1. Interpreting
Epidemiologic
Results

2. Interpreting Results DECISION H0 True (No assoc.) H1 True (Yes assoc.)
Four possible outcomes of any epidemiologic study:
DECISION
H0 True
(No assoc.)
H1 True
(Yes assoc.)
Do not reject H0
(not stat. sig.)
Correct decision
Type II
(beta error)
Reject H0
(stat. sig.)
Type I
(alpha error)

3. When evaluating the incidence of disease
Interpreting Results
When evaluating the incidence of disease
between the exposed and non-exposed groups, we need guidelines to help determine whether there is a true difference between the two groups, or perhaps just random variation
from the study sample.

4. Interpreting Results “Conventional” Guidelines:
• Set the fixed alpha level (Type I error) to 0.05
This means, if the null hypothesis is true, the
probability of incorrectly rejecting it is 5% of less.
The “p-value” is a measure of the compatibility of
the data and the null hypothesis.
DECISION
H0 True
H1 True
Do not reject H0
(not stat. sig.)
Reject H0
(stat. sig.)
Type I
(alpha error)

5. Interpreting Results Example: IE+ = 15 / (15 + 85) = 0.15D+ D- E+ 15 85 E- 10 90
IE+ = 15 / ( ) = 0.15
IE- = 10 / ( ) = 0.10
RR = IE+/IE- = 1.5, p = 0.30
Although it appears that the incidence of disease may be higher in the exposed than in the non-exposed (RR=1.5), the p-value of 0.30 exceeds the fixed alpha level of This means that the observed data are relatively compatible with the null hypothesis. Thus, we do not reject H0 in favor of H1 (alternative hypothesis).

6. Interpreting Results Conventional Guidelines:
• Set the fixed beta level (Type II error) to 0.20
This means, if the null hypothesis is false, the
probability of not rejecting it is 20% of less.
The “power” of a study is (1 – beta). This means
having 80% probability to reject H0 when H1 is true.
DECISION
H0 True
H1 True
Do not reject H0
(not stat. sig.)
Type II
(beta error)
Reject H0
(stat. sig.)

7. Interpreting Results Example: N Incid. E- 200 0.10 E+ 0.18 0.21 0.24RR
1.8
2.1
2.4
Power
58%
82%
95%
With the above sample size of 400, and if the alternative hypothesis is true, we need to expect a RR of about 2.1 (power = 82%) or higher to be able to reject the null hypothesis in favor of the alternative hypothesis.

8. Interpreting Results Factors that affect the power of a study:
1. The fixed alpha level (the lower the level, the
the lower the power).
2. The total and within group sample sizes (the smaller the sample size, the lower the power --
unbalanced groups have lower power than
balanced groups).
3. The anticipated effect size (the higher the
expected/observed effect size, the higher
the power).

9. Interpreting Results Trade-offs between fixed alpha and beta levels:
Reducing the fixed alpha level
(e.g. to < 0.01) is considered “conservative.” This reduces the likelihood of a type I error (erroneously rejecting the null hypothesis), but at the expense of increasing the probability of a type II error if the alternative hypothesis is true.

10. Interpreting Results Trade-offs between fixed alpha and beta levels:
Increasing the fixed alpha level
(e.g. to < 0.10) reduces the probability of a type II error (failing to reject H0 when H1 is true), but at the expense of increasing the probability of a type I error if the null hypothesis is true.

11. Interpreting Results Expos-ure N Incid. Risk ratio P- value Power * RR**
None
1000
0.10
1.0
---
Low
500
0.15
1.5
0.006
77%
1.52
Medium
250
0.02
60%
1.64
High
100
0.12
27%
2.08
*Power with given sample size and risk ratio ( = 0.05)
**Risk ratio needed for 80% power with given sample size

12. It is an arbitrary quantity with no direct relationship to biology
Interpreting Results
The p-value is NOT the
index of causality
It is an arbitrary quantity
with no direct relationship to biology

13. Interpreting Results
Since science is based on measurement, the analysis of epidemiologic data is more of a
measurement problem than a problem in decision making (e.g. whether or not p < 0.05).
This leads to a range of possible values
(“confidence interval”) around the point
estimate).

14. Interpreting Results
Confidence Interval: Range of values for a point estimate that has a specified probability of including the true value of the parameter.
Confidence Level: (1.0 – ), usually expressed as a percentage (e.g. 95%).
Confidence Limits: The upper and lower end points of the confidence interval.

15. Interpreting Results Example: IE+ = 15 / (15 + 85) = 0.15D+ D- E+ 15 85 E- 10 90
IE+ = 15 / ( ) = 0.15
IE- = 10 / ( ) = 0.10
RR = IE+/IE- = 1.5, p = 0.30
95% C.I. (0.71, 3.07)
Our best estimate is that the risk of disease is 1.5 times higher in persons exposed compared to persons not exposed, however, we are 95% confident that the true value lies somewhere between 0.71 and 3.07.

