Estimating risk

04/10/2023 Dr. Tarek Tawfik 1

Estimating Risk

Dr. Tarek Tawfik Amin

Public Health Department, Cairo [email protected]

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.

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.

Probability Odds (chance) Risk

Proportion (%)0-1 (100%)

Ratio Probability/(1-probaility) 0 to infinity

Ratio (rate)0 to infinity

The 10 year probability of OP hip fracture among those aged 70 years is 0.23 (23%).

The Odds for OP hip fracture is 0.23/(1.0.23)=0.30

Incidence of OP hip fracture among those aged 70 years.

No denominator Denominator

Attack rate is an other example


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 non-exposed 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.


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.

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 non-exposed individuals? (RR=relative risk).

Relative risk (RR) =

Risk in exposed (incidence in the exposed)

Risk in non-exposed (incidence in the non-exposed)

Basic Structure of cohort study

Disease-free

Dis

eased

Disease-free

Unexposedto factor

Exposed to factor

Population

Develop Disease (a)

Disease-free(b)

Develop Disease (c)

Disease-free(d)

Sam

ple

Starting point

Present time Future timeFollow

Com

parin

g th

e in

cid

en

ce o

f dis

ease in

each

gro

up

The Relative Risk is calculated for exposure

Disease-free

Dis

eased

Population

Diseased (cases)

Disease-free(controls)

Exposed to factor(a)

Unexposed to factor(b)

Unexposed to factor(d)

Exposed to factor(c)

Sam

ple

Trace Present time

Starting pointPast time

Basic structure of case-control design

The O

dds “ch

ance

of e

xposu

re

Is calcu

late

d b

etw

een b

oth

gro

ups

The following table depicts the outcomes of isoniazid/placebo trial among children with HIV (death within 6 months).

Total Alive Dead (within 6 months)

Interventions

131 110 21 Placebo

132 121 11 Isoniazid

What is the risk of dying?

Risk=21/131=0.160

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

Relative risk (RR)

Total No breast cancer

Breast cancer Mammography

100 b-90 a-10 Positive

100,100 d-998980 c-20 Negative

In Cohort design

RR= a/(a+b)÷c/(c+d)10/(100) ÷20(100,100)=0.1/0.0002= 500

The relative risk (RR)

Total No lung cancer

Lung cancer

600 582 18 Smokers

1200 1194 6 Non

Cohort

stu

dy

Risk for smokers=18/600=0.03Risk for non-smokers=6/1200=0.005RR=0.03/0.005=6

Interpreting the Relative Risk(measure the strength of the association)

Risk in exposed equal to risk in non-exposed (no association).Risk in exposed greater than risk in non-exposed (positive association; possibly causal).Risk in exposed less than risk in non-exposed (negative association; possibly protective).

If RR = 1

If RR > 1

If RR < 1

Calculating the Relative Risk in Cohort Studies

Then follow to see whether

Incidence rate of disease

Totals Disease does not develop

Disease develops

a a+b

c c+d

a+b

c+d

b

d

a

c

First select

a c

a+b c+d

Exposed

No exposed

=incidence in exposed =incidence in non-exposed

Hypothetical Cohort3,000 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.

Incidence per 1,000/year

Totals Do not develop CHD

Develop CHD

28.0

17.4

3,000

5,000

2,916

4,913

84

87

Smoke cigarettes

Do not smoke

cigarettes

Incidence among the exposed=84/3,000 = 28.0 per 1,000

Incidence among the non-exposed =87/5000= 17.4 per 1,000

Relative risk= Incidence in exposed

Incidence in non-exposed=

28.0/17.4 = 1.61


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).

MI in subsequent 10 years

Smoking status at baseline

Total No Yes

5899

1819

7718

5336 (90.5%)

1732 (95.2%)

7068(71.6%)

563 (9.5%)

87 (4.8%)

650 (8.4%)

Ever smoked

Never smoked

Total

The estimated relative risk=(563/5899)(87/1819)

=2.00CI = 1.60-2.49

(does not include 1)

The middle aged man who has eversmoke is twice as likely to suffer a

MI over the next 10 years period as a man who has never smoked.

