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Introduction to observational medical
studies and measures of association
HRP 261
January 5, 2005
Read Chapter 1, Agresti
To Drink or Not to Drink?
Volume 348:163-164 January 9, 2003
Ira J. Goldberg, M.D.
A number of epidemiologic studies have found an association of alcohol
intake with a reduced risk of cardiovascular disease. These observations
have been purported to explain the so-called French paradox: the lower
rate of cardiovascular disease in….
…..With this in mind, is it time for a randomized
clinical trial of alcohol?
June 05, 2000
Coffee Chronicles
 BY MELISSA AUGUST, ANN MARIE BONARDI, VAL CASTRONOVO, MATTHEW

JOE'S BLOWS Last week researchers reported that coffee might help prevent
Parkinson's disease. So is the caffeine bean good for you or not? Over the years,
studies haven't exactly been clear:
According to scientists, too much coffee may cause...
 1986 --phobias, --panic attacks
 1990 --heart attacks, --stress, --osteoporosis
 1991 -underweight babies, --hypertension
 1992 --higher cholesterol
 1993 --miscarriages
 1994 --intensified stress
 1995 --delayed conception
But scientists say coffee also may help prevent...
 1988 --asthma
 1990 --colon and rectal cancer,...
 2004—Type II Diabetes (*6 cups per day!)
February 14, 1996
Personal Health: Sorting out contradictory findings about
fat and health.
By Jane E. Brody
MANY health-conscious Americans are beginning to feel as if they are being tossed
around like yo-yos by conflicting research findings. One day beta carotene is hailed as a
life-saving antioxidant and the next it is stripped of health-promoting glory and even
tainted by a brush of potential harm. Margarine, long hailed as a heart-saving alternative
to butter, is suddenly found to contain a type of fat that could damage the heart.
Now, after women have heard countless suggestions that a low-fat diet may reduce their breast cancer risk,
Harvard researchers who analyzed data pooled from seven studies in four countries report that this advice
may be based more on wishful thinking than fact.
The researchers, whose review was published last week in The New England Journal of Medicine, found no
evidence among a number of studies of more than 335,000 women that a diet with less than 20 percent of
calories from fat reduced a woman's risk of developing breast cancer. Nor was risk related to the types of fats
the women ate, the study reported.
Is Fat Important? …….
Statistics Humor

The Japanese eat very little fat and suffer fewer heart attacks than the British
or the Americans.

On the other hand, the French eat a lot of fat and also suffer fewer heart attacks
than the British or the Americans.

The Japanese drink very little red wine and suffer fewer heart attacks than the
British or the Americans.

The Italians drink excessive amounts of red wine and also suffer fewer heart
attacks than the British or the Americans.

Conclusion: Eat and drink whatever you like. It's speaking English that kills
you.
Assumptions and aims of
medical studies

1) Disease does not occur at random but is
related to environmental and/or personal
characteristics.
 2) Causal and preventive factors for
disease can be identified.
 3) Knowledge of these factors can then be
used to improve health of populations.
Medical Studies
The General Idea…
Evaluate whether a risk factor (or preventative factor)
increases (or decreases) your risk for an outcome (usually
disease, death or intermediary to disease).
?
Exposure
Disease
Observational vs.
Experimental Studies
Observational studies – the population is observed without
any interference by the investigator
Experimental studies – the investigator tries to control the
environment in which the hypothesis is tested (the
randomized, double-blind clinical trial is the gold standard)
Confounding: A major problem
for observational studies
?
Exposure
Disease
Confounder
Confounding: Example
Alcohol
Lung cancer
Smoking
Why Observational Studies?

Cheaper
 Faster
 Can examine long-term effects
 Hypothesis-generating
 Sometimes, experimental studies are not
ethical (e.g., randomizing subjects to
smoke)
What is risk for a biostatistician?
Risk = Probability of developing a disease or other
adverse outcome (over a defined time period)
In Symbols: P(D)
Conditional Risk = Risk of developing a disease
given a particular exposure
In Symbols: P(D/E)
Odds = Probability of developing a disease divided
by the probability of not developing it
P( D)
In Symbols: P(D)/P(~D)
odds of disease 
1  P ( D)
Possible Observational
Study Designs
Cross-sectional studies
Cohort studies
Case-control studies
Cross-Sectional (Prevalence)
Studies
Measure disease and exposure on a random sample of
the population of interest. Are they associated?
Marginal probabilities of exposure AND disease are valid, but only
measures association at a single time point.
Introduction to the 2x2 Table
Exposure (E)
Disease (D)
a
No Exposure
(~E)
b
No Disease (~D)
c
d
a+c = P(E)
b+d = P(~E)
Marginal probability
of exposure
Marginal probability of
disease
a+b = P(D)
c+d = P(~D)
Agresti Example: Belief in
Afterlife
Yes
Females
435
No or
undecided
147
Males
375
134
810
281
pbelieve/ female
difference
Z

s.e.(difference)
582
509
1091
435
375

 .747; pbelieve/ male 
 .737
582
509
.747  .737
.01

 .37
(.747)(1  .747) (.737)(1  .737) .027

582
509
Cross-Sectional Studies

Advantages:
– Cheap and easy
– generalizable
– good for characteristics that (generally) don’t
change like genes or gender

