EPB PHC 6000 EPIDEMIOLOGY FALL, 1997

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Unit 4 Analytic Epidemiology
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Unit 4 Learning Objectives 1. Understand
hypothesis formulation in epidemiologic
studies. 2. Understand and calculate measures of
effect (risk difference, risk ratio, rate ratio,
odds ratio) used to evaluate epidemiologic
hypotheses. 3. Understand statistical parameters
used to evaluate epidemiologic hypotheses and
results --- P-values --- Confidence
intervals --- Type I and Type II error --- Power
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• Unit 4 Learning Objectives (cont.)
• 4. Recognize the primary study designs used to
  evaluate epidemiologic hypotheses
• --- Randomized trial
• --- Prospective retrospective cohort
  studies
• --- Case-control study
• --- Case-crossover study
• --- Cross-sectional study

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Assigned Readings Textbook (Gordis) Chapter
11 Rothman Random error and the role of
statistics. In Epidemiology an Introduction,
Chapter 6, pages 113-129.
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Analytic Epidemiology
Study of the DETERMINANTS of health-related events
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Hypothesis Formulation
Scientific Method (not unique to
epi) --- Formulate a hypothesis --- Test the
hypothesis
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Basic Strategy of Analytical Epi
1. Identify variables you are interested
in Exposure Outcome 2. Formulate a
hypothesis 3. Compare the experience of two
groups of subjects with respect to the exposure
and outcome
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Basic Strategy of Analytical Epi
Note Assembling the study groups to compare,
whether on the basis of exposure or disease
status, is one of the most important elements of
study design. Ideally, we would like to know
what happened to exposed individuals had they not
been exposed, but this is counterfactual since,
by definition, such individuals were exposed.
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Hypothesis Formulation
The Biostatisticans way H0 Null
hypothesis (assumed) H1 Alternative
hypothesis The Epidemiologists way Direct
risk estimate (e.g. best estimate of risk of
disease associated with the exposure).
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Hypothesis Formulation
Biostatistican H0 There is no association
between the exposure and disease of
interest H1 There is an association between
the exposure and disease of interest (beyond
what might be expected from random error alone)
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Hypothesis Formulation
Epidemiologist What is the best estimate of the
risk of disease in those who are exposed compared
to those who are unexposed (i.e. exposed are at
XX times higher risk of disease). This moves
away from the simple dichotomy of yes or no for
an exposure/disease association to the
estimated magnitude of effect irrespective of
whether it differs from the null hypothesis.
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Hypothesis Formulation
Association Statistical dependence between two
variables Exposure (risk factor, protective
factor, predictor variable, treatment)
Outcome (disease, event)
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Hypothesis Formulation
Association The degree to which the rate of
disease in persons with a specific
exposure is either higher or lower than
the rate of disease among those without
that exposure.
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Hypothesis Formulation
Ways to Express Hypotheses 1. Suggest possible
events The incidence of tuberculosis will
increase in the next decade.
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Hypothesis Formulation
Ways to Express Hypotheses 2. Suggest
relationship between specific exposure and
health-related event A high cholesterol intake
is associated with the development (risk) of
coronary heart disease.
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Hypothesis Formulation
Ways to Express Hypotheses 3. Suggest
cause-effect relationship. Cigarette smoking
is a cause of lung cancer
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Hypothesis Formulation
Ways to Express Hypotheses 4. One-sided vs.
Two-sided One-sided example Helicobacter
pylori infection is associated with increased
risk of stomach ulcer Two-sided
example Weight-lifting is associated with risk
of lower back injury
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Hypothesis Formulation

• Guidelines for Developing Hypotheses
• State the exposure to be measured as
• specifically as possible.
• State the health outcome as
• specifically as possible.
• Strive to explain the smallest amount
• of ignorance

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Hypothesis Formulation
Example Hypotheses POOR Eating junk food is
associated with the development of cancer.
GOOD The human papilloma virus (HPV) subtype
16 is associated with the development of cervical
cancer.
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Measures of Effect

