Iovaldi ML. Riesgo relaꢀvo y odds raꢀo (razón de posibilidades): Conceptos básicos. Rev Argent Cir. 2023;115(4):310-315
RR = (a / (a + b)) / (c / (c + d))
For a rare event of 0.02%, an RR or OR of
2 would raise the risk from 0.02% to 0.04%. If the
event is common (20%), a risk of 2 with treatment or
exposure will double the risk to 40%. So, we should not
limit ourselves to the analysis of our table because we
would overlook the populaꢀon perspecꢀve defined in
5% confidence intervals, calculated with R, library the inclusion criteria.
7
2
.57 # relaꢀve risk
OR = (a/b) / (c/d)
2
,87 # odds raꢀo, which is slightly overesꢀmated.
9
epiR
Relaꢀve risk
Odds raꢀo
2.57 (0.96 - 6.87)
2.87 (0.97 - 8.46)
RR reducꢀon (RRR)
When the RR is greater than 1, the RRR is RR-1; when
The confidence interval includes the value 1 in the RR is less than 1, the RRR is 1-RR4
,10
.
the relaꢀve risk and odds raꢀo Fig. 1).
In this case: RRR = 2.57-1 = 1.57. Without a
thorough analysis, this would mean a 1.57-fold increase
in the posiꢀve effect of the treatment, which is not
supported by its confidence interval.
2
Chi-square (chi ) = 3.89 and p = 0.049.
■
FIGURE 1
From the RR to the number needed to treat (NNT)11
RELATIVE RISK AND 95% CI
Although we are dealing with a borderline
staꢀsꢀcal situaꢀon, I will use the same results to add
other concepts.
ARR: absolute risk reducꢀon is the difference in risk
between those who were exposed and those who were
not, or those who received treatment and those who
received a placebo. Referring to Table 3, the absolute
risk difference between the treatment group and the
placebo group is 0.16 - 0.06 = 0.10. Let’s assume the
outcome is a favorable response to treatment.
The NNT is defined as the inverse of the absolute risk
reducꢀon; 1 / RAR = 1/ 0.10 = 10. Ten is the number of
paꢀents who need to be treated in order to achieve one
addiꢀonal favorable outcome.
Forest plot reduced to its minimum expression due to being a single
study with only one variable (proporꢀons). RR with its corresponding
9
5% CI. “JAMA” format.
This is a borderline staꢀsꢀcal significance
p-value just below 0.05) which was thoroughly debated
(
in 2001 in a leꢃer to the editor between Raúl Borracci
8
and Carlos Tajer , which I recommend reading for
those interested in further understanding the subject.
The lower limits of the confidence intervals are also
borderline (just below 1) and the confidence intervals
are non-significant.
The total number of paꢀents exposed to risk
is not available in case-control studies. Case-control
studies begin by looking at the endpoint (event yes/
event no). Researchers then examine the risk factors in
retrospect; therefore, as it is impossible to calculate the
relaꢀve risk (RR), the OR is used.
If the event is favorable to the paꢀent, it is
advisable to use the acronym NNTB (number needed
to treat to benefit). For unfavorable events, NNTH
(
number needed to treat to harm) is recommended.
The method to calculate CIs for NNT is complex
1
2
and is done using the CI for AAR . The CIs for the NNT
are not symmetrical because the distribuꢀon is non-
normal. The values are shown in Table 4.
Both measures can be used in prospecꢀve
studies, although RR is recommended because it is
based on the random assignment of groups to one
treatment or another. In epidemiology, a database is
created with the individuals included and prospecꢀvely
observing occurrence or non-occurrence of events.
Logisꢀc regression models yield OR (log odds),
that must be transformed. In prospecꢀve studies, it is
convenient to adjust them to RR when the risk of the
outcome of interest is greater than 0.1 (10%) due to the
■
TABLE 4
Lower limit
Value
0.10
10
Upper limit
0.195
ARR
NNT
0.005
5
213
ARR: absolute risk reducꢀon; NNT: number needed to treat. Expres-
sed as values and 95% CI lower and upper limits. The NNT was roun-
ded to whole numbers.
In this case, the treatment resulted in a
favorable difference in the response outcome of the
treated group. However, the width of the confidence
interval for both measures does not permit a valid
conclusion in this situaꢀon, despite the RR being 2.57
and the OR being 2.87.
9
overesꢀmaꢀon menꢀoned above .
The interpretaꢀon of risk should not ignore
the previous absolute risk in the populaꢀon, and the
prevalence of the event in the populaꢀon is used for
1
0
this purpose .