This document provides definitions and examples of key concepts for estimating risk from epidemiological studies, including probability, odds, relative risk, and absolute risk. It discusses how relative risk is calculated from cohort and case-control study designs. Relative risk compares the risk of an outcome between exposed and unexposed groups to determine if exposure is associated with increased risk. The odds ratio, which estimates relative risk, is presented as the measure used to assess association in case-control studies. Examples are provided to demonstrate calculating and interpreting these risk measures.

1. Estimating Risk
Dr. Tarek Tawfik Amin
12/18/2013
Dr. Tarek Tawfik

2. Objectives
• By the end of this session, attendees should
be able to:
1- Differentiate between probability, Odd, and
risk with it variants.
2- Recall the basics for calculating Odds and
relative risk and interpret the results.
3- Define the indications of applying the risk
parameters.

3. Definitions of terms: Probability, risk and Odd
• Probability: Is the proportion (%) of times an event
would occur if an observation was repeated many times.
• Risk: Is the probability of an event among those
experiencing the event divided by the number who
could experience it (at risk).
• Odds: Probability of an event divided by the
probability of the event not happening.

4. Probability
Proportion (%)
0-1 (100%)
The 10 year
probability of OP
hip fracture among
those aged 70 years
is 0.23 (23%).
Odds (chance)
Risk
Ratio
Probability/(1probaility)
0 to infinity
The Odds for OP
hip fracture is
0.23/(1.0.23)=0.30
Ratio (rate)
0 to infinity
No denominator
Denominator
Incidence of OP hip
fracture among
those aged 70 years.
Attack rate is an
other example

5. Risk

6. A-Absolute Risk
The incidence of a disease in a population is termed absolute risk.
Can indicate the magnitude of risk in a group of people with a
certain exposure, but:
It does not take into consideration the risk of disease in the nonexposed individuals,
It does not indicate whether the exposure is associated with an
increased risk of disease.
Absolute risk doe not stipulate an explicit comparison.
Rubella in 1st trimester: what is the risk that my child will be
malformed? Abortion will be decided on the basis of this
information.
12/18/2013
Dr. Tarek Tawfik

7. B-Relative risk: Determination that a certain disease is
associated with a certain exposure.
By using the (case-control) and cohort studies we can assess
whether there is an excess risk of disease in persons who have
been exposed.
Comparing different risks among different groups to assess the
presence of excessive risk (the incidence rate „attack rates‟ and
the difference in the risks).
Estimation of relative risks are vital in determining who will
be at a higher risk following the exposure.
12/18/2013
Dr. Tarek Tawfik

8. Relative Risk (concept)
o Case-control and cohort studies are designed to
determine whether there is an association between
exposure to a factor and development of a disease.
If an association exists, how strong is it?
o In cohort study: what is the ratio of the risk of disease
in exposed individuals to the risk of disease in nonexposed individuals? (RR=relative risk).
Risk in exposed (incidence in the exposed)
Relative risk (RR) =
Risk in non-exposed (incidence in the non-exposed)

9. Basic Structure of cohort study
Diseased
Disease-free
The Relative Risk is calculated for exposure
Develop
Disease (a)
Sample
Exposed
to factor
Develop
Disease (c)
Diseasefree
Unexposed
to factor
Disease-free
(d)
Future time
Present time
Starting point
Disease-free
(b)
Follow
Comparing the incidence of disease in each group
Population

10. Basic structure of case-control design
Population
Diseased
Unexposed to factor
(b)
Diseased
(cases)
Sample
The Odds “chance of exposure
Is calculated between both groups
Exposed to factor
(a)
Disease-free
Exposed to factor
(c)
Disease-free
(controls)
Unexposed to factor
(d)
Trace
Past time
Present time
Starting point

11. The following table depicts the outcomes of isoniazid/placebo trial among children
with HIV (death within 6 months).
What is the risk of dying?
Interventions Dead (within
Alive
Total
6 months)
Placebo
21
110
131
Risk=21/131=0.160
Isoniazid
11
121
132
Risk=11/132=0.083
Absolute risk difference (ARD)=risk in placebo-risk in isoniazid= 0.077
Net relative risk (NRR)=risk in placebo/risk in isoniazid= 1.928
Relative risk reduction (RRR)=risk in placebo-risk in isoniazid/risk in placebo= 0.48
Number needed to treat (NNT)=1/ARD=1/0.077=13

12. Relative risk (RR)
Mammography
Breast cancer
No breast cancer
Total
Positive
a-10
b-90
100
Negative
c-20
d-998980
100,100
In Cohort design
RR= a/(a+b)÷c/(c+d)
10/(100) ÷20(100,100)=0.1/0.0002= 500

13. The relative risk (RR)
Lung cancer
Smokers
Non
18
6
No lung
cancer
582
1194
Risk for smokers=18/600=0.03
Risk for non-smokers=6/1200=0.005
RR=0.03/0.005=6
Total
600
1200

14. Interpreting the Relative Risk
(measure the strength of the association)
If RR = 1
If RR > 1
If RR < 1
Risk in exposed equal to risk in nonexposed (no association).
Risk in exposed greater than risk in nonexposed (positive association; possibly
causal).
Risk in exposed less than risk in nonexposed (negative association; possibly
protective).