Odds ratio

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.


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.

Odds =

Odds = P/(1-P) or 60 %/40 % = 1.5:1 = 1.5Probability of wining is 60 %, while the odds

(chance) of wining is 1.5 times.

Probability that Little Beauty will win the race

Probability that Little Beauty will lose the race

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 case-control studies, however they can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions).

OR

• Rare disease assumption (prevalence < 10%).

• Case control-design • Regression analysis • Meta-analysis

Calculation

Total None Diseased Case control study

a+b Exposed+ not diseased (b)

Cases+ exposed (a)

Exposed

c+d Not exposed+ not diseased

(d)

Cases-not exposed (c)

Non-exposed

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 outcomeOR>1 Exposure associated with higher odds of outcomeOR<1 Exposure associated with lower odds of outcome

Odds ratio


Lung cancer Case control study

110 b-30 a-80 Smoking

90 d-70 c-20 None

80x70=560030x20=6005600/600=9.3

Or 80/20÷30/70=9.3

The Odds ratio (OR)


Lung cancer

110 30 80 Smokers

90 70 20 Non

Case

contr

ol st

udy

Odds for smokers=80/30=2.67Odds for non-smokers=20/70=0.29OR=80*70/30*20=9.33

Odds Ratios in Case-Control and Cohort Studies

Do not develop disease

Develop

disease

Cohort

b a Exposed

d c Not exposed

Controls Cases Case-control

b a History of exposure

d c No history of exposure

Odds ratio= Odds that an exposed person

Develops diseaseOdds that a non-exposed Person develops disease

=a/b c/d

=ad bc

Odds ratio= Odds that a case was exposed

Odds that a control was exposed =a/c b/d

=ad bc

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.

Total

Never used HRT/ former user of

HRT

Current users of HRT

1327

3262

4589

1287 (30%)

3023

4310

40 (14%)

239

279

With hip fracture (cases)

Without hip fracture (controls)

Total

The observed Odds ratio= (40X3023)(239X1287)

=0.39C.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 HRTBeing current user of HRT

reduced the risk of hip fracture by 61%.

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 case-control 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.

Odds Ratios and Relative risk

Total Do not develo

p disease

Disease develop

s

10,000

10,000

9800

9900

200

100

Exposed

Not exposed

Total Do not develop disease

Develop disease

100

100

50

75

50

25

Exposed

Not exposed

Relative risk =200/10,000

100/10,000= 2Odds Ratio=200X9900100X9800=

2.02

Relative Risk= 50/10025/100

=2Odds ratio= 50X7525X50

=3Odds ratio inflated due to high prevalence of the outcome (>10%)

In cohort, the discrepancy between RR and OddsIs less (the denominator is always large)


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.


Calculating the Odds ratio in a Matched Pairs Case-Control 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.

2X2 tableControl

Cases Not exposed Exposed

b The case was exposed and the

control was not

a Both the case and control

were exposed

Exposed

dNeither the case nor the control

was exposed

cThe case was not exposed

and the control was exposed

Not 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


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.

Total Normal control

Cases < 8lbs 8+ lbs

26 18 8 8+ lbs

45 38 7 < 8 lbs

71 56 15 Total

Odds ratio= 18/7 = 2.57

2= 4.00P = 0.046


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?


Attributable Risk for the Exposed Group

Exposed Group

In nonExposed

group

Leve

l of risk

Background risk

In the non-exposed group

In exposed group

Incidence due to exposure

Incidence not dueto exposure


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


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

Example for calculating the attributable risk in the exposed group

Incidence per 1,000 per year

Total Do not develop CHD

Develop CHD

Smoking status

28.0

17.4

3,000

5,000

2,916

4,913

84

87

Smoke cigarettes

Do not smoke cigarettes

Incidence among smokers = 84/3,000 = 28.0 per 1,000Incidence 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 %?????


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.


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).


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.


AR in total population

* Proportion of incidence in the total population =

(incidence in the total population) – (incidence in the non-exposed group)/ incidence in the total population = 22.1-17.4/22.1= 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.

Thank you

Estimating risk

Health & Medicine

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