measuresofassociation-09022 6131128-phpapp01.ppt

There are several prominent *Shakti Peethas* located near Rishikesh and in the broader region of Uttarakhand, dedicated to different forms of Goddess Shakti. Some of the significant ones include:

### 1. *Chandrabadni Temple (Chandrabadni Devi)*
- *Location*: Near Devprayag, about 50 km from Rishikesh
- *Significance*: It is believed that the torso of Goddess Sati fell at this spot. The temple is located on a hilltop and offers stunning panoramic views of the surrounding mountains and rivers. It is a revered Shakti Peetha in the region.

### 2. *Kunjapuri Devi Temple*
- *Location*: About 25 km from Rishikesh
- *Significance*: This temple is considered one of the 52 Shakti Peethas in India. The temple offers magnificent views of the Himalayan peaks, including Swarga Rohini, Bandarpunch, and Gangotri. It’s a popular pilgrimage site, especially during the Navratri festival.

### 3. *Surkanda Devi Temple*
- *Location*: Near Dhanaulti, about 80 km from Rishikesh
- *Significance*: This temple is part of the Shakti Peetha circuit in Uttarakhand and is dedicated to Goddess Parvati. The head of Sati is believed to have fallen at this location. The temple is situated at an altitude, and the trek to the temple is a pilgrimage in itself.

### 4. *Dhari Devi Temple*
- *Location*: Near Srinagar, Garhwal, about 100 km from Rishikesh
- *Significance*: The temple is located on the banks of the Alaknanda River. Dhari Devi is considered the guardian deity of Uttarakhand, and her upper half is worshipped here. It is also connected to the story of the Kedarnath floods, adding a spiritual significance to the temple.

These temples are revered and hold immense spiritual significance for devotees of Goddess Shakti. They are often visited during pilgrimages to Char Dham and other spiritual circuits in Uttarakhand.

1. MEASURES OF ASSOCIATIONMEASURES OF ASSOCIATION
Presenter: P. Ganeshkumar
Moderator: Dr. Pragati Chhabra

2. Overview of the presentationOverview of the presentation
Association
Types of association
Measures of association
◦Ratio measures
◦Difference measures
Relationship between OR & RR
Causation
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3. ASSOCIATIONASSOCIATION
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4. Types of associationTypes of association
Positive/Negative
Direct/Indirect
Causal/Non causal
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5. Types of association….contd.Types of association….contd.
Positive: Occurrence of higher value of a
predictor variable is associated with
occurrence of higher value of another
dependent variable.
Ex:education and suicide
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6. Types of association……contd.Types of association……contd.
Negative–Occurrence of higher value of a
predictor variable is associated with lower
value of another dependent variable.
Ex – Female literacy and IMR
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7. Types of association……contd.Types of association……contd.
Direct
directly associated i.e. not via a known third
variable.
Salt intake-------------- Hypertension.
Indirect
associated through a known third variable.
Salt intake  Hypertension CAD.
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8. Types of association……contd.Types of association……contd.
Causal
independent variable must cause change in
dependent variable.
Definite condition of causal associations are
time and direction
Ex –salt intake and hypertension
Non-causal
non-directional association between two
variables.
Ex –alcohol use and smoking
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9. Association-typesAssociation-types
Spurious association
artificial, fortuitous, false
or all non-causal associations due to
chance, bias or confounding.
Ex: Increased water intake and crime rate
in summer.
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10. 24-Dec-08 10
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11. Population
Incidence(%) A B
In exposed 40 90
In non-exposed 10 60
Difference in
incidence rates(%)
30 30
Ratio of incidence
rates
4.0 1.5
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1.The question lies is how to determine whether a certain disease is associated
with a certain exposure.
2.Calculation of excess risk and its usage.
3.Interpretation from ratio of incidence rate compared to the difference in the
incidence rate.

