measure of disease occurrence and its association with exposure

Measure of disease occurrence and its association with exposure

Dr. Premananda BharatiProfessor and Head

Biological Anthropology UnitIndian Statistical Institute

203, B.T. Road, Kolkata – 700 108West Bengal, India

E-mail: [email protected]

1

Measuring Disease Occurrence

• Occurrence of disease is the fundamental outcome measurement of epidemiology.

• Occurrence of disease is typically a binary (yes/no) outcome.

• Occurrence of disease involves time.

occurrence of disease: the frequency and distribution of diseases and their determinants in the population

Measuring disease occurrence

Number of cases of disease

Population

–Number of cases of a disease in a given population at a specific time

–Proportion of the population that had the disease at a given time

–Probability of having the disease

prevalence

Number of NEW cases of disease during a period

Population at the beginning of the period


–Number of new cases of a disease in a given population at a specific time

–Proportion of the population that acquires or develops a disease in a period of time

–Probability of developing a disease

incidence(cumulative incidence)

Incidence Rate

Number of NEW cases of disease

Total person-time of observation

• Proportion of the population that acquires or develops a disease in a period of time

• Speed of developing a disease

Denominator:- is a measure of time - the sum of each individual’s time at risk and free from disease


Cumulative Incidence = 3 cases / 6 persons = 50%

Incidence Rate = 3 cases / 22 person-years = 0.14

= 14 cases / 100 person-years

2003 2004 2005 2006 2007 2008 2009

l

x

xll x

l

l

l

Person 1 3

4

6

3

1

5

22 p.y

Person 2

Person 3

Person 4

Person 5

Person 5

Time-person

• Cumulative incidence during an outbreak

Expressed for the entire epidemic period, from thefirst to the last case

• Not really a rate but a proportion!


Outbreak of cholera in country X in March 1999

Number of cases 490

Population 18,600

Attack rate 2.6%

Attack Rate:The number of cases of disease in a specific population divided by the total population at risk for a limited time period, usually expressed as a percentage.

• Attack rate is a Cumulative Incidence; it shows the risk (probability) of disease to occur in a population

• In regard to risk, measles is the most important disease to public health while rubella being the least

Hypothetical Data

Measles Chickenpox Rubella

Children exposedChildren ill

Attack rate

251201

0.80

238172

0.72

21882

0.38

Attack rate = Number of Ill persons (new cases)Population at risk exposed

Which Disease if More Important to Public Health? Measure of Disease Occurence


Descriptive

Prevalence Incidence

Probability ofhaving the disease

Probability ofdeveloping the disease

RISKBurden

Cases Non cases

Exposed a b a+b

Non exposed c d c+d

a+c b+d

Risks, Odds and 2x2 tables

Risk of being a case in exposed = a / (a+b)Risk of being a case in non exposed = c / (c+d)

Odds of exposure among cases = (a/(a+c))/(c/(a+c))= a/cOdds of exposure among non cases = (b/(b+d))/d/(b+d))= b/d

Prevalence vs Incidence

• Prevalence– Burden of disease -> public health planning

• Incidence– Trends over time -> public health implications– Fundamental for studies of causality– Exclude prevalent cases to focus on causes of

disease, not on causes of “survival with disease”

Two Types of Prevalence• Point prevalence - number of persons with a specific

disease at one point in time divided by total number of persons in the population

• Period prevalence - number of persons with disease in a time interval (eg, one year) divided by number of persons in the population– Prevalence at beginning of an interval plus any incident

cases

• Risk factor prevalence may also be important

Incidence or Prevalence?

HIV/AIDS infection rates drop in Uganda

Infection rates of the HIV/AIDS epidemic among Ugandan men, women and children dropped to 6.1% at the end of 2000 from 6.8% a year earlier, an official report shows…the results were obtained after testing the blood of women attending clinics in 15 hospitals around the country.

Cumulative Incidence

• Definition: The proportion of individuals who experience the event in a defined time period (E/N during some time T) = cumulative incidence

• Example: Diabetic medications and fracture: “The cumulative incidence of a first fracture among women reached 15.1% at 5 years with rosiglitazone, 7.3% with metformin, and 7.7% with glyburide.”

Example of Incidence Rate

The number of events divided by the amount of person-time observed (E/NT) = incidence rate or density (not a proportion)

• Example: “The incidence of a first fracture among women was 2.74 per 100 patient-years with rosiglitazone, 1.54 per 100 patient-years with metformin, and 1.29 per 100 patient years with glyburide.”

Cumulative Incidence

• Most intuitive measure of incidence since it is just proportion of those observed who got the disease

• Proportion=probability=risk

• Basis for Survival Analysis

• Two primary methods for calculating

– Kaplan-Meier method

– Life table method

Cumulative Incidence vs Proportion with Fracture

• The cumulative incidence of a first fracture reached 15.1% at 5 years with rosiglitazone, 7.3% with metformin, and 7.7% with glyburide. Takes into account follow-up time.

