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MEASURES OF DISEASE ASSOCIATION

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Title: MEASURES OF DISEASE ASSOCIATION


1
MEASURES OF DISEASE ASSOCIATION
  • Nigel Paneth

2
MEASURES 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.
  •  
  • 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)

6
THE 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.)

7
ODDS 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?

8
MEASURES 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.

9
1. ATTRIBUTABLE RISK (AR)
  • The incidence of disease in the exposed
    population whose disease can be attributed to the
    exposure.
  • AR Ie - Iu

10
2. ATTRIBUTABLE RISK FRACTION (ARF)
  • The proportion of disease in the
    exposed population whose disease can be
    attributed to the exposure.
  • ARF (Ie - Iu)/Ie

11
3. POPULATION ATTRIBUTABLE RISK (PAR)
  • The incidence of disease in the total population
    whose disease can be attributed to the exposure.
  • PAR Ip - Iu

12
4. 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

13
Note 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).  Ip P (Ie) Q (Iu)
14
EXAMPLE 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

15
INFERRING 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
  •  
  • (Ie - Iu)/Ie

16
  • We get
  • ARF RR (Iu) - Iu
  • RR (Iu)
  •  
  • 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?

18
INFERRING A POPULATION ATTRIBUTABLE RISK FRACTION
FROM A RELATIVE RISK  (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

19
Therefore, 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)
20
Going From A Relative Risk To An Attributable
Risk Fraction Contd
  • Iu can be factored out and cancelled 

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).

22
EXAMPLE OF HOW FAILURE TO UNDERSTAND WHAT AN ODDS
RATIO MEANS CAN LEAD TO TROUBLE
23
Schulman 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

24
The number of White and Black patients who
doctors thought should be referred for cardiac
catheterization based on their symptoms
25
Risk 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

26
THIS 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.

27
HEART 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.
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