Estimating risk

Dr. Rizwanul KarimDepartment of Epidemiology

Study Population

NEW TREATMENTCURRENT TREATMENT

DO NOT IMPROVEIMPROVEDO NOT

IMPROVEIMPROVE

Randomly Assigned

Defined Population

NOT EXPOSEDEXPOSED

NODISEASEDISEASENO

DISEASEDISEASE

Not Randomly Assigned

People with the disease

People without the disease

“Cases” “Controls”

Start With :

and

Then determine Exposure History:

and People without the disease

Were exposed

Were not exposed

People with the disease

Were exposed

Were not exposed

“Cases” “Controls”

Risk

• Risk generally refers to the probability of some untoward event.

• Risk is the probability that people who are exposed to certain risk factors will subsequently develop a particular disease more often than similar people who are not exposed

Risk factors

• Risk factor: Characteristics associated with an increased risk of becoming diseased are called risk factors.

• Exposure : Exposure to a risk factor means that a person, before becoming ill, has come in contact with or has manifested the factor in question.

The incidence of a disease in a population is termed the absolute risk. 

Absolute risk can indicate the magnitude of the risk in a group of people with a certain exposure, but because it does not take into consideration the risk of disease in non-exposed individuals, it does not indicate whether the exposure is associated with an increased risk of the disease.

How do we determine whether a certain disease is associated with a certain exposure

A food borne disease outbreak: Percent of people Sick among those who ate and those who did not eat specific foods

Food Ate (% Sick) Did Not Eat ( % Sick )Egg salad 83 30Macaroni 76 67Cottage cheese 71 69Tuna salad 78 50Ice cream 78 64other 72 50

How do we determine whether a certain disease is associated with a certain exposure

Food borne disease outbreak : Ways of calculating excess Risk(A) (B) (C) (D)

Food Ate (% Sick) Did not Eat (% Sick) (A)/(B) (A) – (B) (%)

Egg salad 83 30 2.77 53Macaroni 76 67 1.13 9Cottage cheese 71 69 1.03 2Tuna salad 78 50 1.56 28Ice cream 78 64 1.21 14other 72 50 1.44 22

Determining excess risk

One approach, is to calculate the ratio of the attack rate in those who ate each food to the attack rate in those who did not eat the food. An alternate approach for identifying any excess risk in exposed individuals is to subtract the risk in those who did not eat the food from the risk in those who did eat the food. The difference represents the excess risk in those who were exposed.

Measuring excess risk

whether a certain exposure is associated with a certain disease, we must determine whether there is an excess risk of disease in exposed populations by comparing the risk of disease in exposed populations to the risk of disease in non-exposed populations.

Ways to express and compare riskWays to express and compare risk

Measures of Effect

Expression Question Definition Absolute Risk What is the incidence of disease in

a group initially free of condition?

Attributable risk( Risk difference )

What is the incidence of diseaseAttributable to Exposure

Relative Risk(Risk ratio)

How many times more likely are exposed persons to become diseased, relative to non-exposed persons

group in the people of # timeof periodgiven aover cases new of #

I

EE IIAR

E

E

IIRR

Ways to express and compare riskWays to express and compare risk

Measures of Effect

Expression Question Definition

Population –attributable risk What is the incidence of disease in a population, associated with the prevalence of a risk factor (exposure)

Population –attributable fraction

What fraction of disease in a population is attributable to exposure to a risk factor?

PARARP *

T

PP I

ARAF

Where = Incidence in Exposed persons, = Incidence in the Non-Exposed

persons; = Prevalence of Exposure to a risk factor; and = Total incidence of disease

in a population .

EIEITIP

Calculating measures of effect: Cigarette smoking and Calculating measures of effect: Cigarette smoking and Death from lung cancerDeath from lung cancer

Death rate (absolute risk) from lung cancer in smokers 0.96/1000/yearDeath rate (absolute risk) of cancer in cigarette non-smokers 0.07/1000/yearPrevalence of cigarette smoking 56%Total death rate from lung cancer 0.56/1000/year

Compared RiskCompared Risk

Attributable risk = 0.96/1000/year – 0.07/1000/year = 0.89/1000/year

Relative risk = 0.96/1000/year ÷ 0.07/1000/year = 13.7

Population-attributable risk = 0.89/1000/year X 0.56 = 0.50/1000/year

Population –attributable fraction = 0.50/1000/year ÷ 0.56/1000/year = 0.89

An excess risk can be calculated in the two following ways:

