MEASURES OF DISEASE ASSOCIATION Nigel Paneth 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
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The chances of something happening can be expressed as a risk or as an odds:
RISK = the chances of something happening the chances of allthings happening
ODDS= the chances of something happening the chances of itnothappening
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.
Example 1. Bookies are taking bets on the World Series. They are giving 3:1 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
Example 2. Among 100 people at baseline, 20 develop influenza over a year.
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
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.)
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?
Four closely related measures are used:
Note: all of these measures assume that the association between exposure and disease has already been shown to be causal.
The incidence of disease in the exposed population whose disease can be attributed to the exposure.
AR = Ie - Iu
The proportion of disease in the exposed population whose disease can be attributed to the exposure.
ARF = (Ie - Iu)/Ie
The incidence of disease in the total population whose disease can be attributed to the exposure.
PAR = Ip - Iu
The proportion of disease in the total population whose disease can be attributed to the exposure.
PARF = (Ip - Iu)/Ip
Ip can be linked to Ie and Iuif 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)
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
ARF = RR (Iu) - Iu
Dividing through by Iu gives
ARF = RR - 1
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?
Replacing Ie with Iu x RR, we get:
P(Ie) + Q(Iu) – Iu
P(Iu)RR + Q(Iu) – Iu
P(Iu)RR + Q(Iu)
Iu can be factored out and cancelled:
Iu(P x RR + Q - 1)
Iu (P x RR + Q)
If we now replace Q with 1-P (since P + Q = 1):
P x RR + 1 - P - 1
P x RR + 1 - P
or: Cont’dP (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).
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
305 divided by 326
305 x 35
326 x 55
Logistic-regression analysis indicated that blacks (odds ratio, 0.60; 95 percent confidence interval, 0.4 to 0.9; P=0.02) were less likely to be referred for cardiac catheterization than whites.
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
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.
A table published with the study shows that actually concluded that the likelihood of women and blacks being referred for the tests was 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.