16. Interpreting Results lower limit = (0.73)e-0.44 = 0.47
Example Calculation of 95% C.I. For Odds Ratio: D+ D- E+ 32
825 E- 56
1,048
32 / 56
OR = = 0.73
825 / 1,048
95% C.I. = (OR)exp [(+ 1.96(sqrt(1/a + 1/b + 1/c + 1/d))]
= (0.73)exp [ (sqrt(1/32 + 1/ /56 + 1/1,048))]
= (0.73)exp [ (sqrt(0.0513))]
=(0.73)e+0.44
lower limit = (0.73)e-0.44 = 0.47
upper limit = (0.73)e+0.44 = 1.13

17. Interpreting Results Interpretation of C.I. For OR and RR: 32 / 56
825 E- 56
1,048
32 / 56
OR = = 0.73
825 / 1,048
95% C.I. = 0.47, 1.13
If the 95% confidence interval includes the null value
of 1.0, then the test result is not “statistically significant.”
Because the OR and RR have a lower bound of 0, but no upper bound, the 95% C.I. will tend to be skewed to the right of the point estimate.

18. Interpreting Results Interpretation of C.I. For OR and RR:
The C.I. provides an idea of the likely magnitude of the effect and the random variability of the point estimate.
On the other hand, the p-value reveals nothing about the magnitude of the effect or the random variability of the point estimate.
In general, smaller sample sizes have larger C.I.’s due to uncertainty (lack of precision) in the point estimate.

19. Analytic
Study Designs

20. Analytic Study Designs
• Randomized trial
• Prospective & retrospective cohort studies
• Case-control study
• Case-crossover study
• Cross-sectional study (prevalence survey)

21. Analytic Study Designs
Randomized trial:
• Used to evaluate new approaches to treatment and prevention
• Can be conducted in clinical settings (individual subjects), or in the community (groups of subjects)
• Investigator (experimenter) selects (assigns) the exposure status of each subject or group (e.g. therapeutic regimen)

22. Analytic Study Designs
Randomized trial:
• Subjects/groups are assigned at random to the exposure
• Participants are followed and the occurrence of disease is compared between the exposure groups (e.g. risk ratio or rate ratio)
• Due to randomization (comparability), may provide the most reliable evidence

23. Analytic Study Designs
Prospective cohort (“follow-up”) study:
• Disease free individuals are selected and their exposure status is ascertained
• Subjects are followed for a period of time to record and compare the incidence of disease between exposed and non-exposed individuals (e.g. risk ratio or rate ratio)
• Good for examining effect of rare exposures and for establishing temporal relationship between exposure and disease

24. Analytic Study Designs
Prospective cohort (“follow-up”) study:
Exposure Disease ? ?
Exposure may or may not have occurred at study entry
Outcome definitely has not occurred at study entry

25. Analytic Study Designs
Retrospective cohort study:
• Investigator has access to exposure data on a group of people
• The study sample is divided into exposed and non-exposed groups
• Both the exposures and outcomes of interest have already occurred (hence “retrospective”)
• The disease experience of exposed and non- exposed groups is compared (e.g. risk ratio or rate ratio)

26. Analytic Study Designs
Retrospective cohort study:
Exposure Disease ? ?
Both exposure and disease have already occurred

27. Analytic Study Designs
Case-control study:
• Subjects selected on basis of their disease status (hence good for rare diseases)
• An appropriate group of “control” subjects (comparison group) is selected
• Both the exposures and outcomes of interest have already occurred
• The presence of the exposure is compared between the two groups (e.g. odds ratio)

28. Analytic Study Designs
Case-crossover study:
• Only subjects (cases) who have experienced the disease of interest are selected
• Investigator postulates a critical exposure period (“empirical induction period”) for the exposure of interest
• Presence of the exposure is compared between the critical exposure period and other periods of exposure (e.g. conditional odds ratio)
• Good for studying effects of transient exposures

29. Analytic Study Designs irrelevant (non-causal)
Case-crossover study:
(A)
(B)
Hypothesized
irrelevant (non-causal)
exposure
Hypothesized
relevant (causal)
exposure
Outcome
event
“Empirical
induction period”
Compare presence of exposure between hypothesized
non-causal (A) and hypothesized causal (B) periods
of exposure

30. Case-Crossover Study
Hypothesis: Heavy physical insertion (HPI) is associated with short-term (within 48 hours) risk of myocardial infarction
Person
HPI: hours prior to MI
HPI: 0-48 hours prior to MI 1 No 2
Yes 3 4 5 6 7 8
How do we
calculate
the
conditional
odds ratio
(COR)?

31. Case-Crossover Study
Hypothesis: Heavy physical insertion (HPI) is associated with short-term (within 48 hours) risk of myocardial infarction
Person
HPI: hours prior to MI
HPI: 0-48 hours prior to MI 1 No 2
Yes 3 4 5 6 7 8
Use only the
discordant pairs
COR =
HPI: 0-48
HPI: 49-96
= 3 / 2 = 1.5

32. Cross-Sectional Study
• Both a descriptive and analytic study design
• Snapshot of the health status of populations at a certain point in time
• For each subject, exposure and disease outcome are assessed simultaneously (hence also called a “prevalence study/survey”)
• Compare prevalence of disease in persons with and without the exposure of interest
(e.g. prevalence ratio – same formula as
risk ratio)