12. In other words, Difference measures are
measures of association in which absolute
differences between groups being
compared .
Ratio measures are measures of
association in which relative differences
between groups being compared.
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13. Absolute differencesAbsolute differences((Syn: Difference measuresSyn: Difference measures))
Main goal is often an absolute reduction in the
risk of an undesirable outcome.
When outcome of interest is continuous, the
assessment of mean absolute differences between
exposed and unexposed individuals may be an
appropriate method for the determination of
association.
Preferred by public health or preventive activist.
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14. Relative differences Relative differences (Syn:Ratio measures)(Syn:Ratio measures)
Can be assessed for discrete outcomes.
To assess causal associations.
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15. Types of measures of association used Types of measures of association used
in analytic epidemiologic studies.in analytic epidemiologic studies.
Type Example Usual application
Absolute differenceAR (Attributable
Risk)
Primary prevention impact:
search for causes.
PAR(Population
Attributable risk)
Primary prevention impact
Efficacy Impact of intervention on
recurrences, case fatality
etc.
Mean differences
(continuous
outcome)
Search for determinants
Relative differenceRelative risk/rateSearch for causes
Relative odds
(ODDS ratio)
Search for causes
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16. Relative riskRelative risk
If an association exist, then how strong is
it?
What is the ratio of the risk of disease in
exposed individuals to the risk of disease
in unexposed individual?
Risk in exposed
Relative risk= _______________
Risk in unexposed
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17. Diseased Nondiseased
Exposed a b
Unexposed c d
Relative risk of developing the disease is expressed as the
ratio of the risk(incidence) in exposed individuals (q+) to
that in unexposed individual(q-)
Total
exposed = a+b
Total unexposed
= c+d
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18. Incidence among exposed
Relative risk = ________________
Incidence among unexposed

a/a+b
RR = q+/q- = ------------------
c/c+d
Diseased Nondiseased
Exposed a b
Unexposed c d
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19. Hypothetical cohort study of the one year incidence rate o
f acute MI.
Myocardial infarction
Blood
pressure
Present Absent Total
Severe
hypertension
180(a) 9820(b)10000
Normal 30(c) 9970(d)10000
Relative risk = IE/IU
Incidence among exposed = 180/10000 = 0.0180
Incidence among unexposed = 30/10000=0.0030
RR = 0.0180/0.0030 = 6.00
ar
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OR/RR