Disadvantages
– difficult to determine cause and effect
2. Cohort studies:
1.
Sample on exposure status and track
disease development (for rare exposures)

Marginal probabilities (and rates) of developing
disease for exposure groups are valid.
Example: The Framingham
Heart Study

The Framingham Heart Study was established in
1948, when 5209 residents of Framingham, Mass,
aged 28 to 62 years, were enrolled in a prospective
epidemiologic cohort study.
 Health and lifestyle factors were measured (blood
pressure, weight, exercise, etc.).
 Interim cardiovascular events were ascertained
from medical histories, physical examinations,
ECGs, and review of interim medical record.
Cohort Studies
Disease
Exposed
Target
population
Disease-free
cohort
Disease-free
Disease
Not
Exposed
Disease-free
TIME
The Risk Ratio, or Relative Risk (RR)
Exposure (E)
Disease (D)
a
No Exposure
(~E)
b
No Disease (~D)
c
d
a+c
b+d
risk to the exposed
RR 
P(D / E )
P(D /~E)
a /( ac)

b /(bd )
risk to the unexposed
Hypothetical Data
Congestive
Heart Failure
No CHF
High Systolic BP
Normal BP
400
400
1100
2600
1500
3000
400
/
1500
RR 
 2.0
400 / 3000

Advantages/Limitations:
Cohort Studies
Advantages:
– Allows you to measure true rates and risks of disease
for the exposed and the unexposed groups.
– Temporality is correct (easier to infer cause and effect).
– Can be used to study multiple outcomes.
– Prevents bias in the ascertainment of exposure that may
occur after a person develops a disease.

Disadvantages:
– Can be lengthy and costly! More than 50 years for
Framingham.
– Loss to follow-up is a problem (especially if nonrandom).
– Selection Bias: Participation may be associated with
exposure status for some exposures
Case-Control Studies
Sample on disease status and ask
retrospectively about exposures (for rare
diseases)
 Marginal probabilities of exposure for cases and
controls are valid.
• Doesn’t require knowledge of the absolute risks of disease
• For rare diseases, can approximate relative risk
Case-Control Studies
Exposed in
past
Disease
(Cases)
Target
population
Not exposed
Exposed
No Disease
(Controls)
Not Exposed
Example: the AIDS epidemic
in the early 1980’s

Early, case-control studies among AIDS cases and
matched controls indicated that AIDS was
transmitted by sexual contact or blood products.
 In 1982, an early case-control study matched
AIDS cases to controls and found a positive
association between amyl nitrites (“poppers”) and
AIDS; odds ratio of 8.6 (Marmor et al. 1982).
This is an example of confounding.
Case-Control Studies in
History

In 1843, Guy compared occupations of men with
pulmonary consumption to those of men with
other diseases (Lilienfeld and Lilienfeld 1979).
 Case-control studies identified associations
between lip cancer and pipe smoking (Broders
1920), breast cancer and reproductive history
(Lane-Claypon 1926) and between oral cancer and
pipe smoking (Lombard and Doering 1928). All
rare diseases.
 Case-control studies identified an association
between smoking and lung cancer in the 1950’s.
The Odds Ratio (OR)
Exposure (E)
Disease (D)
a
No Disease (~D)
c
No Exposure
(~E)
b
d
c+d=controls
a /( a  b) a
b /( a  b) b ad

 
c /( c  d )
c bc
d /( c  d ) d
Odds of exposure
in the cases The proportion of cases and
P ( E /controls
D ) are set by the
therefore, they
P (~ Einvestigator;
/ D)
do not represent the risk
P ( E / (probability)
~ D)
of developing
P (~ E /disease.
~ D)
Odds of exposure
in the controls
OR 
a+b=cases
The Odds Ratio (OR)
Exposure (E)
Disease (D)
a
No Disease (~D)
c
OR 
P( E / D)
P (~ E / D )
P( E /~ D)
P (~ E / ~ D )
No Exposure
(~E)
b
d
a+b=cases
c+d=controls
a /( a  b) a
b /( a  b) b ad

 
c /( c  d )
c bc
d /( c  d ) d
The Odds Ratio
OR 
P( E / D)
P (~ E / D )
P( E /~ D)
P (~ E / ~ D )
P( D / E )
P (~ D / E ) 1
P( D /~ E )
P (~ D / ~ E ) 1
P ( D& E )
P ( D &~ E )
P (~ D & E )
P (~ D & ~ E )

Via Bayes’ Rule

P( D / E )
P( D /~ E )
 RR
When disease is rare: P(~D)  1
“The Rare Disease Assumption”