15. Calculating the Relative Risk in Cohort Studies
Then follow to see whether
Disease develops
a
First
select
a+b
b
c
d
Totals
a+b
Incidence rate of
disease
a
a+b
Exposed
No exposed
a
Disease does not
develop
= incidence in exposed
c
c+d
c+d
c
c+d
= incidence in non-exposed

16. Hypothetical Cohort
3,000 smokers and 5,000 non-smokers to investigate the relation of smoking to
the development of coronary heart disease (CHD) over a 1-year period.
Develop CHD
Do not develop
CHD
Totals
Incidence per
1,000/year
Smoke cigarettes
84
2,916
3,000
28.0
Do not smoke
cigarettes
87
4,913
5,000
17.4
Incidence among the exposed=
84/3,000 = 28.0 per 1,000
Relative risk =
Incidence in exposed
Incidence in non-exposed =
Incidence among the non-exposed
= 87/5000 =17.4 per 1,000
28.0/17.4 = 1.61

17. Example: the British Heart Study
A large cohort study of 7735 men aged 40-59 years
randomly selected from general practices in 24 British
towns, with the aim of identifying risk factors for ischemic
heart disease. At recruitment to the study, the men were
asked about a number of demographic and lifestyle,
including information on cigarette smoking habits.
Of the 7718 men who provided information on smoking
status, 5899 (76.4 %) had smoked at some stage during their
lives (including those who were current smokers and those
who were ex-smokers).
Over subsequent 10 years, 650 of these 7718 men (8.4 %)
had a myocardial infarction (MI).
12/18/2013
Dr. Tarek Tawfik

18. MI in subsequent 10 years
Yes
No
Total
Ever smoked
563 (9.5%)
5336 (90.5%)
5899
Never smoked
87 (4.8%)
1732 (95.2%)
1819
Total
650 (8.4%)
7068(71.6%)
7718
Smoking status at baseline
The estimated relative risk=
(563/5899)
(87/1819)
= 2.00
CI = 1.60-2.49
(does not include 1)
The middle aged man who has ever
smoke is twice as likely to suffer a
MI over the next 10 years period as
a man who has never smoked.

19. Odds ratio

20. The Odds ratio (relative odds)
In order to calculate a relative risk, we must have values for
the incidence in the exposed and non-exposed, as can be
obtained in the cohort study.
In a case-control study, however, we do not know the
incidence in the exposed population or the incidence in the
non-exposed population because we start with diseased people
(cases) and non-diseased people (controls).
Hence, we can not estimate the RR in case-control study
directly and we implement another measure of association
called Odds ratio.

21. Defining the Odds ratio in Cohort and Case-control
studies.
Suppose we betting on a horse named Little Beauty, which has a
60% probability of wining the race (P). Little Beauty, therefore has a
40 % probability of losing (1-P). What are the odds that the horse
will win the race?
The odds is defined as: the ratio of the number of ways the event can
occur to the number of ways the event can not occur.
Probability that Little Beauty will win the race
Odds =
Probability that Little Beauty will lose the race
Odds = P/(1-P) or 60 %/40 % = 1.5:1 = 1.5
Probability of wining is 60 %, while the odds (chance) of wining is 1.5
times.
12/18/2013
Dr. Tarek Tawfik

22. Odds ratio (OR)
o An odds ratio (OR) is a measure of association
between an exposure and an outcome.
o The OR represents the odds that an outcome will
occur given a particular exposure, compared to the
odds of the outcome occurring in the absence of
that exposure.
o Odds ratios are most commonly used in casecontrol studies, however they can also be used in
cross-sectional and cohort study designs as well
(with some modifications and/or assumptions).

