Title: MEASURES OF DISEASE ASSOCIATION
1MEASURES OF DISEASE ASSOCIATION
2MEASURES OF DISEASE ASSOCIATION
-
- The chances of something happening can be
expressed as a risk 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
3- Thus a risk is a proportion, But an odds is
a ratio.
- Â
- An odds is a special type of ratio, one in which
the numerator and denominator sum to one.
4- Example 1. Bookies are taking bets on the World
Series. They are giving 31 odds on the Yankees.
What does this mean?
- It means that they
think that there it is three times as likely that
the Yankees will not win the world series as that
they will win. - Expressed as a risk, the Yankees
are expected to win one in four opportunities
5- Example 2. Among 100 people at baseline, 20
develop influenza over a year.
- The risk is 1 in 5 (i.e. 20 among 100)
- The odds is 1 to 4 (i.e. 20 compared to 80)
6THE RELATIVE RISK(RISK OR RATE RATIO)
- The relative risk is a ratio of two risks.
- Assume that among the 100 people at risk, 50 are
men and 50 women. If 15 men and 5 women develop
influenza, then the relative risk of developing
influenza in men, as compared with women, is - Risk in men 15/50
- divided by
- Risk in women 5/50
- 15/50 5/50 3.0
- (Note that from the way the question was put, the
two risks are cumulative incidence rates.)
7ODDS RATIO
- The odds ratio is a ratio of two odds
- The odds in men 15/35
divided by The odds in women 5/35
- 15/35 5/45 3.9
- We conclude that the odds of men getting
influenza over the year are 3.9 times as high as
the odds of women getting influenza.
- Thought question note that the odds
ratio in this example (3.9) is larger than the
relative risk (3.0). Is this always the case?
Is this important?
8MEASURES OF PUBLIC HEALTH IMPACT
- Four closely related measures are used
- Attributable risk
- Attributable (risk) fraction
- Population attributable risk
- Population attributable (risk) fraction
- Note all of these measures assume
that the association between exposure and disease
has already been shown to be causal.
91. ATTRIBUTABLE RISK (AR)
- The incidence of disease in the exposed
population whose disease can be attributed to the
exposure.
- AR Ie - Iu
102. ATTRIBUTABLE RISK FRACTION (ARF)
- The proportion of disease in the
exposed population whose disease can be
attributed to the exposure.
- ARF (Ie - Iu)/Ie
113. POPULATION ATTRIBUTABLE RISK (PAR)
- The incidence of disease in the total population
whose disease can be attributed to the exposure.
- PAR Ip - Iu
124. POPULATION ATTRIBUTABLE RISK FRACTION (PARF)
- The proportion of disease in the total population
whose disease can be attributed to the
exposure.
- PARF (Ip - Iu)/Ip
13Note Ip can be linked to Ie and Iu if one knows
the proportions of the population who are
exposed (P) and unexposed (Q), (P and Q add to
1). Â Ip P (Ie) Q (Iu)
14EXAMPLE OF THESE MEASURES (data are invented)
- Red-meat eaters have a relative risk of 2.0 for
colon cancer.
- If Iu 50/100,000/year, then
Ie 100/100,00/year.
- If 25 of the population are red-meat eaters,
what is Ip?
- Ip P (Ie) Q (Iu) , so
- Ip .25(100/100,000) .75 (50/100,000)
- Population incidence of colon cancer is thus
62.5 /100,000/year
-
15INFERRING AN ATTRIBUTABLE RISK FRACTION FROM A
RELATIVE RISK
- Note that Ie Iu times the relative risk
(RR) So substituting Iu x
RR for Ie in the equation for attributable risk
fraction - Â
- (Ie - Iu)/Ie
16- We get
- ARF RR (Iu) - Iu
- RR (Iu)
- Â
- Dividing through by Iu gives
- ARF RR - 1
- RR
17- In other words, if we find a truly causal
relative risk of 2.0 for a disease in relation to
an exposure, we can assume that 50 of the
disease in the exposed population is due to the
exposure. - Since the courts use a probability of 50 or
greater as a threshold in liability cases, RR of
2.0 has recently taken on great significance in
lawsuits. It has been argued that when RR 2.0,
it is more likely than not that the disease was
due to the exposure in an exposed individual.
What do you think of this legal reasoning?
