Scale ordered categories all category
intervals are equal equal interval distances
reflect equal differences in magnitude no
absolute 0 point meaningless ratios of magnitude

• Nominal Scale
• categories with different names
• simple categorization
• no quantitative distinction
• eg. occupation, gender

Ordinal Scale set of categories with different
names an organized ordered sequence, with
observations ranked in size eg. job performance
Ratio Scale interval scale with an absolute 0
meaningful ratios of numbers do reflect ratios
of magnitude eg. inches
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Part II Descriptive Statistics Chapters 3 The
Histogram
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Descriptive Statistics

• Descriptive statistics reduce this

Frequency Distribution Table x f in 1,000s
0 0.25 1 0.50 2
0.50 3 0.50 4
1 5 1 6 2 7
2 8 3 9 9
10 3 11 2 12
4.50 13 12.50 14 2 15
2.50 16 3.75
50.00

• example educational level of the U.S.
  population 50,000 U.S. families are sampled

Years (x) 0 1 4 8 12 6 10 7 16 2 0 6 14 5 1
7 9 8 4 9 0 1 4 8 12 6 10 7 16 2 0 6 14 5 1
7 9 8 4 9 14 5 1 7 9 8 4 9 0 1 4 8 12 6 0
7 16 2 0 6 14 5 1 7 9 8 4 9 1 2 8
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Descriptive Statistics
Frequency Distribution Table x frequency
0 250 1 500
2 500 3 500 4
1,000 5 1,000 6
2,000 7 2,000 8
3,000 9 9,000 10 3,000 11
2,000 12 4,500 13
12,500 14 2,000 15
2,500 16 3,750 50,000.00
Frequency Distribution Table x freq in 1,000s
0 0.25 1 0.50
2 0.50 3 0.50 4
1 5 1 6 2
7 2 8 3 9
9 10 3 11 2 12
4.50 13 12.50 14 2
15 2.50 16 3.75
50.00
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Descriptive Statistics
Grouped Frequency Distribution Table x f in
1,000s 0 - 5 3,750 5 - 8
7,000 8 - 9 9,000 9 - 12
9,500 12 - 13 12,500 13 - 16
4,500 16 3,750 50,000
Frequency Distribution Table x f in 1,000s
0 0.25 1 0.50 2
0.50 3 0.50 4
1 5 1 6 2 7
2 8 3 9 9
10 3 11 2 12
4.50 13 12.50 14 2 15
2.50 15 3.75
50.00

• summarize masses of data into smaller useful sets
• example educational level of the U.S.
  population 50,000 U.S. families are sampled and
  distribution summarized by a frequency
  distribution grouped frequency distribution

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Descriptive Statistics

• Such summaries can also be done graphically
  using a histogram

Ed Level 0 - 5
years 3,750 7.5 5 - 8 years
7,000 14.0 8 - 9 years 9,000 18.0
9 - 12 years 9,500 19.0 12 - 13
years 12,500 25.0 13 - 16 years
4,500 9.0 16 years/ more
3,750 7.5
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Descriptive Statistics

• Such summaries can also be done graphically
  using a histogram

Ed Level 1960 0
- 5 years 3,750 7.5 5 - 8
years 7,000 14.0 8 - 9 years 9,000
18.0 9 - 12 years 9,500 19.0
12 - 13 years 12,500 25.0 13 - 16
years 4,500 9.0 16
years/ more 3,750 7.5
0 5 8 9 12 13 16
more
Years of Education
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Descriptive Statistics
0 5 8 9 12 13
16 more
Years of Education

• Distributions can be summarized in a number of
  ways
• graphically - the histogram
• by listing the characteristics of the
  distribution
• the shape
• the distributions measure of central tendency
• the variability of the distribution

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Descriptive Statistics How we read and create
histograms?
0 5 8 9 12 13 16
more
Years of Education

• Note
• no vertical (Y) axis
• horizontal (X) scale is in years of education
• blocks cover ranges in the horizontal axis termed
  class intervals
• the area of a block is proportional to the of
  people with education in the corresponding class
  interval

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Drawing a histogram
Step 1 obtain the distribution table which
provides the percentage of data points in each
class interval
Ed Level 1960 0
- 5 years 3,750 7.5 5 - 8
years 7,000 14.0 8 - 9 years 9,000
18.0 9 - 12 years 9,500 19.0
12 - 13 years 12,500 25.0 13 - 16
years 4,500 9.0 16
years/ more 3,750 7.5
Note numbers in the class intervals appear
twice we need to decide what to do with people
who fall right on the line between two class
intervals eg. 5 years of education
Endpoint convention Class interval includes the
left endpoint, excludes the right endpoint
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Educational Level 1960 0 - 5
years 7.5 5 - 8 years 14
8 - 9 years 18 9 - 12 years 19
12 - 13 years 25 13 - 16 years
9 16 years/ more 7.5
Step 2 draw the horizontal axis
Note the class interval sizes vary
Because of this it is incorrect to draw the
horizontal axis like this
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Educational Level 1960 0 - 5
years 7.5 5 - 8 years 14
8 - 9 years 18 9 - 12 years 19
12 - 13 years 25 13 - 16 years
9 16 years/ more 7.5
Step 2 draw the horizontal axis
Note the class interval sizes vary
Because of this it is incorrect to draw the
horizontal axis like this
0 5 8 9 12 13
16 more
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Educational Level 1960 0 - 5
years 7.5 5 - 8 years 14
8 - 9 years 18 9 - 12 years 19
12 - 13 years 25 13 - 16 years
9 16 years/ more 7.5
Step 2 draw the horizontal axis
Note the class interval sizes vary
Because of this it is incorrect to draw the
horizontal axis like this
0 5 8 9 12 13
16 more
The correct way to draw the horizontal axis is
0 5 8 9 2 13
16 more
Years of Education
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Step 3 draw the blocks
Educational Level 1960 0 - 5 years 7.5
What about the units on the vertical axis
Issue block heights their percent ????
BUT 0 - 5 years contains 5 one year units
which together contain 7.5 of the data
25
As drawn the area of the entire block equals
20
Per Year
thus each one year unit should contain 7.5 over 5
or 1.5 per one year unit and our vertical
axis is a density scale in percent per unit
(here unit year)
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5 x 7.5 37.5
7.5
10
Percent
5
0 5 8 9
12 13 16 more
Years of Education
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Step 3 draw the blocks
Educational Level 1960 0 - 5 years 7.5
5 - 8 years 14 8 - 9 years 18 9 - 12
years 19 12 - 13 years 25 13 -
16 years 9 16 years/ more
7.5
Incorrect
Correct
25
20
15
Percent per Year
10
5
0 5 8 9
12 13 16 more
Years of Education
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Review Points
1. Distribution table contains the number/ per
class interval
Educational Level 1960 0 - 5 years 7.5
5 - 8 years 14 8 - 9 years 18 9 - 12
years 19 12 - 13 years 25 13 -
16 years 9 16 years/ more
7.5
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2. Horizontal axis reflects the varying lengths
of the class interval
0 5 8 9
12 13 16 more
Years of Education
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3. Plot the per common unit total class
interval of common units in the class
interval
Note area under the histogram 100 so the
vertical axis is a Density scale as it reflecting
the proportion of the total cases (100) in the
histogram that fall within each particular class
interval
25
20
15
Percent per Year
10
5
0 5 8 9
12 13 16 more
Years of Education
37
4. The height of a block indicates the degree of
crowding
versus interval 9 to 12
interval 16 or more
greater proportion/more people
more crowded
25
20
15
Percent per Year
10
5
0 5 8 9
12 13 16 more
Years of Education