20. Interpreting Relative risk of a Interpreting Relative risk of a
disease.disease.
RR = 1 No association
RR > 1 Positive association
(possibly causal)
RR < 1 Negative association
(possibly protective)
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21. Framingham study during first 12 yearsFramingham study during first 12 years
Serum
cholesterol
Men Women
30-49 yr 50-62 30-49 50-62
Incidence rates (per 1000)
<190 38.2 105.7 11.1 155.2
190-219 44.1 187.5 9.1 88.9
220-249 95.0 201.1 24.3 96.3
250+ 157.5 267.8 50.4 121.5
Relative risks
<190 1.0 2.8 0.3 4.1
190-219 1.2 4.9 0.2 2.3
220-249 2.5 5.3 0.6 2.5
250+ 4.1 7.0 1.3 3.2
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22. Statistical test for RRStatistical test for RR
The relative risk can theoretically range from 0 to positive
infinity , with their expected values, assuming no association,
being 1.
This non-symmetric distribution is not easy to evaluate using
the conventional statistical tests.
These ratio measures are usually transformed, therefore,
using the natural logarithm
◦to yield distributions symmetric around an expected value of 0
◦and approximately normal in shape, analogous to the distributions of
the difference measures.
For ease of interpretation and reporting, the measures and
their confidence limits are transformed back to their original
form after performing the desired statistical tests.
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23. Lower limit 95% CI(RR)
Upper limit 95% CI(RR)
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)(log96.1log)(log%95 RRSERRRRCI 
)()(
)(log
dcc
d
baa
b
RRSE
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RR
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24. RR-STATISTICAL TESTRR-STATISTICAL TEST
From MI cohort study example.
RR= 6.0
SE(log RR) =
Lower limit 95% CI(RR)
Upper limit 95% CI(RR)
◦Hypothesis testing is done by usual chi-square or fisher
exact test for 2 x 2 contingency table.
9820
180(10000)
9970
30(10000)
= 0.197
6.0
0.197
6.0
0.197
= 4.08
= 8.83
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25. Odd’s ratio(Relative odds)Odd’s ratio(Relative odds)
In 1951 cornfield pointed out that odd’s ratio of the
disease and odd’s ratio of the exposure are
mathematically equivalent.
In case control study , we don’t know the incidence of
the disease in the exposed or unexposed since we start
with the diseased people (cases) and nondiseased
people(controls).
Hence calculation of RR can’t be made directly in Case-
Control study.
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26. Odd’s of an event can be defined as the ratio of
the number of the ways the event can occur to
the number of ways the event cannot occur.
Probability of the event can occur
Odds = -------------------------------------------------
Probability of the event cannot
occur
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27. Odds ratio in a cohort studyOdds ratio in a cohort study
Odds that an exposed person
develop disease = a/b
Odds that an unexposed person
develop disease = c/d
Odds ratio = (a/b ) / (c/d) = ad/bc
Develop
disease
Do not
develop
disease
Exposed a b
Unexposed c d
What are the odds that the disease will develop in an exposed
person?
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28. Odds ratio in a case-control studyOdds ratio in a case-control study
What are the odds that a case was exposed?
Cases(with
disease)
Controls
(without
disease)
H/O of expos a b
No H/O expos c d
Odds that a case was exposed = a/c
Odds that a control was exposed = b/d
Odds ratio or Relative odds = (a/c ) / (b/d) = ad/bc
Also called Cross-product ratio.
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29. Odds ratio or the cross-products ratio
can be viewed as
product of the two cells
that support the
hypothesis of an
association
product of the two cells
that negate the
hypothesis of an
association
Cases(with
disease)
Controls
(without
disease)
H/O of expos a b
No H/O expos c d
:
ad bc:
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30. Odds ratio in a matched case Odds ratio in a matched case
control studycontrol study
Controls are often selected by matching each
controls to a case according to variables that
are known to be related to disease risk either
by individual matching or matching pairs.
For example,4 types of case-control
combinations are possible in regard to
exposure history,if exposure is
dichotomus(either the person is exposed or
unexposed)
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31. Concordant pairs
Pairs in which both the case and
controls were exposed.(a)
Pairs in which neither the case nor
the control were unexposed (d)
Discordant pairs
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)
CASE- CONTROL PAIRS
CONTROL
Exposed Unexposed
CASE
Expsoed a b
Unexposed c d
Calculation of the odds ratio is based on discordant pairs.
Odds ratio (matched pairs)= b/c
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32. Birth weight of index child: matched pairs comparison of Birth weight of index child: matched pairs comparison of
cases and normal controls(>8 lb vs. <8 lb).cases and normal controls(>8 lb vs. <8 lb).
Risk factors for brain tumors in children.Risk factors for brain tumors in children.
Am. J Epidemiol 109Am. J Epidemiol 109
Odds ratio = 18/7 = 2.57
CASE- CONTROL PAIRS
Normal controls
8+ lb < 8 lb
Cases
8+ lb 8 18
< 8 lb 7 38
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33. Relationship between OR and RRRelationship between OR and RR
OR is a valid measure of association in its own
right and it is often used as an approximation of
the relative risk’.
Use of OR as an estimate of the relative risk
biases it in a direction opposite to the null
hypothesis, i.e. it tends to exaggerate the
magnitude of the association.
When the disease is relatively rare , this built-in
bias is negligible .
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34. Mathematical relationship between the Mathematical relationship between the
OR and RROR and RR
Assume
q+  incidence (probability)in exposed.
q-  incidence (probability) in unexposed.
Then odds ratio is

