Relative risk
In a cohort study we select two groups by a given chracteristic and
proceed to observe prospectively if a given event occurs. Examples may be:
(1) An experimental study with a control group and a treatment group, where
we measure if a given problem occurs.
(2) A group of heavy smokers and a group of occasional smokers are
studied for two years and the appearance of cardiac problems is recorded.
(3) Groups of exposed and non-exposed subjects are studied to see if they
develop a disease.
As a rule of thumb, we select independent groups by what we consider a
cause and measure in a follow-up study if a given event occurs.
In this application you can fix the probability of the event in each group and
the size of each group. Then, we simulate the experiment and compute
the results. In that case, the appropriate measure is the Relative risk (RR)
defined as:
$$RR=\frac{P(Event|Exposed)}{P(Event|No Exposed)}$$
Odds ratio
Consider an event with probability \(p\). The odds for this event are defined as:
$$odds=\frac{p}{1-p}$$
That is, the odds indicate how many times is more probable that an event occurs
that it dosen't occur. For instance, if the probability of having a cardiovascular
event at 50 years is 0.3, the odds are 0.3/0.7= 0.43
The odds ratio (OR) is defined as the quotient of the odds of an event in two different siruations.
For instance, if the probability of having a cardiovascular event at 50 years is 0.3, and 0.4 at 60 years,
the OR (60 years vs. 50 years are:
$$OR=\frac{0.4/0.6}{0.3/0.7}=1.56$$
Then, the odds of a cardiovascular disease are 1.56 times greater at 60 years vs. 50 years.
If OR>1 then the putative risk factor is directly correlated with the disease, If OR=1,
then there is no association, whereas of OR<1 then the association is inverse.
In practice, supose you have a group of \(n_1\) cases, and \(x_1\) of them
present the risk In a group of \(n_2\) controls, we observe
\(x_2\) with the risk. Then the OR is computed as:
$$OR=\frac{x_1 \times (n_2 - x_2)}{(n_1 \times x_1)\times x_2 }$$
Table of results: Estimation of RR
How to compute the RR
Table of results: Estimation of OR
OR can be computed as a measure of association
Enter table
Analize a 2x2 cohort study of Non Exposed and Exposed people. We want to evaluate if the disease is
more probable in The exposed group. Group Non exposed is the reference. You should explore the different possible situations
by changing the values of the observations in the table.
95% CI for RR (Non exposed as a reference)
Table of results
How to compute the OR
Enter table
We supose a case-control design. We want to evaluate if there is an association between
cases and the presence of a potential risk factor. You should explore the different possible situations by changing the
values of the observations in the table.
Analysis (Case-control design)
95% CI for OR (No risk as a reference)