• Used to evaluate the research hypotheses
• Reflects the disease experience of
• groups of persons with and without the
• exposure of interest
• Often referred to as a point estimate
• (best estimate of exposure/disease
• relationship between the two groups)

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Measures of Effect
Risk Difference (RD) Relative Risk
(RR) --- Risk Ratio (RR) --- Rate Ratio
(RR) Odds Ratio (OR)
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Measures of Effect
Risk Difference (RD) The absolute difference
in the incidence (risk) of disease between the
exposed group and the non-exposed (reference)
group
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Risk Difference
Hypothesis Asbestos exposure is associated

with mesothelioma Results Of 100
persons with high asbestos exposure,
14
develop mesothelioma over 10 years Of 200
persons with low/no asbestos exposure,
12 develop
mesothelioma over 10 years
D D-
E
E-

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Risk Difference
Hypothesis Asbestos exposure is associated
with mesothelioma Result
s Of 100 persons with high asbestos exposure,
14 develop mesothelioma over 10 years Of 200
persons with low/no asbestos exposure,
12 develop mesothelioma over
10 years
D D-
E 14 100
E- 12 200

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Risk Difference
Hypothesis Asbestos exposure is associated with
mesothelioma Results Of 100 persons with
high asbestos exposure, 14 develop mesothelioma
over 10 years Of 200 persons with low/no
asbestos exposure, 12 develop mesothelioma over
10 years
D D-
E 14 86 100
E- 12 188 200

RD IE IE-
RD (14 / 100) (12 / 200)
RD 0.14 0.06 0.08
The absolute 10-year risk of mesothelioma is 8
higher in persons with asbestos exposure compared
to persons with low or no exposure to asbestos.
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Measures of Effect
Risk Ratio Rate Ratio Compares the
incidence of disease (risk) among the exposed
with the incidence of disease (risk) among the
non-exposed (reference) by means of a
ratio. The reference group assumes a value of
1.0 (the null value)
Relative Risk (RR)
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The null value (1.0)
CIexposed 0.0026 CInon-exposed
0.0026 CIexposed 0.49 CInon-exposed
0.49 IRexposed 0.062 per
100K IRnon-exposed 0.062 per 100K
RR 1.0
RR 1.0
RR 1.0
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The null value (1.0)
If the relative risk estimate is gt 1.0, the
exposure appears to be a risk factor for
disease. If the relative risk estimate is lt
1.0, the exposure appears to be protective of
disease occurrence.
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Risk Ratio
Hypothesis Being subject to physical abuse
in childhood is associated with lifetime risk of
attempted suicide Results Of
2,240 children not subject to physical abuse,
16 have attempted suicide. Of 840 children
subjected to physical abuse,
10 have attempted suicide.
E E-
D
D-