23. OR
•
•
•
•
Rare disease assumption (prevalence < 10%).
Case control-design
Regression analysis
Meta-analysis

24. Calculation
Case control
study
Exposed
Non-exposed
Diseased
None
Total
Cases+ exposed
(a)
Exposed+ not
diseased (b)
a+b
Cases-not
exposed (c)
Not exposed+ not
diseased (d)
c+d
Odds ratio= a/c÷b/d= ad/bc
Prevalence among the diseased/prevalence among the non-diseased
OR=1 Exposure does not affect odds of outcome
OR>1 Exposure associated with higher odds of outcome
OR<1 Exposure associated with lower odds of outcome

25. Odds ratio
Case control
study
Lung cancer
No lung cancer
Total
Smoking
a-80
b-30
110
None
c-20
d-70
90
80x70=5600
30x20=600
5600/600=9.3
Or 80/20÷30/70=9.3

26. The Odds ratio (OR)
Lung cancer
Smokers
Non
80
20
No lung
cancer
30
70
Odds for smokers=80/30=2.67
Odds for non-smokers=20/70=0.29
OR=80*70/30*20=9.33
Total
110
90

27. Odds Ratios in Case-Control and Cohort Studies
Cohort
Exposed
Not exposed
Develop
disease
Do not
develop
disease
a
c
Odds ratio=
Odds that an exposed person
Develops disease
Odds that a non-exposed
Person develops disease
= a/b
c/d
= ad
bc
b
d
Case-control
Cases
Controls
History of
exposure
a
b
No history of
exposure
c
d
Odds ratio =
Odds that a case was exposed
Odds that a control was exposed
= a/c
b/d
= ad
bc

28. Example: HRT
A total of 1327 women aged 50 to 81 years with hip
fractures, who lived in a largely urban area in Sweden,
were investigated in this un-matched case-controls
study. They were compared with 3262 controls within
the same age range selected from the National register.
Interest was centered on determining whether
postmenopausal hormone replacement therapy (HRT)
substantially reduced the risk of hip fracture.
The results in the table show the number of women
who were current users of HRT and those who had
never used or formerly used HRT in cases and
controls.

29. Current users of
HRT
Never used HRT/
former user of HRT
Total
With hip fracture (cases)
40 (14%)
1287 (30%)
1327
Without hip fracture (controls)
239
3023
3262
Total
279
4310
4589
The observed Odds ratio =
(40X3023)
(239X1287)
=0.39
C.I = 0.28 to 0.56
A postmenopausal woman
in this age range in Sweden
who was a current user of
HRT thus had 39 % of the
risk of hip fracture of a
woman who had never used
or formerly used HRT
Being current user of HRT
reduced the risk of hip
fracture by 61%.

30. When is the Odds Ratio a Good Estimate of the
Relative Risk?
In case-control, only the odds ratio can be calculated as a measure of
association, whereas in a cohort, either the relative risk or the odds ratio is a
valid measure of association.
Nevertheless, estimate of RR can be used in interpreting casecontrol study in the following occasions:
When the cases are representative, with regard to history of exposure, of all
people with disease in the population from which the cases are drawn.
When the controls are representative with regard to history of exposure, of all
people without the disease in the population from which the cases were drawn.
When the disease being studied dose not occur frequently.

31. Odds Ratios and Relative risk
Disease
develops
Exposed
Not
exposed
Do not
develop
disease
Total
200
9800
10,000
10,000
100
9900
Develop
disease
Do not
develop
disease
Total
Exposed
50
50
100
Not
exposed
25
75
100
Relative risk=
200/10,000
100/10,000 =2
Odds Ratio=
200X9900
100X9800=
2.02
In cohort, the discrepancy between RR and Odds
Is less (the denominator is always large)
Relative Risk =
50/100
25/100
=2
Odds ratio =
50X75
25X50
=3
Odds ratio inflated due to high
prevalence of the outcome (>10%)

33. Remember
 The relative odds (odds ratio) is a useful measure of
association in both case-control and prospective
studies “Cohort”.
 In a cohort study, the relative risk can be calculated
directly.
 In a case-control study, the relative risk cannot be
calculated directly, so that the relative odds or odds
ratio (cross-product ratio) is used as an estimate of the
relative risk when the risk of the disease is low.
12/18/2013
Dr. Tarek Tawfik

34. Calculating the Odds ratio in a Matched Pairs CaseControl Study.
According to the type of exposure, case-control study can be classified into four
groups:
- pairs in which both cases and controls
were exposed.
Concordant pairs - pairs in which neither the cases nor the
controls were exposed.
- pairs in which the case was exposed but
the control was not.
Discordant pairs - pairs in which the control was exposed
and the case was not.
12/18/2013
Dr. Tarek Tawfik

35. 2X2 table
Control
Cases
Exposed
Not exposed
Exposed
a
Both the case and control were
exposed
b
The case was exposed and the control was
not
Not exposed
c
The case was not exposed and the
control was exposed
d
Neither the case nor the control was
exposed
Calculation entail the discordant pairs only (b and c), we ignore
the concordant pairs, because they do not contribute to our
knowledge of how cases and controls differ in regard to past
history of exposure.
The odds ratio will then equals = b /c

36. Case-control study of brain tumors in children.
o A number of studies have
suggested that children
with higher birth weights
are at increased risk for
childhood cancer.
o In the next analysis,
exposure is defined as birth
weight greater than 8 lbs.
Normal control
Cases
8+ lbs
< 8lbs
8+ lbs
8
18
26
< 8 lbs
7
38
45
Total
15
56
71
Odds ratio =
18/7 = 2.57
2= 4.00
P = 0.046
12/18/2013
Total
Dr. Tarek Tawfik

