Transcript Lecture 4 - Measures of association

Measures of association
1) Measures of association based on ratios
– Cohort studies
•
•
•
•
Rate ratio
Incidence proportion ratio Generic name: “Relative Risk”
Hazard ratio
Odds ratio (OR)
– Case control studies
• OR of exposure and OR of disease
• OR when the controls are a sample of the total
population
– Prevalence ratio (or Prevalence OR) as an
estimate of the risk ratio
2) Measures of association based on
absolute differences: attributable risk
1. Measures of association based on ratios
(relative measures of “effect”)
The relative measures of association should assume the names of the measures of
disease frequency on which they are based.
Examples:
•
Rate ratio: Ratio of two rates [denominator of rate: person-time]
•
Incidence proportion ratio: Ratio of two incidence proportions [denominator of
rate: persons without adjustment for duration of follow-up]
•
Hazard ratio: Ratio of two hazards (cumulative incidences) [denominator of
hazard: persons, with adjustment for duration of follow-up (time to event)]
•
Odds ratio (or relative odds): Ratio of two odds [usually based on incidence
proportions]
(Even though many of the concepts discussed in this lecture also apply to rate
ratios and hazard ratios, for simplification purposes, the discussion is based
on the ratio of incidence proportions, which is usually called “risk ratio” or
“relative risk”)
(Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer
in men and women. Am J Epidemiol 2004;160:248-258)
(Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer
in men and women. Am J Epidemiol 2004;160:248-258)
(Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer
in men and women. Am J Epidemiol 2004;160:248-258)
Adjusts for multiple variables in addition to
duration of follow-up (time to event)
(Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer
in men and women. Am J Epidemiol 2004;160:248-258)
**
**
“*Relative risks adjusted for potential confounders were approximated by Cox proportional
hazards regression…”
** Cases/Person-years= rates of pancreatic cancer
(Skinner HG, et al. A prospective study of folate intake and the risk of pancreatic cancer
in men and women. Am J Epidemiol 2004;160:248-258)
Jacobs EJ, Multivitamin use and colorectal incidence in a US cohort: does timing matter?
Am J Epidemiol 2003;158:621-628)
Jacobs EJ, Multivitamin use and colorectal incidence in a US cohort: does timing matter?
Am J Epidemiol 2003;158:621-628)
Correct terminology? Incidence proportion ratios?
Rate ratios?
Results
Wrong! It should be “hazard ratio”
Cohort studies (assume that duration of
follow-up is same in exposed and unexposed)
Hypothetical cohort study (based on the Framingham study results) of the one-year
incidence of acute myocardial infarction for individuals with severe systolic
hypertension (HTN, ≥180 mm Hg) or normal systolic blood pressure (<120 mm Hg).
Severe
Systolic
HTN
Number
Yes
No
Myocardial infarction
Present
Absent
9820
Incidence
proportion (q)
0.0180
10000
180
10000
30
Oddsdis
0.01833
9970
0.0030
0.00301
180
0.0180
10000
RR 

 6.00
30
0.0030
10000
Odds RatioDISEASE
q+
0.0180
10
.  q + 1.0  0.0180



0.0030
q
10
.  q  1.0  0.0030
180
9820  0.01833 6.09
30
0.00301
9970
The OR can also be calculated from the “cross-products
ratio”:
Severe
Systolic
HTN
Yes
Number
No
Myocardial infarction
Present
Absent
Incidence (q)
Oddsdis
10000
180 (a)
9820 (b)
0.0180
0.01833
10000
30 (c)
9970 (d)
0.0030
0.00301
OR disease
a
a
a+b
a+b
q+
 a 
b
a
1 

1  q+
a + b  a + b b ad




 
q
c
c
c bc
1  q
c+d
c+d
d
d
 c 
1 

c
+
d

 c+d
OR disease
180  9970

 6.09
9820  30
When (and only when) the OR is used to estimate the
risk ratio, there is a “built-in” bias:
q+
q+
1  q
q+ 1  q
1  q+
OR 