The ratio of the risks (or of the incidence rates):

The difference in the risks (or in the incidence rates):

exposed-non in therisk Diseaseexposedin risk Disease

exposed)-nonin risk disease– exposedin risk (disease

Measuring risk

An Example Comparing two way of calculating excess riskPOPULATION

(A) (B)

Incidence (%)

In exposed 40 90

In non-exposed 10 60

Difference in incidence rates 30 30

Ratio of incidence rates 4.0 1.5

The Concept of Relative Risk

If we carry out a cohort study“the ratio of the risk of disease in exposed individuals to the risk of disease in non-exposed individuals?“ is called the relative risk.

Relative risk =

exposed-nonin Risk exposedin Risk

Relative risk

The relative risk can also be defined as the probability of an event (developing a disease) occurring in exposed people compared to the probability of the event in non-exposed people, or as the ratio of the two probabilities.

How do we interpret the value of a relative risk? There are three possibilities

Interpreting Relative Risk (RR) of a DiseaseIf RR = 1 Risk in exposed equal to risk in non-exposed

(no association)If RR > 1 Risk in exposed greater than risk in non-

exposed (positive association; possibly causal)If RR < 1 Risk in exposed less than risk in non-exposed

(negative association; possibly protective)

Relative riskRisk calculation in a cohort study

Then follow to see whetherDisease develop

Disease does not develop

totals Incidence rates of disease

First select

exposed a b a + b

Not exposed c d c + d

= Incidence in exposed = Incidence in non-exposed

baa

dcc

baa dc

c

Relative risk =

Relative risk =

dccbaa

exposed-nonin Incidenceexposedin Incidence

Smoking and coronary heart disease ( CHD): A hypothetical cohort study of 3,000 cigarette smokers and 5,000 nonsmokers

CHD develops CHD does not develop

Totals Incidence per 1000 /year

Smoke cigarettes

84 2916 3,000 28.0

Do not smoke cigarettes

87 4913 5,000 17.4

61.14.170.28

exposed-nonin Incidenceexposedin Incidence

dccbaa

Odds

• Odds, is the ratio of two probabilities,”p”the probability of an event) to that of “(1-p)”1- the probability of the event.

• Odds and probability contain the same information, but they express it differently:Odds = probability of an event /(1- the probability of the event)Probability = Odds / (1+ Odds)

The Odds Ratio (Relative Odds)

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, in a case-control study we cannot calculate the relative risk directly. We shall see how another measure of association, the odds ratio, can be obtained from either a cohort or a case-control study and can be used instead of the relative risk.

we have learned, the proportion of the exposed population in whom disease develops and the proportion of the non-exposed population in whom disease develops in a cohort study.

Similarly, in case-control studies, we have discussed the proportion of the cases(occurrence of disease) who were exposed and the proportion of the controls(non-occurrence of disease) who were exposed

Defining the Odds Ratio in Cohort and in Case-Control Studies

Suppose we are betting on a horse named Epi Beauty, which has a 60% probability of winning the race (P).Epi Beauty therefore has a 40% probability of losing (1 - P).

If these are the probabilities, what are the odds that the horse will win the race?

the odds of an event can be defined as the ratio of the number of ways the event can occur to the number of ways the event cannot occur.

Measuring odds

It is important to keep in mind the distinction between probability and odds. Probability of winning = 60%

Odds of winning =

5.1%40%60

1

race thelose lBeauty wil Epiy that Probabilitrace win thelBeauty wil Epiy that Probabilit

orppodds

odds

5.1%40%60

Odds = probability of an event /(1- the probability of the event) = 60/40 = 1.5

Probability = Odds / (1+ Odds) = 1.5/(1+1.5) = .6

The odds that the disease will develop in an exposed person ,looking only at the top row in which we see that there are  (a + b) exposed persons; the odds that the disease will develop in them are a:b 

Or .

The probability (P) that the disease will develop in an exposed person, is the incidence of the disease in the top row (exposed persons),

which equals .

ba

baa

Recall From the Epi Beauty example.)

