EPB PHC 6000 EPIDEMIOLOGY FALL, 1997

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Interpreting Epidemiologic Results
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Interpreting Results
Four possible outcomes of any epidemiologic study
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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.
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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.
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Interpreting Results
Example
IE 15 / (15 85) 0.15 IE- 10 / (10 90)
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 (RR1.5), the p-value of 0.30 exceeds
the fixed alpha level of 0.05. 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).
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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.
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Interpreting Results
Example
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.
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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 (thesmaller 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).
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Interpreting Results
Trade-offs between fixed alpha and beta levels
Reducing the fixed alpha level (e.g. to lt
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.
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Interpreting Results
Trade-offs between fixed alpha and beta levels
Increasing the fixed alpha level (e.g. to
lt 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.
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Interpreting Results
Power with given sample size and risk ratio (?
0.05) Risk ratio needed for 80 power with
given sample size
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Interpreting Results
The p-value is NOT the index of causality It is
an arbitrary quantity with no direct relationship
to biology
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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 lt 0.05). This
leads to a range of possible values (confidence
interval) around the point estimate).
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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.
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Interpreting Results
Example
IE 15 / (15 85) 0.15 IE- 10 / (10 90)
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.
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Interpreting Results
Example Calculation of 95 C.I. For Odds Ratio
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 1.96 (sqrt(1/32
1/825 1/56 1/1,048)) (0.73)exp 1.96
(sqrt(0.0513)) (0.73)e0.44 lower
limit (0.73)e-0.44 0.47 upper limit
(0.73)e0.44 1.13
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Interpreting Results
Interpretation of C.I. For OR and RR
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.
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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.
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Analytic Study Designs
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Analytic Study Designs
Randomized trial Prospective retrospective
cohort studies Case-control study
Case-crossover study Cross-sectional study
(prevalence survey)
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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)
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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
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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
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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
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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)
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Analytic Study Designs
Retrospective cohort study
Exposure Disease

?
?
Both exposure and disease have already occurred
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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)
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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
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Analytic Study Designs
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
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Case-Crossover Study
Hypothesis Heavy physical insertion (HPI) is
associated with short-term (within 48 hours) risk
of myocardial infarction
How do we calculate the conditional odds
ratio (COR)?
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Case-Crossover Study
Hypothesis Heavy physical insertion (HPI) is
associated with short-term (within 48 hours) risk
of myocardial infarction
Use only the discordant pairs COR HPI
0-48 ------------- HPI 49-96 3 / 2 1.5
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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)