• “Among the 1,840 women, 111 reported a first fracture: 60 (9.3%) of those treated with rosiglitazone, 30 (5.1%) of those treated with metformin, and 21 (3.5%) of those treated with glyburide.” The numbers of cases reported in this is useful but the proportions are not. Does not take into account follow-up time.

Calculating cumulative incidence with differing follow-up times

• The Problem: Since rarely have equal follow-up on everyone, can’t just divide number of events by the number who were initially at risk

• The Solution: Kaplan-Meier and life tables are two methods devised to calculate cumulative incidence among persons with differing amounts of follow-up time

Cumulative incidence with Kaplan-Meier estimate

• Requires date last observed or date outcome occurred on each individual (end of study can be the last date observed)

• Analysis is performed by dividing the follow-up time into discrete pieces– calculate probability of survival at each event

(survival = probability of no event)

Calculating Cumulative Incidence

• Probability of 2 independent events occurring is the product of the probabilities for each occurring alone

– If event 1 occurs with probability 1/6 and event 2 with probability 1/2, then the probability of both event 1 and 2 occurring = 1/6 x 1/2 = 1/12

• Probability of living to time 2 given that one has already lived to time 1 (i.e. conditional on survival to time 1) is independent of the probability of living to time 1

Cumulative survival calculated by multiplying probabilities foreach prior failure time: e.g., 0.9 x 0.875 x 0.857 = 0.675 and0.9 x 0.875 x 0.857 x 0.800 x 0.667 x 0.500 = 0.180

Kaplan-Meier Cumulative Incidence of the Outcome

• Cannot calculate by multiplying each event probability (=probability of repeating event) – (in our example, 0.100 x 0.125 x 0.143 x 0.200 x 0.333 x 0.500

= 0.0000595)

• Obtain by subtracting cumulative probability of surviving from 1; eg, (1 - 0.180) = 0.82

• Since it is a proportion, it has no time unit, so time period has to be added; e.g, 2-year cumulative incidence

“The cumulative incidence of a first fracture reached 15.1% at 5 years with rosiglitazone, 7.3% with

metformin, and 7.7% with glyburide.”

Life Expectancy

RateMortality

1 expectacy Life

Example: for a mortality rate of .0267 per year

years 5.37 year.0267

1 expectacy Life

Mortality Rate and Life Expectancy

years 37.5 2

years 50)(25 expectancy life hascohort This

year 0267.0years 50)(25

deaths 2 of ratemortality a hascohort This 1

Tuberculosis and Age

0

50

100

150

200

250

0-14 15-24 25-34 35-44 45-54 55-64 65+

Per 100 000Per 100 000

Age group, yearsAge group, years

Tuberculosis Rate by Age

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70

Per 100 000Per 100 000

Age, yearsAge, years

19271927

19471947

19801980

Measures of Association

• Absolute– Risk difference

• Relative – Risk ratios– Odds ratios

exposed - unexposed

exposed / unexposed


• The relative risk of myocardial infarction in men compared with women is : 5

• The absolute risk difference between men and women is : 4 cases/1000 PY

5 cases/1000 PY - 1 case/1000 PY = 4 cases/1000 PY

Risk ratio = Riskmen

Riskwomen

=5 cases/1000 PY

1 case/1000 PY= 5

Association

• Statistical relationship between two or more events, characteristics, or other variables

• Statistical relationship between exposure and disease

• Association is not causation!

Risk Factor• A factor (exposure) found to be associated

with a health condition• an attribute or exposure that increases the

probability of occurrence of disease– behaviour– genetic– environmental– social

-- time

-- person

-- place


• Relative risk• Odds ratio• Attributable risk/population

attributable risk percent• Standardized mortality ratios

2 x 2 Table

Used to summarize frequencies of disease and exposure and used for calculation of association

Disease

Exposure Yes No Total

Yes a b a + b

No c d c + d

Total a + c b + c a + b + c + d

a- = number of individuals who are exposed and have the diseaseb = number who are exposed and do not have the disease c = number who are not exposed and have the diseased = number who are both non-exposed and non-disease

2 x 2 Table

Used to summarize frequencies of disease and exposure and used for calculation of association

Disease


Yes (exposed) a b total # exposed

No (unexposed) c d total # unexposed

Total total #with

disease

total #with nodisease

Total Population

• Case-Control Study100% of diseased individuals sampled25% of disease-free individuals sampled

p1 = 8 / 31 = 0.26 ≠ 0.08; p0 = 32 / 249 = 0.13 ≠ 0.036

RR = p1 / p0 = (8/31) / (32/249) = 2.01 ≠ 2.25 OR = (8 x 217) / (23 x 32) = 2.36

Exposure Not Exposure Total

Disease 8 32 40No Disease 23 217 240

Total 31 249 280

Relative Risk• The ratio of the risk of disease in persons exposed compared to

the risk in those unexposed

• Often, a measure of association between incidence of disease and exposure of interest