Similarly, there are (c + d) non-exposed persons; the probability that the

disease will develop in non-exposed persons is

and the odds of the disease developing in these non-exposed persons

are c:d or .

pp1

dcc

dc

Odds ratio in cohort study

Odds ratio in Cohort studies

In a cohort study, to answer the question of whether there is an association between the exposure and the disease, we can either use the relative risk or we can use the odds ratio (also called the relative odds). In a cohort study, the odds ratio is defined as the ratio of the odds of development of disease in exposed persons to the odds of development of disease in non-exposed persons, and

it can be calculated as bcad

dcba

Odds ratio in a Cohort study

Develop disease

Do not developDisease

Exposed a b

Not Exposed c d

bcad

dcba

disease developsperson exposed-nonan that Odds

disease developsperson exposedan that Odds

Odds ratio in a case control study

Calculation of Proportions Exposed in a Case-Control studyFirst select

Cases ( with disease) Controls(without disease)

Then MeasureThe Exposure

Were exposed a bWere not exposed c d

totals a + c b + d

Proportion exposedcaa db

b

Odds ratio in a Case-control study

Cases(with

disease)

Control(without disease)

History of Exposure

a b

No historyOf Exposure

c d

bcad

dbca

exposed wascontrol a that odds

exposed wascase a that Odds

In a case-control study, we cannot calculate the relative risk directly to determine whether there is an association between the exposure and the disease.

This is because, having started with cases and controls rather than with exposed and non-exposed persons, we do not have information about the incidence of disease in exposed versus non-exposed persons.

However, we can use the odds ratio as a measure of the association between exposure and disease in a case-control study,

The odds of a case having been exposed are a:c or

The odds of a control having been exposed are b:d or

in a case-control study, is defined as the ratio of the odds that the cases were exposed to the odds that the controls were exposed. This is calculated as follows: .

bcad

dbca

ca

db

The odds ratio or the cross-products ratio can be viewed as the ratio of the product of the two cells that support the hypothesis of an association

(cells a and d- diseased people who were exposed and non-diseased people who were not exposed),

to the product of the two cells that negate the hypothesis of an association

(cells b and c-non-diseased people who were exposed and diseased people who were not exposed).

When Is the Odds Ratio a Good Estimate of the Relative Risk?

When is the odds ratio (relative odds) obtained in a case-control study a good approximation of the relative risk in the population? When the following three conditions are met:

• When the cases studied are representative, with regard to history of exposure, of all people with the disease in the population from which the cases were drawn.

• When the controls studied 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 does not occur frequently.

Recall that there are a + b exposed persons. Because most diseases with which we are dealing occur infrequently, very few persons in an exposed population will actually develop the disease; consequently, 

a, is very small compared to b, and one can approximate a + b as b, or (a + b)  ≅ b. Similarly, very few non-exposed persons (c + d) develop the disease, and we can approximate c + d as d, or (c + d)  ≅ d. 

Therefore, we may calculate a relative risk as follows:

dcba

dccbaa

Disease develop

Do not DevelopDisease

Exposed 200 9,800 10,000

Not exposed

100 9,900 10,000

2000,10/100000,10/200

The Odds ratio is a good estimate of the relative risk when a disease is infrequent

Relative risk =

Odds ratio = 02.2800,9100900,9200

XX

Disease develop

Do not DevelopDisease

Exposed 50 50 100

Not exposed

25 75 100

2100/25100/50

The Odds ratio is not a good estimate of the relative risk when a disease is not infrequent

Relative risk =

Odds ratio = 350257550

XX

REMEMBER

1.The relative odds (odds ratio) is a useful measure of association, in and of itself, in both case-control and prospective studies.

2.In a cohort study, the relative risk can be calculated directly.

3.In a case-control study, the relative risk cannot be calculated directly, so that the relative odds or odds ratio (cross-products ratio) is used as an estimate of the relative risk when the risk of the disease is low.