q
1  q+
q
q 1  q+
1  q
RR
“bias”
Example:
Severe
Systolic
HTN
Yes
Number
No
ORDISEASE
Myocardial infarction
Present
Absent
Incidence (q)
Oddsdis
10000
180 (a)
9820 (b)
0.0180
0.01833
RR=6.0
10000
30 (c)
9970 (d)
0.0030
0.00301
OR=6.09
180
 9820  6.09
30
9970
OR dis
1  0.003
 6.0 
 6.09
1  0.018
OR  RR 
1  q
1  q+
• For risk factors (q+>q-, RR>1.0) as in the previous
example:
(1-q-)>(1-q+)
and the resulting bias is, by definition, >1.0.
Therefore, OR>RR.
• For protective factors (q+<q-, RR<1.0) :
(1-q-)<(1-q+)
and the resulting bias is, by definition, <1.0.
Therefore, OR<RR.
IN GENERAL:
• The OR is always further away from
1.0 than the RR.
• The higher the incidence, the higher
the discrepancy.
Relationship between RR and OR
… when probability of the event (q) is low:
q
q
1 q
1 q
  10
.
or, in other words, (1-q)  1, and thus, the “built-in bias” term,
1  q+
and OR  RR.
Example:
Severe
Systolic
HTN
Yes
Number
No
Myocardial infarction
Present
Absent
10000
180
9820
10000
30
9970
OR  6.0 
180
RR  10000  6.00
30
10000
1  0.003
0.997
 6.0 
 6.09
1  0.018
0.982
180
OR  9820  6.09
30
9970
Relationship between RR and OR
… when probability of the event (q) is high:
Example:
Cohort study of the one-year recurrence of acute myocardial infarction
(MI) among MI survivors with severe systolic hypertension (HTN, ≥180
mm Hg) and normal systolic blood pressure (<120 mm Hg).
Severe
Systolic
HTN
Yes
Number
No
Recurrent MI
Present
Absent
10000
3600
6400
10000
600
9400
OR  6.0 
q
0.36
0.06
3600
RR  10000  6.00
600
10000
1  0.06
0.94
 6.0 
1  0.36
0.64
3600
OR  6400  8.81
600
9400
OR vs. RR: Advantages
• OR can be estimated from logistic regression (to be discussed
later in the course).
• OR can be estimated from a case-control study because…
…OR of exposure = Odds ratio of disease
CASE-CONTROL STUDIES
Case-control studies
A) Odds ratio of exposure and odds ratio of disease
Hypothetical cohort study of the one-year incidence of acute
myocardial infarction for individuals with severe systolic hypertension
(HTN, 180 mm Hg) and normal systolic blood pressure (<120 mm Hg).
Severe
Systolic
HTN
Yes
Number
No
Myocardial infarction
Present
Absent
10000
180
9820
10000
30
9970
Oddsdis exp
OR dis 
Oddsdis non -exp
same
Hypothetical case-control study assuming that all members of the
cohort (cases and non cases) were identified*
Severe Syst HTN
Cases
Controls
Yes
180
9820
No
30
9970
OR exp 
180
 9820  6.09
30
9970
Oddsexp cases
Oddsexp non -cases
180
 30  6.09
9820
9970
Case-control studies
A) Odds ratio of exposure and odds ratio of disease
Hypothetical cohort study of the one-year incidence of acute
myocardial infarction for individuals with severe systolic hypertension
(HTN, 180 mm Hg) and normal systolic blood pressure (<120 mm Hg).
Severe
Systolic
HTN
Yes
Number
No
Myocardial infarction
Present
Absent
10000
180
9820
10000
30
9970
Oddsdis exp
OR dis 
Oddsdis non -exp
same
Hypothetical case-control study assuming that all members of the
cohort (cases and non cases) were identified
Severe Syst HTN
Cases
Controls
Yes
180
9820
No
30
9970
OR exp
180
 9820  6.09
30
9970
Oddsexp cases

Oddsexp non -cases
180
 30  6.09
9820
9970
Retrospective (case-control) studies can estimate the OR of disease
because:
ORexposure = ORdisease
Because ORexp = ORdis, interpretation of the OR is always “prospective”.
Calculation of the Odds Ratios: Example of Use of
Salicylates and Reye’s Syndrome
Past use of
salicylates
Yes
Cases
Controls
26
53
No
1
87
Total
27
140
Odds Ratios
(26/1) ÷ (53/87) =
42.7
Interpretation: Always “prospective” Children using
salicylates have an odds (≈risk) of Reye’s syndrome that is
almost 43 times higher than that of non-users
(Hurwitz et al, 1987, cited by Lilienfeld & Stolley, 1994)
Cohort study:
Severe
Systolic
HTN
Number
Yes
Myocardial infarction
Present
Absent
10,000
180
9,820
No
10,000
30
9,970
Total
20,000
210
19,790
ORdis 
Odds dis exp
Odds
dis un exp
180
9820

