Download Basic summaries for epidemiological studies

Basic summaries for
epidemiological
studies
(Session 04)
SADC Course in Statistics
Learning Objectives
At the end of this session, you will be able to
• correctly distinguish and use ideas of
prevalence and incidence
• explain the concepts of risk in relation to
health outcomes, and of what may be
“causal” factors
• use the concepts of relative risk and odds
ratio in relation to simple epidemiological
studies
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Attribute Data
An attribute is an ascertainable characteristic
either present or absent in an individual, so
that the “measurement” on an individual
can be represented as either 1 or 0.
Many measures in epidemiology are of this
type e.g. a test for HIV seropositivity yields
such a 0/1 response. This may still involve
expert interpretation & judgment, with
possibility of false positives and false
negatives.
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Point Prevalence
Prevalence concerns the number of instances
of attribute in the popn, usually at a point in
time, relative to the number at risk, i.e.
expressed as a proportion, a percentage,
per 1000 or even per million where +s are
rare. So point prevalence (as a %age) is
No. individuals with + attribute at time point
No. of indiv.s in population at risk at time point
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X
100
4
Period Prevalence
This refers to number of cases known to
have been prevalent during a period e.g. a
year.
Numerator above wd be replaced by sum of
(1) no. of prevalent cases at start of year,
and (2) no. of new cases arising during the
period.
Denominator usually then a mid-year figure
for population at risk.
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Prevalence: notes
• Occasionally “prevalence” is used for absolute
number of cases/instances – best not to call
this “prevalence”!
• Both point and period prevalence are snapshot
figures. They are NOT rates.
• Period prevalence sensible for short-duration
condition where numbers can rise/fall fast.
• No. “at risk” needs thought e.g. males only for
prostate conditions.
• Prevalences can be age-specific.
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Incidence
Incidence (always a rate ~ a flow statistic)
as a population measure is normally on a
yearly rate basis. As a proportion:No. of new cases arising in a period of 1 yr.
Mid-yr. population at risk
As with prevalence, often put as %, ‰ etc
• Watch out for non-experts confusing or
misusing the terms prevalence & incidence!
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Relationship of prevalence & incidence
When prevalence P is relatively small and
condition is of limited duration (say
averaging time T) and population is in a
“steady state”, then approximately:-
P=IxT
where I = incidence.
Exercise ~ try to express in words a rough
justification for the above expression.
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Probability, risk or cumulative incidence
Sometimes a study population is relatively
small, or a sample can be followed up.
Then we can calculate “risk” or cumulative
incidence as:-
No. new cases arising in one year
No. healthy individuals in popn at start of yr
This is then an estimated probability; note
the mortality rate of session 14 is an
example of this.
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Sources of risk: 1
Much of epidemiology concerns “risk factors”
that may be “causes” of the disease.
There are logical difficulties in proving
causation, & often a complex set of predisposing and influencing factors.
In simplest case, consider just one risk factor
e.g. cigarette smoking, and reduce the risk
factor ~ as well as disease attribute ~ to
present/absent.
Discuss what might be more realistic model!
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Sources of risk: 2
With one Yes/No attribute and one “present/absent”
risk factor a 2x2 table of frequencies could be:Diseased
Not
Total
diseased
Risk factor
present
a
b
a+b
c
d
c+d
b+d
a+b+c+d
= n
Risk factor
absent
Total
a+c
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Cohort study
This involves selecting, & following through a
period of time, individuals some with risk
factor present, some absent. Outcome
observation = no. with disease at endpoint.
In a general population cohort study only n is
fixed. If low general exposure to risk,
(a + b) will be small relative to n ~ costly,
so where possible (a + b), (c + d) often
selected e.g. to be equal sample sizes.
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Cohort study relative risk: 1
With observed frequencies a, b, c, d as above
the disease risk (over the study duration)
among:the risk-factor + group is: a/(a + b)
the risk-factor – group is: c/(c + d)
The relative risk is the ratio of these two
risks:a . (c + d)
RR =
(a + b). d
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Cohort study relative risk: 2
The relative risk is the ratio of these two
risks:a . (c + d)
RR =
(a + b). c
Often disease rates are relatively low, so
a/
a/ ; c/
c/ and then
≈
≈
(a + b)
b
(c + d)
d
RR ≈ a.d/b.c – described as the “odds ratio”
or “approximate relative risk”, with
a/ being odds of getting disease, having the
b
exposure, c/d odds not having the exposure.
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Cohort study relative risk: 3
Example ~ population of miners
Asbestos
Lung cancer +
No LC i.e. –
Total
Exposured
58
372
430
Not exposed
27
343
370
Total
85
715
800
RR = (58/430)/(27/370) = 1.85
Odds ratio = (58/372)/(27/343) = 1.98
Similar representations of extra risk factor due to
occupational asbestos exposure.
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Case-control relative risk
In a case-control study (module I1, sess. 05)
numbers of lung cancer positive “cases”
and lung cancer negative “controls” would
be fixed by design. RR cannot be
calculated, but the same odds ratio can, &
is used as approximation to relative risk.
Odds ratios are statistically modelled by
professional epidemiologists to account for
numerous complicating factors.
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Confounding: 1
Counfounders are “nuisance” variables that
make over-simple conclusions misleading!
Example ~ suppose in a study population the
TRUE average figures are as below, so
tea/coffee drinking adds 4 mg Hg to
diastolic blood pressure:Average diastolic BP
Overweight
Not overweight
Tea/coffee drinker
94
74
Non-drinker of tea/coffee
90
70
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Confounding: 2
Now say numbers of individuals in study are:Numbers of individuals
Overweight
Not overweight
Tea/coffee drinker
300
100
Non-drinker of tea/coffee
50
150
If study ignores obesity and calculates simple
averages, it could expect diastolic BPs as follows:Drinkers: [(94 x 300) + (74 x 100)]/(300 + 100)
= 89;
non-drinkers: [(90 x 50) + (70 x 150)]/(50 + 150) = 75.
Misleading 14 mg difference. Confounders only
corrected if someone thinks of them!
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Practical work follows to
ensure learning objectives
are achieved…
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