Transcript Health Statistics

Measure of disease occurrence and its
association with exposure
Dr. Premananda Bharati
Professor and Head
Biological Anthropology Unit
Indian Statistical Institute
203, B.T. Road, Kolkata – 700 108
West Bengal, India
E-mail: [email protected]
1
Measuring Disease Occurrence
occurrence of disease: the frequency and
distribution of diseases and their determinants in
the population
• 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.
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
Measuring disease occurrence
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)
Measuring disease occurrence
Incidence Rate
• Proportion of the population that acquires or develops a
disease in a period of time
• Speed of developing a disease
Number of NEW cases of disease
Total person-time of observation
Denominator:
- is a measure of time
- the sum of each individual’s time at risk
and free from disease
Time-person
Person 1 l
3
Person 2 l
4
x
Person 3 l
Person 4l
Person 5 l
6
3
1
x
x
Person 5l
5
22 p.y
2003
2004
2005
2006
2007
2008
2009
Cumulative Incidence = 3 cases / 6 persons = 50%
Incidence Rate = 3 cases / 22 person-years = 0.14
= 14 cases / 100 person-years
Measuring disease occurrence
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.
•
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%
Which Disease if More Important to Public
Health? Measure of Disease Occurence
Hypothetical Data
Measles
Chickenpox
Rubella
Children exposed
Children ill
251
201
238
172
218
82
Attack rate
0.80
0.72
0.38
Attack rate =
Number of Ill persons (new cases)
Population at risk exposed
• 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
Measuring disease
occurrence
Descriptive
Prevalence
Probability of
having the disease
Burden
Incidence
Probability of
developing the disease
RISK
Risks, Odds and 2x2 tables
Cases Non cases
Exposed
a
b
Non exposed
c
d
a+c
b+d
a+
b
c+d
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/c
Odds 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 patientyears 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 followup 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 for
each prior failure time: e.g., 0.9 x 0.875 x 0.857 = 0.675 and
0.9 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
1
Life expect acy
Mort alit yRat e
Example: for a mortality rate of .0267 per year
1
Life expectacy
 37.5 years
.0267 year
Mortality Rate and Life Expectancy
2 deaths
T hiscohorthas a mortalityrateof
 0.0267year1
(25 50) years
(25  50) years
This cohort has life expectancy
 37.5 years
2
Tuberculosis and Age
Per 100 000
250
200
150
100
50
0
0-14
15-24
25-34
35-44
45-54
Age group, years
55-64
65+
Tuberculosis Rate by Age
Per 100 000
700
600
1927
500
400
300
1947
200
100
1980
0
0
10
20
30
40
Age, years
50
60
70
Measures of Association
• Absolute
– Risk difference
exposed - unexposed
• Relative
– Risk ratios
– Odds ratios
exposed / unexposed
Measures of Association
• The relative risk of myocardial infarction in
men compared with women is : 5
Risk ratio =
Riskmen
Riskwomen
=
5 cases/1000 PY
1 case/1000 PY
= 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
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
Measures of Association
• 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
Yes
No
Total
Yes
a
b
a+b
No
c
d
c+d
a+c
b+c
a+b+c+d
Exposure
Total
a- = number of individuals who are exposed and have the disease
b = number who are exposed and do not have the disease c = number who are not exposed and have the disease
d = 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
No
Yes (exposed)
a
b
total # exposed
No (unexposed)
c
d
total # unexposed
Exposure
Total
total #
with
disease
total #
with no
disease
Total
Total Population
• Case-Control Study
100% of diseased individuals sampled
25% of disease-free individuals sampled
Exposure
Not Exposure
Total
Disease
8
32
40
No Disease
23
217
240
Total
31
249
280
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
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
RR
=
Incidence rate of disease in unexposed
Disease
Yes
No
Total
Yes
a
b
a+b
No
c
d
c+d
a+c
b+c
a+b+c+d
Exposure
Total
a / (a + b)
Relative Risk
=
c / (c + d)
Relative Risk
Smokers
Nonsmokers
Develop Do Not
CHD
Develop
CHD
84
2916
87
4913
Totals
3000
Incidence
per
1000/yr
28.0
5000
17.4
Incidence in smokers = 84/3000 = 28.0
Incidence in non-smokers = 87/5000 = 17.4
Relative 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 nonexposed 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
Obese
Non Obese
Total
Number with
exposure
Developed
Diabetes
Cumulative
Incidence rate
227
27
27/227
773
1,000
33
60
33/773
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
Measures of Disease Association
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
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
OR
=
odds of disease in unexposed
Disease
Yes
No
Total
Yes
a
b
a+b
No
c
d
c+d
a+c
b+c
a+b+c+d
Exposure
Total
[a / (a + b)] / [1 – (a/(a+b))]
Odds Ratio
=
[c / (c + d)] / [1 – (c/(c+d))]
Odds Ratio
Disease
Yes
No
Total
Yes
a
b
a+b
No
c
d
c+d
a+c
b+c
a+b+c+d
Exposure
Total
[a/b]
Odds Ratio
=
[c/d]
[ ad ]
=
[ bc ]
Based on the Odds Ratio formula, what is the Odds Ratio
for each disease status in this famous smoking study?
Smoking and Carcinoma of the Lung
# of
Disease
# of
nonsmokers
smokers
Status
Males
Lung cancer
647
2
Males
Controls
622
27
Females
Lung cancer
41
19
Females
Controls
28
32
Calculation of Odds Ratio example
Smokers
Non Smokers
Totals
Lung Cancer (cases)
41
19
60
No lung cancer (controls)
28
32
60
• 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
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
Iexposed – Iunexposed
Exposed
Unexposed
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)
Population Attributable Risk (PAR)
• 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
PAR  Ipopulation - Iunexposed
Population Attributable Risk
Risk
Ipopulation- Iunexposed
Population
Unexposed
Population Attributable Risk
Percent (PAR%)
• PAR expressed as a percentage of total risk in
population
Ipopulation - Iunexposed
PAR% 
x 100
Ipopulation
Population Attributable Risk (PAR ):
Fast driving
Dead
Not dead
Risk
Fast
100
1900
2000
0.050
Slow
80
7920
8000
0.010
180
9820
10000
0.018
PAR  0.018 - 0.010  0.008
0.018 - 0.010
PAR% 
x 100  44%
0.018
• 44% of driving-related deaths in
population were presumably due to
fast driving