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q
q
q
q
q
q
q
q
OR
1
1
1
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q
q
q
q
OR
1
1
RR
BIAS
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35. This bias is responsible for the discrepancy between the
relative risk and the odds ratio estimates(built-in bias).
If the association between the exposure and the
outcome is positive,
Then q- < q+ , thus (1-q-)>(1-q+).
Then bias term will therefore be greater than
1.0,leading an overestimation of the relative risk by the
odds ratio.
By analogy, if the factor is protective , the opposite
occurs – that is, (1-q-) < (1-q+) and the odds ratio will
again overestimate the strength of association.










q
q
1
1
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36. Hypertension/myocardial infarction example
OR = RR x built in bias
= 6.09.
◦Since , the probability of MI is low for both exposed
and the unexposed groups , the probability odds of
developing the disease approximate the probabilities.
◦As a result, the probability odds ratio of the disease
(exposed vs unexposed) approximates the relative risk.









0180.01
0030.01
0.6
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37. Incidence of local reactions in the vaccinated and
placebo groups, influenza vaccination trial.
Seltser et al
Local reaction
GroupPresentAbsentTotalProbability Probability odds
Vaccine650 19202570650/2570= 0.2529650/(2570-650)
=650/1920
= 0.3385
Placebo170 22402410170/2410=0.0705170/(2410-170)
= 170/2240
= 0.0759
59.3
0705.0
2529.0
2410
170
2570
650
RR 46.4
0759.0
3385.0
2240
170
1920
650
OR
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38. OR = RR X built in bias
46.4244.159.3
2529.01
0705.01
59.3 


OR
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

q
q
RROR
1
1
Hence when the condition has a high incidence and when prospective data are
available , there will be considerable bias when using OR to estimate RR.
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39. Example. Example.
Vaccine : local reaction
OR
local reaction(+ ) 46.4
2240
170
1920
650

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
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
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

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OR
local reaction(- )
46.4
1
22.0
170
2240
650
1920

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











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40. Example. Example.
Vaccine : local reaction
RR
local
reaction(+ )
RR
local
reaction(- )
59.3
2410
170
2570
650














59.3
1
8.0
2410
2240
2570
1920














1.Sensitivity of the relative risk to the magnitude of the outcome.
2.Relative risk of common endpoint approaches 1.0.
3.This is well appreciated when studying the complement of rare outcomes.
4.The more frequent the outcome becomes, the more the odds ratio will
overestimate the risk ratio when it is more than1 or underestimate the risk
ratio when it is less than 1.
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41. Relationship between RR and OR by Relationship between RR and OR by
the incidence of the outcome.the incidence of the outcome.
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42. ATTRIBUTABLE RISK (AR)ATTRIBUTABLE RISK (AR)
How much of the disease that occurs can be attributed to
a certain exposure?
AR is defined as the amount of proportion of disease
incidence (or disease risk) that can be attributed to a
specific exposure.
AR in exposed persons(eg. AR of lung cancer in smokers)
AR for the population includes both exposed and
unexposed persons(AR of lung cancer in population which
consists of both smokers and non-smokers)
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43. TermsTerms
AR is a measure of association based on the
absolute difference between two risk estimates.
It is often used to imply a cause-effect
relationship and should be interpreted as a true
etiologic fraction only when there is a
reasonable certainty of a causal connection
between exposure and outcome.
When causality has not been firmly established
then the AR is termed as excess fraction.
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44. AR in exposed individualsAR in exposed individuals
It is merely a difference between the risk
estimates of different exposure levels and a
reference exposure level.
If q
+ = risk in exposed individual.
q
- = risk in unexposed individual.
AR
exp = q
+ - q
-
It measures the excess risk for a given exposure
category associated with the exposure
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45. Example: MI and HT
Cumulative incidence of MI
among hypertensive indivs. q
+ = 0.018 (1.8%).
Cumulative incidence of MI
among normotensives (reference or
unexposed category) q
- = 0.003(0.3%).
Excess risk associated with
exposure to hypertension = (0.018-0.003)
= 0.015(1.5%).
Interpretation:
if the excess incidence were completely reversible, the cessation of
the exposure(severe HT) would lower the risk in the exposed
group from 0.018 to 0.003.
That is the absolute excess incidence that would be prevented by
eliminating hypertension is 1.5%
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46. Percent ARexp:
When AR is expressed as a percentage.
%AR exp
Interpretation:
The percentage of the total risk in the
exposed attributable to the exposure.
The percentage of the MI attributable to the
severe HT= 83.3%
100