The Odds Ratio (OR)
Exposure (E)
Disease (D)
a = P (D& E)
No Exposure
(~E)
b = P(D& ~E)
No Disease (~D)
c = P (~D&E)
d = P (~D&~E)
Odds of disease in
the exposed
OR 
a
c
b
d
ad

bc
Odds of disease in the
unexposed
Properties of the OR (simulation)
6
5
P 4
e
r
c 3
e
n
t
2
1
0
0
0.35
0.7
1.05
1.4
1.75
2.1
Simulated Odds Ratio
2.45
2.8
3.15
3.5
Properties of the lnOR
10
Standard deviation =
Standard deviation =
1 1 1 1
  
a b c d
8
P
e
r
c
e
n
t
6
4
2
0
-1.05
-0.75
-0.45
-0.15
0.15
0.45
lnOR
0.75
1.05
1.35
1.65
1.95
Hypothetical Data
Amyl Nitrite Use
AIDS
20
No Amyl
Nitrite
10
No AIDS
6
24
(20)( 24)
OR 
 8.0
(6)(10)
95% CI  (8.0)e
1.96
1 1 1
1
  
20 6 10 24
1.96
, (8.0)e
1 1 1
1
  
20 6 10 24
30
30
Note that the
size of the
smallest 2x2 cell
determines the
magnitude of
the variance
 (2.47 - 25.8)
Odds Ratios in the literature
Highest Quintile of Mercury (in toenails)
and Risk of Heart Attacks (NEJM Nov 02)
OR= 1.47 (.99-2.14)
•Things
•What
•“An
to think about:
does an Odds Ratio of 1.47 mean?
increased risk of 47%”—is this misleading?
When can the OR mislead?
When is the OR is a good
approximation of the RR?
General Rule of
Thumb:
“OR is a good
approximation as long
as the probability of the
outcome in the
unexposed is less than
10%”
February 25, 1999 Volume 340:618-626
From: “The Effect of Race and Sex on Physicians' Recommendations for Cardiac
Catheterization”
February 25, 1999 Volume 340:618-626
From: “The Effect of Race and Sex on Physicians' Recommendations for Cardiac
Catheterization”




Study overview:
Researchers developed a computerized survey instrument
to assess physicians' recommendations for managing
chest pain.
Actors portrayed patients with particular characteristics
(race and sex) in scripted interviews about their symptoms.
720 Physicians at two national meetings viewed a recorded
interview and was given other data about a hypothetical
patient. He or she then made recommendations about that
patient's care.
Media headlines on Feb 25th,
1999…
Wall Street Journal: “Study suggests race, sex influence
physicians' care.”
New York Times: Doctor bias may affect heart care,
study finds.”
Los Angeles Times: “Heart study points to race, sex
bias.”
Washington Post: “Georgetown University study finds
disparity in heart care; doctors less likely to refer
blacks, women for cardiac test.”
USA Today: “Heart care reflects race and sex, not
symptoms.” ABC News: “Health care and race”
Their results…
The Media Reports: “Doctors
were only 60 percent as likely
to order cardiac
catheterization for women
and blacks as for men and
whites.”
A closer look at the data…
The authors failed to report the
risk ratios:
RR for women: .847/.906=.93
RR for black race: .847/.906=.93
Correct conclusion: Only a 7%
decrease in chance of being
offered correct treatment.
Lessons learned:

90% outcome is not rare!
 OR is a poor approximation of the RR here,
magnifying the observed effect almost 6-fold.
 Beware! Even the New England Journal doesn’t
always get it right!

SAS automatically calculates both, so check how
different the two values are even if the RR is not
appropriate. If they are very different, you have to
be very cautious in how you interpret the OR.
SAS code and output
for generating OR/RR from
2x2 table
Cath
No Cath
Female
305
55
360
Male
326
34
360
data cath_data;
input IsFemale GotCath Freq;
datalines;
1 1 305
1 0 55
0 1 326
0 0 34
run;
data reversed; *Fix quirky reversal of SAS 2x2 tables;
set cath_data;
IsFemale=1-IsFemale;
GotCath=1-GotCath;
run;
proc freq data=reversed;
tables IsFemale*GotCath /measures;
weight freq; run;
SAS output
Statistics for Table of IsFemale by GotCath
Estimates of the Relative Risk (Row1/Row2)
Type of Study
Value
95% Confidence Limits
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Case-Control (Odds Ratio)
0.5784
0.3669
0.9118
Cohort (Col1 Risk)
0.9356
0.8854
0.9886
Cohort (Col2 Risk)
1.6176
1.0823
2.4177
Sample Size = 720
Furthermore…stratification
shows…
Advantages and Limitations:
Case-Control Studies

Advantages:
– Cheap and fast
– Great for rare diseases

Disadvantages:
– Exposure estimates are subject to recall bias (those
with the disease are searching for reasons why they got
sick and may be more likely to report an exposure) and
interviewer bias (interviewer may prompt a positive
response in cases).
– Temporality is a problem (did exposure cause disease or
disease cause exposure?)
Final Note: controlling for
confounders in observational
studies

1. Confounders can be controlled for in the
design phase of a study (restriction or
matching).
 2. Confounders can be controlled for in the
analysis phase of a study (stratification or
multivariate regression).