 6.09
30
9970
In a retrospective (case-control) study, an unbiased sample of the cases and
controls (non-cases) yields an unbiased OR
It is not necessary that the sampling fraction be the same in both cases and
controls. As cases are less numerous, the sampling fraction for cases is usually greater
than that for controls. For example, a majority of cases (e.g., 90%) and a smaller
sample of controls (e.g., 20%) could be chosen (assume no random variability).
Severe Syst HTN
Yes
Cases
162
Controls
1964
No
27
1994
Toal
210 x 0.9 = 189
19790 x 0.2 = 3958
OR exp 
Oddsexp in cases
Odds exp in cntls
162
 27  6.09
1964
1994
Case-control studies
B) OR when controls are a sample of the total population
Risk factor
CASES
NON-CASES
Present
a
b
TOTAL
POPULATION
a+b
Absent
c
d
c+d
OR exp 
Odds exp cases
Odds exp non -cases
a
 c
b
d
OR exp
Odds exp cases

Odds exp population
a
 c
a+b
c+d
a
 a + b  RR
c
c+d
In a case-control study, when the control group is a sample of the total
population (rather than only of the non-cases), the odds ratio of exposure is an
unbiased estimate of the INCIDENCE PROPORTION RATIO (or, if adjustment
for duration of follow-up is done, of the HAZARD RATIO)
Example:
Hypothetical cohort study of the one-year recurrence of acute myocardial
infarction (MI) among MI survivors with severe systolic hypertension (HTN,
≥180 mm Hg) or normal systolic blood pressure (<120 mm Hg).
Severe
Systolic
HTN
Yes
Recurrent MI
Total
population
Present
Absent
3,600
6,400
10,000
No
600
9,400
10,000
3,600
10,000
RR 
 6.00
600
10,000
Example:
Hypothetical cohort study of the one-year recurrence of acute myocardial
infarction (MI) among MI survivors with severe systolic hypertension (HTN,
180 mm Hg) or normal systolic blood pressure (<120 mm Hg).
Severe
Systolic
HTN
Yes
Recurrent MI
Total
population
Present
Absent
3,600
6,400
10,000
No
600
9,400
10,000
• Using a traditional case-control
strategy, cases of recurrent MI are
compared to non-cases, i.e.,
individuals without recurrent MI:
OR exp
3600
 600  8.81  ORdis
6400
9400
3600
10,000
RR 
 6.00
600
10,000
Example:
Hypothetical cohort study of the one-year recurrence of acute myocardial
infarction (MI) among MI survivors with severe systolic hypertension (HTN,
180 mm Hg) or normal systolic blood pressure (<120 mm Hg).
Severe
Systolic
HTN
Yes
Recurrent MI
Present
Absent
3,600
6400
10,000
No
600
9400
10,000
• Using a traditional case-control
strategy, cases of recurrent MI are
compared to non-cases, i.e.,
individuals without recurrent MI:
OR exp
3600
 600  8.81  ORdis
6400
9400
Total
population
3600
10,000
RR 
 6.00
600
10,000
• Using a case-cohort strategy,
the cases are compared to the
total population:
OR exp
3,600
3,600
10,000
 600 
 6.00  RR
10,000
600
10,000 10,000
Severe
Systolic
HTN
Yes
Recurrent MI
Total
population
Present
Absent
3,600
6,400
10,000
No
600
9,400
10,000
Total
4,200
15,800
20,000
Note that it is not necessary to have the total groups of cases and non-cases or the total
population to estimate the odds of exposure. It is sufficient to obtain sample estimates
of the odds of exposure in cases and either non-cases (to obtain the odds ratio of
disease) or the total reference population (to obtain the risk ratio). Example: samples of
20% cases and 5% total population:
ORexp
720
120