Incidence rate of disease in exposed

Incidence rate of disease in unexposed=RR

a / (a + b)

c / (c + d)=Relative Risk

Disease


Yes a b a + b

No c d c + d


Relative Risk

Develop CHD

Do Not Develop

CHD

Totals Incidence per

1000/yr Smokers 84 2916 3000 28.0

Non-smokers

87 4913 5000 17.4

Incidence in smokers = 84/3000 = 28.0Incidence in non-smokers = 87/5000 = 17.4Relative risk = 28.0/17.4 = 1.61

Interpretation of Relative Risk

• 1 = No association between exposure and disease– incidence rates are identical between groups

• > 1 = Positive association – exposed group has higher incidence than non-exposed

group• < 1 = Negative association or protective effect

– non-exposed group has higher incidence– example: .5 = half as likely to experience disease

• A relative risk of 1.0 or greater indicates an increased risk

• A relative risk less than 1.0 indicates a decreased risk

Measures of Association:2. Risk Ratios

• Summary measure of association in Cohort Studies

• Formula:risk of disease in persons with exposure

risk of disease in persons without exposure

• Fundamental concept in cohort studies:• 1. classify persons on the basis of exposure • 2. follow to measure the incidence (or risk) of

disease during follow-up.

Risk Ratio Calculation in Cohort Study

Number with exposure

Developed Diabetes

Cumulative Incidence rate

Obese 227 27 27/227Non Obese 773 33 33/773Total 1,000 60

Ratio of Incidence = risk ratio = 27/227 / 33/773 = 12 / 4 = 3.0

At times, epidemiologists will choose to express disease frequency in terms of odds

What are odds?

Measures of Disease Association

The chance of something happening can be expressed as a risk and/or as an odds:

Risk = the chances of something happening the chances of all things happening

Odds = the chances of something happening

the chances of it not happening

Example: If I choose a student randomly from this class, how likely

is it that I will choose you?

Risk (probability) = 1/9 = .111

Odds = 1/8 = .125

Example: Among 100 people at baseline, 20 develop influenza over a year.

The risk is 1 in 5 (i.e. 20 among 100) = .2 The odds is 1 to 4 (i.e. 20 compared to 80) = .25

Measures of Disease Association

Odds

• What are odds?• Let p = the probability of an event• 1-p = the probability that the event

does not occur• Odds of the event = p/1-p

– If the probability of an event is 0.7, the the odds of winning are 0.7/0.3 = 2.33

Odds Ratio

• The ratio of the odds of a condition in the exposed compared with the odds of the condition in the unexposed

• Usually applied to prevalence studies rather than incidence studies

odds of disease in exposed

odds of disease in unexposed=OR

[a / (a + b)] / [1 – (a/(a+b))]

=Odds Ratio

Disease


Yes a b a + b

No c d c + d


[c / (c + d)] / [1 – (c/(c+d))]

Odds RatioDisease


Yes a b a + b

No c d c + d


[ a / b ]

=Odds Ratio[ c / d ] =

[ ad ]

[ bc ]

3228FemalesControls

1941FemalesLung cancer

27

622MalesControls

2 647 MalesLung cancer

# of nonsmokers

# of smokers

DiseaseStatus

Smoking and Carcinoma of the LungSmoking and Carcinoma of the Lung

Based on the Odds Ratio formula, what is the Odds Ratio for each disease status in this famous smoking study?

Calculation of Odds Ratio - example

• Odds of smoking if cancer = 41/19 = 2.16• Odds of smoking if no cancer = 28/32 = 0.875• ODDS RATIO of smoking if lung cancer

= 2.16 / 0.875 = 2.5

32

19

Non Smokers

28

41

Smokers

60No lung cancer (controls)

60Lung Cancer (cases)

Totals

Difference Measures• Attributable risk

– # of cases among the exposed that could be eliminated if the exposure were removed

= Incidence in exposed - Incidence in unexposed

• Population attributable risk percent– Proportion of disease in the study population that could be

eliminated if exposure were removed

Incidence in total population - Incidence in unexposed incidence in total population

=

Attributable Risk

Incidence

Exposed Unexposed

Iexposed – Iunexposed

I = Incidence

Attributable Risk

• Rate of disease in the population that can be directly attributed to the exposure

• equals incidence rate in exposed minus incidence rate in the unexposed

A / (A + B) C / (C + D)= -

• Excess risk of disease in total population attributable to exposure

• Reduction in risk which would be achieved if population entirely unexposed

• Helps determining which exposures relevant to public health in community

Population Attributable Risk (PAR)

unexposedpopulation I - IPAR

Population Attributable Risk

Risk

Population Unexposed

unexposed population I -I

• PAR expressed as a percentage of total risk in population

Population Attributable Risk Percent (PAR%)

100 x I

I - I PAR%

population

unexposedpopulation

Dead Not dead Risk

Fast 100 1900 2000 0.050

Slow 80 7920 8000 0.010

180 9820 10000 0.018

Population Attributable Risk (PAR ): Fast driving

44% 100 x 0.018

0.010 - 0.018 PAR%

0.008 0.010 - 0.018 PAR

• 44% of driving-related deaths in population were presumably due to fast driving

measure of disease occurrence and its association with exposure

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