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Analytic Epidemiology

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

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

Textbook (Gordis):

Chapter 11

Rothman: Random error and the role of statistics. In Epidemiology: an Introduction, Chapter 6, pages 113-129.

Scientific Method

(not unique to epi)

--- Formulate a hypothesis

--- Test the hypothesis

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

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.

The “Biostatistican’s” way

H0: “Null” hypothesis (assumed)

H1: “Alternative” hypothesis

The “Epidemiologist’s” way

Direct risk estimate

(e.g. best estimate of risk of disease

associated with the exposure).

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)

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.

“Association”

Statistical dependence between two variables:

• Exposure(risk factor, protective factor,

predictor variable, treatment)

• Outcome(disease, event)

“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.

Ways to Express Hypotheses:

1. Suggest possible events…

The incidence of tuberculosis will

increase in the next decade.

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.

Ways to Express Hypotheses:

3. Suggest cause-effect relationship….

Cigarette smoking is a cause of lung

cancer

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

- 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

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.

- 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)

• Risk Difference (RD)

• Relative Risk (RR)

--- Risk Ratio (RR)

--- Rate Ratio (RR)

• Odds Ratio (OR)

• Risk Difference (RD)

The absolute difference in the incidence (risk) of disease between the exposed group and the non-exposed (“reference”) group

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

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

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

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.

• 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)”}

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

• If the relative risk estimate is > 1.0,

the exposure appears to be a risk

factor for disease.

• If the relative risk estimate is < 1.0,

the exposure appears to be protective

of disease occurrence.

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.

Note that the row and

column headings have

been arbitrarily switched

from the prior example.

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.

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.

RR = IE+ / IE-

RR = (10 / 840) / (16 / 2,240)

RR = 0.0119 / 0.0071 = 1.68

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.

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.

• 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

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.

• 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.

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

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)

OR = (12 / 9) / (88 / 391)

OR = 1.333 / 0.225 = 5.92

OR = (ad) / (bc)

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?)

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

- 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)

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)

The odds ratio will provide a good estimate of the

risk ratio when:

2. The effect size is small or modest.

(40 / 120) 0.333

OR = ------------ = ------- = 1.0

(60 / 180) 0.333

40 / (40 + 60) 0.40

RR = -------------------- ------ = 1.0

120 / 120 + 180) 0.40

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

(20 / 50) 0.40

RR = ------------ = ------- = 4.0

(10 / 100) 0.10

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