 6.0  RR
500
500
Thus… Risk Ratio can be calculated in two ways:
1. Ratio of two incidence proportions, or
2. Exposure odds estimate in cases divided by exposure odds estimate in the
total reference population (study base).
Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in
Busselton, Western Australia. Am J Epidemiol 2003;158:144-149
Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in
Busselton, Western Australia. Am J Epidemiol 2003;158:144-149
Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in
Busselton, Western Australia. Am J Epidemiol 2003;158:144-149
Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in
Busselton, Western Australia. Am J Epidemiol 2003;158:144-149
Total cohort with serum samples: 1,612 individuals × 0.75= 1209
*
* Barlow WE. Robust variance estimation for the case-cohort design. Biometrics
1994;50:1064-1072
Knuiman MW et al, Serum ferritin and cardiovascular disease: a 17-year follow-up study in
Busselton, Western Australia. Am J Epidemiol 2003;158:144-149
†Adjusted for age and other cardiovascular risk factors
To summarize, in a case-control study:
What is the control
group?
What is calculated?
Sample of
NON-CASES
ORexp
Sample of the
TOTAL POPULATION
ORexp 
To obtain ...
Oddsexp cases

Oddsexp non -cases
Odds
RatioDisease
Oddsexp cases
Oddsexp total pop
Risk Ratio
Recapitulation - I
• Measures of association quantify a relationship between a potential risk
factor and an outcome
• Measures of association adopt the names of the measures of disease
occurrence on which they are based:
– Rate ratio: ratio of two rates (based on person-time)
– Incidence proportion ratio: ratio of two incidence proportions (based on
persons)
– Hazard ratio or Cumulative incidence ratio: ratio of two hazards
(based on persons, adjusted for time to event)
– Odds ratio: ratio of two odds:
• In a cohort study, ratio of the odds of disease in exposed and in
unexposed
• In a case-control study, ratio of the odds of exposure in cases
and in controls
Odds ratio of exposure = odds ratio of disease; thus,
interpretation of odds ratio in a case-control study is always
“predictive” or “prospective”
NOTE: “RELATIVE RISK” IS A GENERIC NAME
Recapitulation - II
• The ideal ratio-based measure of association is the
hazard ratio (cumulative incidence ratio):
– Its analytic unit is person;
– It adjusts for differential follow-up duration
between the groups under comparison (e.g.,
exposed and unexposed, intervention and
control);
– Using the Cox regression model, additional
variables (that is, other than duration of
follow-up) can be adjusted for;
– It can be estimated in a case-cohort study.
Recapitulation- III
PROBLEMS WITH RATES, AND THUS RATE RATIOS, BASED ON USING TIME
UNITS (E.G., PERSON-YEARS)
1) ASSUMPTION OF ACUTE (NON-CUMULATIVE) EFFECT: To follow N persons for t time is
equivalent to following t persons for N time
-Person-time= N × t
Example: 20 SMOKERS FOLLOWED FOR 1 YEAR = 1 SMOKER FOLLOWED FOR 20
YEARS= 20 PERSON-YEARS
2) THEORETICALLY, RATES CAN RESULT IN IMPOSSIBLE VALUES
Example:
• One wishes to obtain a one-year case-fatality rate of disease Y, which is highly lethal.
• 50 persons are followed for up to one year:
-Deaths are relatively uniform over the one-year follow-up. Average follow-up for 40
(out of the 50) patients who die is 6 months
-6 individuals are (also uniformly) lost to follow-up after an average of 6 months
No. of person-years= (40 × 6/12) + (6 × 6/12) + (4 × 1)= 27
Rate (%) = (40 ÷ 27) × 100= 148/100 PY
Recapitulation - IV
• Case-control studies:
“traditional” case-control studies
Case-based case-control studies (control
group is usually formed by non-cases)
Odds ratio of exposure = odds ratio of
disease
Case-cohort studies (control group is
formed by a sample of the total cohort)
