1. Analytic Epidemiology
Unit 4:
Analytic Epidemiology

2. 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

3. 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

4. Assigned Readings:
Textbook (Gordis):
Chapter 11
Rothman: Random error and the role of statistics. In Epidemiology: an Introduction, Chapter 6, pages

5. Analytic Epidemiology
Study of the DETERMINANTS of
health-related events

6. Hypothesis Formulation
Scientific Method
(not unique to epi)
--- Formulate a hypothesis
--- Test the hypothesis

7. 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

8. 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.

9. Hypothesis Formulation
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).

10. Hypothesis Formulation
Biostatistican:
H0: There is no association between the
exposure and disease of interest
H1: There is an association between the
(beyond what might be expected
from random error alone)

11. 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.

12. Hypothesis Formulation
“Association”
Statistical dependence between two variables:
• Exposure (risk factor, protective factor,
predictor variable, treatment)
• Outcome (disease, event)

13. 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.

14. Hypothesis Formulation
Ways to Express Hypotheses:
1. Suggest possible events…
The incidence of tuberculosis will
increase in the next decade.

15. 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.

16. Hypothesis Formulation
Ways to Express Hypotheses:
3. Suggest cause-effect relationship….
Cigarette smoking is a cause of lung
cancer

17. 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

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

19. 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.

20. “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)

21. “Measures of Effect” • Risk Difference (RD) • Relative Risk (RR)
--- Risk Ratio (RR)
--- Rate Ratio (RR)
• Odds Ratio (OR)

22. “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

23. “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-

24. “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, develop mesothelioma over 10 years D+ D- E+ 14
100 E- 12
200

25. “Risk Difference” D+ D- E+ 14 86 100 E- 12 188 200
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.

26. {“Relative Risk (RR)”}
“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)”}

27. The ‘null’ value (1.0) CIexposed = 0.0026 RR = 1.0
CInon-exposed =
CIexposed =
CInon-exposed = 0.49
IRexposed = per 100K
IRnon-exposed = per 100K
RR = 1.0
RR = 1.0
RR = 1.0

28. The ‘null’ value (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.

29. “Risk Ratio” E+ E- D+ D- 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, 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.

30. “Risk Ratio” E+ E- D+ 10 16 D- 840 2,240 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, have attempted suicide.
Of 840 children subjected to physical abuse, have attempted suicide. E+ E- D+ 10 16 D-
840
2,240

31. “Risk Ratio” E+ E- D+ 10 16 D- 830 2,224 840 2,240 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 = / = 1.68

32. “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.

33. “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.

34. “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

35. “Rate Ratio” Expos. D+ D- PY High 9 --- 840 Mod 14 900 Low 12 450 D+IR RR
High 9
---
840
0.0107
1.0
Mod 14
900
0.0156
1.46
Low 12
450
0.0267
2.50

36. “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.

37. “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.

38. “Odds Ratio”
Hypothesis: Eating chili peppers is associated with development of gastric cancer.
Cases:
ate chili peppers did not eat chili peppers
Controls:
ate chili peppers did not eat chili peppers D+ D- E+ E-

39. “Odds Ratio” D+ D- E+ 12 (a) 88 (b) E- 9 (c) 391 (d) 21 479
Hypothesis:
Eating chili peppers is associated with
development of gastric cancer.
Cases:
ate chili peppers did not eat chili peppers
Controls: ate chili peppers 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 = / = 5.92
OR = (ad) / (bc)

40. “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?)

41. 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

42. 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)

43. 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 / ( ) 0.40
RR = = 1.0
120 / ) 0.40

44. Odds Ratio & Risk Ratio (20 / 10) 2.0
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