CALCULATING THE ODDS RATIO IN AN UNMATCHED CASE-CONTROL STUDY

Cases ControlsE NE EN NE NN EN NE NE EE NN N

E = ExposedN = Not Exposed

Let us assume that this case-control study is done without any matching of controls to cases. Thus, 6 of the 10 cases were exposed and 3 of the 10 controls were exposed. If we arrange these data in a 2 × 2 table, we obtain the following:

Cases Controls

Exposed 6 3

Non-exposed 4 7

Total 10 10

Measuring odds ratio in unmatched pair

• The odds ratio in this unmatched study equals the ratio of the cross-products:

5.31242

3476ratio Odds

ratio Odds

XXbcad

Example of calculating an Odds Ratio from a case control StudyFirst select

CHD Cases Controls

Then Measure

Past Exposure

Smokers

Non-SmokersTotals 200 (a + c) 400 (b + d)

Proportions of Smoking Cigarette 56% 44%

Odds ratio

112 (a) 176 (b)

88 (c) 224 (d)

62.188176224112

XX

bcad

Calculating Odds ratio

Calculating the odds ratio in a matched pairs case-Control study

In selecting the study population in case-control studies, controls are often selected by matching each control to a case according to variables that are known to be related to disease risk, such as sex, age, or race (individual matching or matched pairs).

The results are then analyzed in terms of case-control pairs rather than for individual subjects.If exposure is dichotomous (a person is either exposed or not exposed), only the following four types of case-control pairs are possible:

Concordant pairs 1. Pairs in which both the case and the control were exposed “a”2. Pairs in which neither the case nor the control was exposed “d”

Discordant pairs 3. Pairs in which the case was exposed but the control was not “b”4. Pairs in which the control was exposed and the case was not “c”

ControlExposed Not-Exposed

CasesExposed a bNot-Exposed c d

The odds ratio for matched pairs is therefore the ratio of the discordant pairs (i.e., the ratio of the number of pairs in which the case was exposed and the control was not, to the number of pairs in which the control was exposed and the case was not).

Odds ratio (matched pairs ) = cb

The concordant pairs (a and d, in which cases and controls were either both exposed or both not exposed) are ignored, because they do not contribute to our knowledge of how cases and controls differ in regard to past history of exposure.

CALCULATING THE ODDS RATIO IN AN UNMATCHED CASE-CONTROL STUDY

Cases ControlsE NE EN NE NN EN NE NE EE NN N

E = ExposedN = Not Exposed = Matched

Control

Exposed Not-Exposed

Cases Exposed

Not-Exposed

2,a 4,b

1,c 3,d

Pairs in which the case was exposed but the control was not “b”

Pairs in which the control was exposed and the case was not “c”

There are four pairs in which the case was exposed and the control was not and one pair in which the control was exposed and the case was not.

414 ratio Odds

cb

Attributable Risk for the Exposed Group

group exposed-non

in Incidence group exposed

in Incidence

The relative risk is important as a measure of the strength of the association,  a major consideration in deriving causal inferences.

How much of the disease that occurs can be attributed to a certain exposure? 

This is answered by another measure of risk, The attributable risk, which is defined as the amount or proportion of disease incidence (or disease risk) that can be attributed to a specific exposure.

Attributable Risk for the Exposed Group

Every person shares the background risk regardless of whether or not he or she has had the specific exposure in question (in this case, smoking) . Thus, both non-exposed and exposed persons have this background risk.

Therefore, the total risk of the disease in exposed individuals is the sum of the background risk that any person has and the additional risk due to the exposure in question.

If we want to know how much of the total risk in exposed persons is due to the exposure, we should subtract the background risk from the total risk

Because the risk in the non-exposed group is equal to the background risk, we can calculate the risk in the exposed group that is a result of the specific exposure by subtracting the risk in the non-exposed group (the background risk) from the total risk in the exposed group.

Incidence attributable to Exposure and incidence not attributable to exposure

In exposedgroup

In non-exposed group

In exposedgroup

In non-exposed group

BackgroundRisk

In exposedgroup

In non-exposed group

{{

Incidence due to Exposure

Incidence notdue to Exposure

Estimating the potential for prevention

group exposedin Incidencegroup exposed-non

in Incidence group exposed

in Incidence

what proportion of the risk in exposed persons is due to the exposure? We could then express the attributable risk as the proportion of the total incidence in the exposed group that is attributable to the exposure by simply dividing the previous formula by the incidence in the exposed group, as follows:

Attributable risk-potential for prevention

The attributable risk expresses the most that we can hope to accomplish in reducing the risk of the disease if we completely eliminate the exposure.

For example, if all smokers were induced to stop smoking, how much of a reduction could we anticipate in lung cancer rates?

From a practical programmatic standpoint, the attributable risk may be more relevant than the relative risk.