Odds ratio of exposure = relative
risk (incidence proportion ratio or
hazard ratio)
Risk factor
CASES
NON-CASES
Present
a
b
TOTAL
POPULATION
a+b
Absent
c
d
c+d
CASE-BASED CASE-CONTROL STUDY
USES A SAMPLE OF NON-CASES:
OR exp 
Odds exp cases
Odds exp non -cases
a
 c
b
d
CASE-COHORT STUDY USES A SAMPLE
OF THE TOTAL COHORT (STUDY BASE):
OR exp 
Odds exp cases
Odds exp population
a
 c 
a+b
c+d
a
 a + b  RR
c
c+d
TO CALCULATE THE RISK RATIO VIA INCIDENCE
PROPORTIONS (OR RATES, OR HAZARDS), A CLASSICAL
COHORT ANALYSIS IS NEEDED
Risk factor
CASES
NON-CASES
Present
a
b
TOTAL
POPULATION
a+b
Absent
c
d
c+d
CASE-BASED CASE-CONTROL STUDY
USES A SAMPLE OF NON-CASES:
OR exp 
Odds exp cases
Odds exp non -cases
a
 c
b
d
CASE-COHORT STUDY USES A SAMPLE
OF THE TOTAL COHORT (STUDY BASE):
OR exp 
Odds exp cases
Odds exp population
a
 c  RR
a+b
c+d
TO CALCULATE THE RISK RATIO IN A CASECOHORT STUDY, ONLY AN ESTIMATE OF THE
ODDS OF EXPOSURE IN THE TOTAL COHORT
(STUDY BASE) IS NEEDED.
NOTE: IN A CASE-COHORT STUDY,
BECAUSE THE OREXP = RR, THE “DISEASE
RARITY” ASSUMPTION IS NOT
NECESSARY
How to calculate the OR when there are
more than two exposure categories
Cases
Controls
Exposed
a
b
Unexposed
c
d
a d
" Cross  product ratio" 
b c
How to calculate the OR when there are
more than two exposure categories
Example:
Univariate analysis of the relationship between parity and
eclampsia.*
Parity
Unexposed: 2 or more
1
Nulliparous
Cases
11
21
68
Controls
40
27
33
* Abi-Said et al: Am J Epidemiol 1995;142:437-41.
7.5
8
7
6
5
OR 4
3
2
1
0
2.9
1
2+
1
Nulliparous
Number of pregnancies
OR
1.0 (Reference)
(21/11)÷(27/40)=2.9
(68/11)÷(33/40)=7.5
How to calculate the OR when there are
more than two exposure categories
Example:
Univariate analysis of the relationship between parity and
eclampsia.*
Parity
2 or more
1
Nulliparous
Cases
11
21
68
Controls
40
27
33
OR
1.0
2.9
7.5
* Abi-Said et al: Am J Epidemiol 1995;142:437-41.
10
Log
scale
Correct display:
7.5
2.9
OR
1
12 for linear trend  29.215, p  0.0001
1
2+
1
Nulliparous
Number of pregnancies
Baseline is 1.0
Detour…
A statistical significant (or non-significant) trend test should
not be automatically interpreted as proof of (or automatically
disprove) the presence of a dose-response association.
Studies with small sample
size may result in a NS
trend test even though
there appears to be a
dose-response association
OR
N=80
P(trend)=0.07
1.0
Exposure level
Studies with large samples
size may result on a
significant trend test even
though there is no doseresponse association
(threshold effect)
?
OR
N=80,000
P(trend)=0.02
1.0
Exposure level
Detour…
A statistical significant (or non-significant) trend test should
not be automatically interpreted as proof of (or automatically
disprove) the presence of a dose-response association.
Studies with small sample
size may result in a NS
trend test even though
there appears to be a
dose-response association
OR
N=80
P(trend)=0.07
1.0
Exposure level
Studies with large samples
size may result on a
significant trend test even
though there is no doseresponse association
(threshold effect)
OR
N=80,000
P(trend)=0.02
1.0
Exposure level
A note on the use of estimates from a
cross-sectional study (prevalence ratio, OR) to estimate the risk ratio
P+
P+ I+ D+
1 - P+ I+ D +
 
If the prevalence is low (~≤5%) 
 
Prevalence Odds=
P
I D 
P I D
1 - P
P+ I+

P I
If this ratio~1.0
Duration (prognosis) of the disease after onset is
independent of exposure (similar in exposed and
unexposed)...
However, if exposure is also associated with shorter survival (D+ < D-), D+/D- <1  the
prevalence ratio will underestimate the RR.
Hypothetical example:
P+ I+

P I
RISK RATIO 
5%
 5
1%
POINT PREVALENCE RATIO 
Real life example? Smoking and emphysema
5% 2 years