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




 
q
qq
%3.83100
018.0
003.0018.0



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47. %AR in case-control studies%AR in case-control studies
100
1
100
1
100
100R% e

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RR
RR
RR
RR
q
q
q
q
q
qq
A xp
%3.83100
0.6
0.10.6
R% e 





xpA
This formula can be used in case-control studies , in which
the incidence data are unavailable, but the odds ratio can be
used as an estimate of the relative risk if the disease is
relatively rare.
100
0.1
R% e 






RR
RR
A xp
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48. EFFICACYEFFICACY
%AR is analogous to percent efficacy
when assessing an intervention such as a
vaccine.
q
+ is replaced by q
cont risk in control
group,eg. Group receiving placebo.
q- is replaced by qinterv risk in those
undergoing intervention
100
int










cont
ervcont
q
qq
Efficacy
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49. AR exp
BACKGROUND RISK
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50. POPULATION ATTRIBUTABLE POPULATION ATTRIBUTABLE
RISKRISK
What proportion of the disease incidence in a total
population can be attributed to a specific exposure?
To know the PAR , we need to know
incidence in total population = qpop
incidence in unexposed group(background risk)=q-
100







 

pop
pop
q
qq
PAR
  )1( eepop pqpqq  
pe prevalence of exposure in total population.
1-pe  prevalence of non-exposure.
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51. Smoking and heart disease: Hypothetical cohort Smoking and heart disease: Hypothetical cohort
study of 3000 cigarette smokers and 5000 non-study of 3000 cigarette smokers and 5000 non-
smokerssmokers
CHD
develops
CHD does
not develop
Total Incidence
per 1000
per year
Smoke 84 2916 3000 (q+)28
Do not smoke87 4913 5000 (q-)17.4
  
1000
1.22
56.0174.44.028. popq
Assuming the proportion of smokers in the pop. Pe : 44%
Therefore the proportion of non-smokers (1- pe ): 56%
  )1( eepop pqpqq  
100










pop
pop
q
qq
PAR %3.21100
1.22
4.171.22







21.3% of the incidence of CHD in the total population can be attributed to
smoking.
If an effective prevention program eliminated smoking, the best that we could
hope to achieve would be reduction of 21.3% in the incidence of CHD in the total
population consisting of both smokers and non-smokers.
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52. 24-Dec-08 52
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53. AR and RRAR and RR
Age adjusted death rates
per 100000
SmokersNon smokers RR AR %AR
Lung cancer140 10 14.0 130 92.9%
CHD 669 413 1.6 256 38.3%
From Doll R,Peto R: Mortality in relation to smoking:20 yrs observation on male British doctors. Br Med J 2:1525-
1536,1976
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1.RR is much higher for lung cancer than for CHD and the attributable risk
expressed as a proportion is also much higher for lung cancer.
2.However if an effective smoking cessation program were available and
smoking were eliminated, would the preventive impact be greater on
mortality from lung cancer or from CHD?
3.If we examine the table we see that if smoking were eliminated, 256 deaths
per 100000 from CHD would be prevented in contrast to only 130 from
lung cancer, despite the fact that the RR is higher for lung cancer and despite
the fact that the proportion of deaths attributable to smoking is greater for
lung cancer.
4.This is due to the fact that the mortality level in smokers is much higher for
CHD than for lung cancer.(669 compared to 140) and the AR is much
greater for CHD than for lung cancer.