18INFERRING A POPULATION ATTRIBUTABLE RISK FRACTION
FROM A RELATIVE RISK Â (this is a little heavier
going)
- Remember that
- PARF (Ip - Iu)/Ip
- and that Ip P(Ie) Q(Iu)
- and that Ie Iu x RR
19Therefore, the equation for PARF can be rewritten
in terms of RR
P(Ie) Q(Iu) Iu
PARF
P(Ie) Q(Iu)
- Replacing Ie with Iu x RR, we get
P(Iu)RR Q(Iu) Iu
PARF
P(Iu)RR Q(Iu)
20Going From A Relative Risk To An Attributable
Risk Fraction Contd
- Iu can be factored out and cancelledÂ
Iu (P x RR Q - 1)
X
PARF
Iu (P x RR Q)
X
If we now replace Q with 1-P (since P Q 1)
P x RR 1 - P - 1
PARF
P x RR 1 - P
21- or P (RR - 1) P (RR - 1) 1
- In other words, if we find a truly causal
relative risk of 2.0 for a disease in relation to
an exposure, and if 50 of the population has the
exposure, then 33 of the disease in the
population is due to the exposure. - (Again, always assuming that we are discussing a
exposure whose causal role has been established).
22EXAMPLE OF HOW FAILURE TO UNDERSTAND WHAT AN ODDS
RATIO MEANS CAN LEAD TO TROUBLE
23Schulman et al The Effect of Race and Sex on
Physicians' Recommendations for Cardiac
Catheterization. N Eng J Med 1999 340 619-625
- To study doctors recommendations for managing
chest pain, the study used actors to portray
patients with particular characteristics in
scripted interviews about their symptoms. - 720 primary care physicians viewed a recorded
interview and were given other data about a
hypothetical patient. He or she then made
recommendations about that patient's care. - The study used multivariate logistic-regression
analysis to assess the effects of the race and
sex of the patients on treatment recommendations
24The number of White and Black patients who
doctors thought should be referred for cardiac
catheterization based on their symptoms
25Risk ratio and odds ratio in this table
- Relative risk or risk ratio for Blacks is
- 305 divided by 326
- 360 360
- or 0.93
- Odds ratio for Blacks is
- 305 x 35
- 326 x 55
- or 0.58
26THIS IS HOW THE AUTHORS DESCRIBED THEIR FINDINGS
- Logistic-regression analysis indicated that
blacks (odds ratio, 0.60 95 percent confidence
interval, 0.4 to 0.9 P0.02) were less likely to
be referred for cardiac catheterization than
whites.
27HEART BIAS STUDY WAS MISINTERPRETED (AP 8/15/99)
-
- The editors of the NEJM say they take
responsibility for media reports which greatly
exaggerated conclusions in a study about possible
gender and sex bias in heart care. The study,
published in the journal on Feb 25, reported what
happened when doctors viewed taped interviews of
actors describing their identical symptoms and
asked what treatment they would recommend. It
found that in cases of equally sick patients,
doctors were less likely to refer blacks and
women than they were white and men to have
cardiac catheterization, a test used to diagnose
heart disease. Several news organizations,
including the AP, interpreted the study to show
that doctors were 40 less likely to order the
tests for women and blacks than for men and
whites -
28- However, a follow up published in the
Journal recently concluded that the likelihood of
women and blacks being referred for the tests was
actually 7 percent less than for men and whites.
- The follow up, written by Dr. Lisa M. Schwartz
and others from the VA Outcomes Group in White
River Junction, Vt., said the misunderstanding
resulted from the original study's use of an
"odds ratio" to report the differences rather
than a more commonly used "risk ratio." - The researchers calculated the odds in favor of
blacks being offered the test and of whites being
offered the test. Then they calculated the ratio
of these two figures. The ratio of blacks' odds
to whites' odds worked out to 0.6, as did the
ratio of women's odds to men's. The media
interpreted this to mean that women and blacks
were 40 percent less likely to be offered
catheterization. But the true difference is much
smaller.
29- A table published with the study shows that
actually 85 percent of women and blacks were
referred for catheterization as were 91 percent
of men and whites. This means that the risk ratio
was .93. In other words, the probability of
referral was 7 percent lower for blacks and women
than for whites and men. - The journal editors said they "take
responsibility for the media's
overinterpretation" of the study's findings and
said they should not have allowed the use of odds
ratios in the study's summary.