 2.5
1%
4 years
2. Measures of association based on absolute differences
• Attributable risk in the exposed:
The excess risk (e.g., incidence) among individuals exposed to a certain risk
factor that can be attributed to the risk factor per se:
AR exp  q+  q
%AR exp 
q+  q
 100
q+
%AR exp
RR - 1

100
RR
Incidence (per 1000)
Or, expressed as a percentage:
Pop AR
ARexp
Unexposed
Exposed
2. Measures of association based on absolute differences
• Attributable risk in the exposed:
The excess risk (e.g., incidence) among individuals exposed to a certain risk
factor that can be attributed to the risk factor per se:
AR exp  q+  q
Or, expressed as a percentage:
%AR exp 
q+  q
 100
q+
%AR exp
RR - 1

100
RR
• Population attributable risk:
The excess risk in the population that can be
attributed to a given risk factor. Usually expressed as
a percentage:
%PopARexp 
q pop' n  q 
q pop' n
100
The Pop AR will depend not only
on the RR, but also on the
prevalence of the risk factor (pexp)
Levin’s formula:*
%PopARexp 
pexp (RR  1)
pexp (RR 1) + 1
100
*Levin: Acta Un Intern Cancer 1953;9:531-41.
Advantage: In case-control studies,
the RR can be replaced by the OR
ARexp
IF NO ONE IN THE
REFERENCE
POPULATION IS
EXPOSED:
PopAR = Zero
Incidence (per 1000)
Unexposed
Population
Exposed
ARexp
IF A CERTAIN PROPORTION, BUT NOT
ALL PERSONS IN THE REFERENCE
POPULATION, ARE EXPOSED:
PopAR < ARexp
Pop AR
Pop AR
Unexposed
Population
Exposed
Incidence (per 1000)
IF EVERYONE IN THE
REFERENCE
POPULATION IS
EXPOSED:
PopAR = ARexp
Incidence (per 1000)
Pop AR
ARexp
Unexposed
Population
Exposed
Chu SP et al. Risk factors for proximal humerus fracture. Am J Epi 2004; 160:360-367
Cases: 448 incident cases identified at Kaiser Permanente. 45+ yrs old, ascertained through
radiology reports and outpatient records, confirmed by radiography, bone scan or MRI.
Pathologic fractures excluded (e.g., metastatic cancer).
Controls: 2,023 controls sampled from Kaiser Permanente membership (random sample).
Dietary Calcium (mg/day)
Odds Ratios (95% CI)
Highest quartile (≥970)
1.00 (reference)
Lowest quartile (≤495)
1.54 (1.14, 2.07)
What is the %AR in those exposed to the
lowest quartile?

Percent ARexposed
RR - 1
OR - 1
1.54  1
100 ~
 100 
 100  35%
RR
OR
1.54
Interpretation: If those exposed to values in the
lowest quartile had been exposed to values in the
highest quartile, their odds (risk) would have
been 35% lower.
What is the Percent AR in the total population due to exposure in the lowest quartile?
Levin’s formula for the Percent ARpopulation
Percent Population AR 
pexp ( RR  1)
pexp ( RR  1) + 1

Pexp (RR  1)
Pexp (RR  1) + 1
 100 ~
pexp (OR  1)
pexp (OR  1) + 1
100
 100 
RR estimate ~ 1.54
Pexp ~ 0.25
0.25 (154
.  1)
 100  11..9%
0.25 (154
.  1) + 1
Interpretation: The exposure to the lowest quartile is responsible for about 12% of the total
incidence of humerus fracture in the Kaiser permanente population
EXAMPLE:
Risk of diarrhea in 36 Peace Corps volunteers in Guatemala:
(based on data in Herwaldt et al: Ann Intern Med 2000;132:982-8)
Total=2521 person weeks, 307 diarrhea episodes (rp=0.122)
Incidence (per person-week)
0.2
– Drank water of unknown source
• Exposed: 594 pw, 105 episodes (r+=0.177/pw)
• Unexposed: 1927 pw, 202 episodes (r-=0.105/pw)
0.177
0.15
0.122
0.105
0.1
0.05
0
Pexp
Unexposed
Population
Exposed
RR= 0.177 ÷ 0.105= 1.69
594