54. CAUSATIONCAUSATION
Causation is an interpretation, not an entity; it should
not be reified.
The 18th-century Scottish philosopher David Hume
pointed out that causation is induced logically, not
observed empirically.
 Therefore we can never know absolutely that
exposure X causes disease Y. There is no final proof
of causation.
it is merely an inference based on an observed
conjunction of two variables (exposure and health
status) in time and space.
This limitation of inductive logic applies, of course, to
both experimental and non-experimental research.
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55. Karl Popper stressed that science
progresses by rejecting or modifying
causal hypotheses, not by actually
proving causation.
a practical data-based approach to the
notion of causation - Bradford Hill’s
criteria of causality.
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56. Bradford Hill’s Bradford Hill’s criteriacriteria
Bradford Hill recognized the importance
of moving from association to causation
as a necessary step for taking preventive
action against environmental causes of
disease.
views
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57. 24-Dec-08 57
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58. STRENGTHSTRENGTH
1.Strong assocaitions are more likely to be
causal than weak.
2.Weaker associations are more likely to be
explained by undetected bias.
3.But weaker association does not rule out
causation.
Eg. Smoking and CHD
4.Strong but non-causal.
Eg: Down syndrome and birth rank.
Confounded by maternal age.
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59. CONSISTENCYCONSISTENCY
Repeated observation of an association in different
populations under different circumstances.
Lack of consistency however does not rule out a
causal association.
Consistency is apparent only after all the relevant
details of a causal mechanism are understood, which
is to say very seldom.
Consistency serves only to rule out hypotheses that
the association is attributable to some factor that
varies across studies.
The results (effect estimates) from the studies could
all be identical even if many were significant and many
were not, the differences arises solely from difference
in standard errors or sizes of the studies.
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60. SPECIFICITYSPECIFICITY
Cause leads to a single effect and not
multiple effects.
Causal hypothesis predicts a relation with
one outcome but no relation with
another outcome; it can be logically
deduced from the causal hypothesis in
question.
Eg: smoking.
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61. TEMPORALITYTEMPORALITY
Necessity for a cause to precede an effect
in time.
It is the only necessary criterion for a
causal relationship between an exposure
and an outcome.
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62. BIOLOGICAL GRADIENTBIOLOGICAL GRADIENT
Presence of a unidirectional dose-response curve.
Monotonic relation.
◦More smoking more tissue damage carcinogenisis.
Threshold relation.
◦DES adenocarcinoma of uterus.
All monotonic are not causal.
◦Eg:Down syndrome and birth rank;confouded by maternal
age.
A non monotonic relation only refutes those causal
hypotheses specific enough to predict a monotonic
dose-response curve.
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63. PLAUSIBILITYPLAUSIBILITY
Biological plausibility of the hypothesis but one
that is far from objective or absolute.
It is too often not based on logic or data ,but
only on prior beliefs.
It is difficult to demonstrate where the
confounder itself exhibits a biological gradient
in relation to the outcome.
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64. COHERENCECOHERENCE
Cause and effect interpretation for an
association does not conflict with what is
known of the natural history and biology of the
disease.
Absence of coherent information as
distinguished, apparently , from the presence of
conflicting information, should not be taken as
evidence against an association being
considered causal.
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65. EXPERIMENTAL EVIDENCEEXPERIMENTAL EVIDENCE
However , is seldom available for most epidemiologic
research questions.
It seems from the hill’s view, that experimental
evidence was the result of removal of some harmful
exposure in an intervention or prevention program,
rather than the results of laboratory experiments.
However experimental evidence is not a criterion
but a test of the causal hypothesis.
Although experimental tests can be much stronger
than other tests, they are often not as decisive as
thought, because of difficulties in interpretation.
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66. ANALOGYANALOGY
Analogy provides a source of more
elaborate hypotheses about the
associations under study; Absence of such
analogies only reflects lack of imagination
or experience , not falsity of the
hypothesis.
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67. REFERENCESREFERENCES
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3.Measures of Association and Hypothesis Testing
by Deborah Rosenberg, PhD and Arden Handler, DrPH
4.Causation and Causal Inference in Epidemiology
Kenneth J.Rothman, DrPH, Sander Greenland, MA, MS, DrPH, C Stat

68. Hypothesis testing for RRfor RR
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