Note that the row and column headings have been
arbitrarily switched from the prior example.
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Risk Ratio
Hypothesis Being subject to physical
abuse in childhood is associated with lifetime
risk of attempted suicide Results Of
2,240 children not subject to physical abuse,
16 have attempted suicide. Of 840 children
subjected to physical abuse,
10 have attempted suicide.
E E-
D 10 16
D-
840 2,240
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Risk Ratio
Hypothesis Being subject to physical
abuse in childhood is associated with lifetime
risk of attempted suicide Results Of
2,240 children not subject to physical abuse,
16 have attempted suicide. Of 840 children
subjected to physical abuse, 10 have attempted
suicide.
E E-
D 10 16
D- 830 2,224
840 2,240
RR IE / IE-
RR (10 / 840) / (16 / 2,240)
RR 0.0119 / 0.0071 1.68
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Risk Ratio
RR IE / IE- 1.68
Children with a history of physical abuse
are approximately 1.7 times more likely to
attempt suicide in their lifetime compared to
children without a history of physical abuse.
The risk of lifetime attempted suicide
is approximately 70 higher in children with
a history of physical abuse compared to
children without a history of physical abuse.
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Rate Ratio
Hypothesis Average daily fiber intake is
associated with risk of colon cancer Results
Of 112 adults with high fiber intake
followed for 840 person yrs, 9 developed
colon cancer. Of 130 adults with moderate
fiber intake followed for 900 person yrs, 14
developed colon cancer Of 55 adults with
low fiber intake followed for 450 person yrs,
12 developed colon cancer.
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Rate Ratio
Expos. D D- PY
High 9 --- 840
Mod 14 --- 900
Low 12 --- 450
Assume that high fiber intake is the reference
group (value of 1.0) Compare the
incidence rate (IR) of colon cancer Moderate
fiber intake versus high fiber intake Low fiber
intake versus high fiber intake
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Rate Ratio
Expos. D D- PY
High 9 --- 840
Mod 14 --- 900
Low 12 --- 450
D D- PY IR RR
High 9 --- 840 0.0107 1.0
Mod 14 --- 900 0.0156 1.46
Low 12 --- 450 0.0267 2.50
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Rate Ratio
RR Imoderate / Ihigh 1.46 RR
Ilow / Ihigh 2.50
Persons with moderate fiber intake are at
1.46 times higher risk of developing colon
cancer than persons with high fiber intake.
Persons with low fiber intake are at 2.50
times higher risk of developing colon cancer
than persons with high fiber intake.
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Measures of Effect
Odds Ratio (OR) Compares the odds of exposure
among those with disease to the odds of exposure
among those without the disease. Does not
compare the incidence of disease between groups.
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Odds Ratio
Hypothesis Eating chili peppers is associated
with development of gastric cancer.
Cases 21 12 ate chili peppers 9 did not
eat chili peppers Controls 479 88 ate chili
peppers 391 did not eat chili peppers
D D-
E
E-

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Odds Ratio
Hypothesis Eating chili peppers
is associated with development
of gastric cancer.
Cases 21 12 ate chili peppers 9 did not
eat chili peppers Controls 479 88 ate
chili peppers 391 did not eat chili peppers
OR (a / c) / (b / d)
D D-
E 12 (a) 88 (b)
E- 9 (c) 391 (d)
21 479
OR (12 / 9) / (88 / 391)
OR 1.333 / 0.225 5.92
OR (ad) / (bc)
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Odds Ratio
OR 5.92
The odds of being exposed to chili peppers
are 5.92 times higher for gastric cancer cases
as compared to controls

• (Interpreting OR as RR if appropriate)
• The incidence (or risk) of gastric cancer is
  5.92
• times higher for persons who eat chili peppers
• as compared with persons who do not eat
• chili peppers (Is this appropriate?)

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Odds Ratio Risk Ratio
Relationship between RR and OR The odds ratio
will provide a good estimate of the risk ratio
when 1. The outcome (disease) is
rare OR 2. The effect size is small or modest
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Odds Ratio Risk Ratio

• The odds ratio will provide a good estimate of
  the
• risk ratio when
• The outcome (disease) is rare

a / (a b ) RR ------------ c / (c d)
D D-
E a b
E- c d

If the disease is rare, then cells (a) and (c)
will be small
OR (a / c) / (b / d)
a / (a b ) a / b ad RR ------------
------ -- OR c / (c d) c / d bc
OR (ad) / (bc)
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Odds Ratio Risk Ratio
The odds ratio will provide a good estimate of
the risk ratio when 2. The effect size is small
or modest.
D D-
E 40 60
E- 120 180

(40 / 120) 0.333 OR ------------ -------
1.0 (60 / 180) 0.333
40 / (40 60) 0.40 RR --------------------
------ 1.0 120 / 120 180) 0.40
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Odds Ratio Risk Ratio
Finally, we expect the risk ratio to be closer to
the null value of 1.0 than the odds ratio.
Therefore, be especially interpreting the odds
ratio as a measure of relative risk when the
outcome is not rare and the effect size is large.
(20 / 10) 2.0 OR ------------ -------
6.0 (30 / 90) 0.333
D D-
E 20 30
E- 10 90

(20 / 50) 0.40 RR ------------ -------
4.0 (10 / 100) 0.10