 0.236 AR = 0.177 – 0.105= 0.072/pw; %AR = (0.072 ÷ 0.177) x 100= 40.7%
exp
exp
594 + 1927
%PopAR
rpop  r
rpop
100 
0.122 0.105
100  14%
0.122
Levin's formula: %PopARexp 
Levin' s Form ula: % PopAR
Pexp (RR  1)
Pexp (RR  1) + 1
100
CAUTION: THE ATTRIBUTABLE
RISK SHOULD BE ESTIMATED
ONLY WHEN THERE IS
REASONABLE CERTAINTY
THAT THE ASSOCIATION IS
CAUSAL
0.236(1.69  1.0)
 100  14%
0.236(1.69  1.0) + 1.0
A special type of %AR in the exposed:
•
Efficacy: the extent to which a specific
intervention or service produces a beneficial
result under ideal conditions. Ideally the
determination of efficacy is based on results of
randomized clinical trials (RCTs).
Incidence of event – Example:
Intervention: 20/200= 10%
Control: 40/200= 20%
%Efficacy 
 Inc
Control
   Inc
 Inc
Control
•
•
Effectiveness: the extent to which a specific
intervention or service, when deployed in the
field, does what it is intended to do for a defined
population.
Intervention


 100 
20%  10%
 100  50%
20%
- or -
Using the formula based on Risk Ratio (or Hazard
Ratio)
Incidencecontrol group
Risk Ratio 
Incidenceint ervention group
Efficiency
– The effects or end-results achieved in
relation to the effort expended in terms of
money, resources and time. The extent to
which the resources used to provide a
specific intervention or service of known
RR  10
.
2.0  10
.
efficacy and effectiveness are minimized. A % Efficacy 

 100  50%
RR
2
.
0
measure of the economy (or cost in
resources) with which a procedure of
known efficacy and effectiveness is carried
out.
– (In statistics, the relative precision with
which a particular study design or
estimator will estimate a parameter of
interest.)
•
Efficacy: the extent to which a specific intervention or
service produces a beneficial result under ideal
conditions. Ideally the determination of efficacy is
based on results of RCTs.
•
Effectiveness: the extent to which a
specific intervention or service, when
deployed in the field, does what it is
intended to do for a defined population.
•
Efficiency
– The effects or end-results achieved in relation to
the effort expended in terms of money, resources
and time. The extent to which the resources used
to provide a specific intervention or service of
known efficacy and effectiveness are minimized.
A measure of the economy (or cost in resources)
with which a procedure of known efficacy and
effectiveness is carried out.
– (In statistics, the relative precision with which a
particular study design or estimator will estimate
a parameter of interest.)
•
Efficacy: the extent to which a specific intervention or
service produces a beneficial result under ideal
conditions. Ideally the determination of efficacy is
based on results of RCTs.
•
Effectiveness: the extent to which a specific
intervention or service, when deployed in the field,
does what it is intended to do for a defined population.
•
Efficiency
– The effects or end-results achieved in
relation to the effort expended in terms
of money, resources and time. The
extent to which the resources used to
provide a specific intervention or
service of known efficacy and
effectiveness are minimized. A
measure of the economy (or cost in
resources) with which a procedure of
known efficacy and effectiveness is
carried out.
– (In statistics, the relative precision
with which a particular study design or
estimator will estimate a parameter of
interest.)
• Efficacy: Does the intervention work under ideal conditions?
• Effectiveness: If we implement the intervention in a “real life”
situation, is it effective?
– Example:
• Efficacy of a vaccine= 90%
• Only 30% of individuals can tolerate its side effects; Thus...
• EFFECTIVENESS= 90% x 30%= 27%
• Efficiency: Cost-effectiveness ratio
Rate Placebo    Rateactive 

Efficacy 
 100
 Rate Placebo 
or
RR  10
.
Efficacy 
RR
Example: HypertensionDetection & Follow-up Project Trial
DBP at
entry
(mmHg)
Stepped
Care (SC)
(Interv.)
Referred
Care (RC)
(Control)
5-Year
Mortality
Rate (%)
SC
RC
Efficacy (Reduction
in Mortality for SC
Group)
90-104
3903
3992
5.9
7.4
{[7.4-5.9] ÷[7.4]} x 100
= 20.3%
105-114
1048
1004
6.7
7.7
13.0%
 115
534
529
9.0
9.7
7.2%
Total
5485
5455
6.4
7.7
16.9%