The relative risk is a measure of the strength of the association and the possibility of a causal relationship, but the attributable risk indicates the potential for prevention if the exposure could be eliminated.

Attributable Risk for the total population – population attributable risk

risk) d(backgroun group exposed-non

in Incidence

population totalin Incidence

If we want to calculate the attributable risk in the total population, the calculation is similar to that for exposed people, but we begin with the incidence in the total population and again subtract the background risk, or the incidence in the non-exposed population. The incidence in the total population that is due to the exposure* can be calculated as shown in formula

*Incidence in the population due to the Exposure = Attributable risk for the Exposed group X Proportion of the population exposed

Population attributable risk

population in total Incidencegroup exposed-non

in Incidence population total

in Incidence

The attributable risk for the total population is a valuable concept for the public health worker. If smoking were eliminated, what proportion of the incidence of lung cancer in the total population (which consists of both smokers and nonsmokers) would be prevented? The answer is: the attributable risk in the total population [ population attributable risk PAR]

This is often both the critical issue and the question that is raised by policy-makers and by those responsible for funding prevention programs. if all smokers in the community stopped smoking, what would the impact of this change be on the incidence of lung cancer in the total community population (which includes both smokers and nonsmokers)?

Attributable risk example

Smoking and Coronary heart disease (CHD) : A hypothetical Cohort of 3,000 cigarette Smokers and 5,000 Nonsmokers

CHD Develop CHD does not develop Total Incidence/thousand/year

Smoke cigarette

84 2,916 3,000 28.0

Do not smoke cigarette

87 4,913 5,000 17.4

Incidence among Smokers =

Incidence among non-Smokers =

thousand/28300084

thousand/4.17500087

Attributable risk- amount

000,16.10

000,14.1728

group exposed-nonin Incidence

group exposedin Incidence

Attributable risk- proportion

%9.37379.00.286.10

0.284.170.28

group exposedin Incidencegroup exposed-non

in Incidence group exposed

in Incidence

Incidence in total population

risk) d(backgroun group exposed-non

in Incidence

population totalin Incidence

000,1

1.2256.000,1

4.1744.0000,1

0.28

populationin smokers-non %

smokers-nonin Incidence

populationin smokers %

smokersin Incidence

we know that the incidence among the smokers is 28.0 per 1,000 and the incidence among the nonsmokers is 17.4 per 1,000. However, we do not know the incidence in the total population. Let us assume that, from some other source of information, we know that the proportion of smokers in the population is 44% (and therefore the proportion of nonsmokers is 56%).

Population attributable risk- amount

000,17.4

000,14.17

000,11.22

group exposed-nonin Incidence

population totalin Incidence

Population attributable risk- amount*

• Population attributable risk

Attributable risk X Prevalence of exposure in the population= ( 10.6 X .44)= 4.66= 4.7/ 1000 population

Population attributable risk- proportion

%3.211.22

4.171.22population in total Incidence

group exposed-nonin Incidence

population totalin Incidence

Question-1Question-1In an epidemiological study for examining the relationship between developmental disorders and prenatal exposure to cocaine, the hospital records of 1000 infants diagnosed with a developmental disorder and 1000 infants attended for other disease were inspected. Of the 1000 children with a developmental disorder, 800 were born to mothers known to have abused cocaine during their pregnancy , compared to 300 of the comparison group infants.what is the study design the researcher adopted here and what is the measure of effect of cocaine abuse?

Question-2Question-2One hundred children known to have been exposed to high levels of lead during the first 12 months of life were followed for 15 years ; 40 developed an affective disorder. A similar group of 100 children who were not exposed to high levels of lead during the first 12 months of life were also followed over the same time period; 5 of the children developed an affective disorder. Find out the relationship between high lead exposure and affective disorder. If we were be able to remove the exposure at their first year of life, what proportion of children could be out of the disorder?

Question-3Question-3

To study the possible association between oral contraceptive use and occurrence of rheumatoid arthritis (RA) , an investigator selected 100 women with confirmed diagnosis of RA and 200 women undergoing treatment in the same hospital for other conditions . Forty percent of the RA patients gave history of oral contraceptive use whereas 40% of the women of other conditions were non-users .what type of study design was employed and estimate the risk of developing RA from oral contraceptive use.