37. Attributable Risk
How much of the disease that occurs can be attributed to a
certain exposure?
Attributable risk is defined as the amount or proportion of
disease incidence (or disease risk) that can be attributed to a
specific exposure.
How much of lung cancer risk experienced by smokers can be
attributed to smoking?
More important than RR as it addresses important clinical
practice and public health. How much of the risk (incidence) of
disease can we hope to prevent if we are able to eliminate
exposure to the agent in question?
12/18/2013
Dr. Tarek Tawfik

38. Attributable Risk for the Exposed Group
Level of risk
12/18/2013
Exposed
Group
Background
risk
In non
Exposed
group
Dr. Tarek Tawfik

39. Incidence due
to exposure
Incidence not due
to exposure
In exposed
group
In the nonexposed group

40. Calculations
The incidence of a disease that is attributable to the exposure in the exposed
group can be calculated as follow:
(incidence in
the exposed group) - (incidence in the non-exposed group)
Then, what proportion of the risk in exposed persons is due to the exposure?
(incidence in the exposed group) - (incidence in the non-exposed group)
incidence in the exposed group
12/18/2013
Dr. Tarek Tawfik

41. Attributable Risk for the Total Population
What proportion of the disease incidence in a total population (both exposed
and non-exposed) can be attributable to a specific exposure?
What would be the total impact of a prevention program on the community?
Calculations entail:
(Incidence in the total population) – (incidence in non-exposed group „background risk‟).
In proportion:
(Incidence in the total population) – (incidence in non-exposed group „background risk‟).
Incidence in total population
12/18/2013
Dr. Tarek Tawfik

42. Example for calculating the attributable risk in the exposed group
Smoking status
Develop CHD
Do not develop
CHD
Total
Incidence per 1,000 per
year
Smoke cigarettes
84
2,916
3,000
28.0
Do not smoke
cigarettes
87
4,913
5,000
17.4
Incidence among smokers = 84/3,000 = 28.0 per 1,000
Incidence among non smokers = 87/5,000 = 17.4 per 1,000
The AR = (incidence in exposed group) – (incidence in the non exposed group) =
28.0 – 17.4 /1,000 = 10.6 /1,000????
In proportion = The AR = (incidence in exposed group) – (incidence in the non
exposed group) /( incidence in exposed group)
= 28.0 – 17.6/ 28.0 = 10.6/28.0 = 0.379 = 37.9 %?????

43. What does this mean?
 The attributable risk = 10.6 /1,000, it means that 10.6 of the
28.0/1,000 incident cases in smokers are attributable to the fact
that these people smoke.
 Thus if we had an effective smoking cessation campaign, we
could prevent 10.6 of the 28/1,000 incident cases of CHD that
smokers experience.
 In proportion, 37.9 % of the morbidity from CHD among
smokers may be attributable to smoking and could presumably
be prevented by eliminating smoking.
12/18/2013
Dr. Tarek Tawfik

44. Attributable risk in total population
The incidence in the total population can be calculated by
subtracting the background risk.
(incidence in the total population) – (incidence in the non-exposed group),
for
calculation we must know the incidence of the disease in the
total population (which we often do not know), or all of the
following three values, from which we can then calculate the
incidence in the total population:
 The incidence among exposed.
 The incidence among the non-exposed.
 The proportion of the total population that exposed (frequently
assumed or judged).
12/18/2013
Dr. Tarek Tawfik

45. AR in total population.
 Assuming that the incidence in the total population of smoking
is 44% (and therefore the proportion of non-smokers is 56%).
 The incidence in the total population can then be calculated as
follows:
(incidence in smokers)(% of smokers in the population) +
(incidence in non-smokers)(% of non-smokers in population).
= (28.0/1,000)(0.44)+(17.4/1,000)(0.56)= 22.1/1,000
Then the AR= 22.1/1,000 – 17.4/1,000 = 4.7/1,000.
 It means that, if we an effective prevention program, how
much reduction in the incidence of the CHD could be
anticipated.
12/18/2013
Dr. Tarek Tawfik

46. AR in total population
Proportion of incidence in the total population =
(incidence in the total population) – (incidence in the nonexposed group)/ incidence in the total population = 22.117.4/22.1= 21.3%.
Thus, 21.3 % of the incidence of CHD in this total population
can be attributed to smoking, and if an effective prevention
program eliminated smoking, the best we could hope to
achieve would be a reduction of 21.3 % in the incidence of
CHD in the total population which consisting of both smoking
and non-smoking.
12/18/2013
Dr. Tarek Tawfik

47. Thank you