And dichotomous data are typically represented in a two by two table.

Here we have test intervention, comparison intervention.

And that a and c represent the number of events for the two intervention groups.

And the marginal total a + b is the total number of participants in

the test intervention group.

And we use Nt to represent that.

And you can also get the total number

in the comparison intervention group by adding up c and d.

And the risk ratio really is a ratio of the risk

on the treatment divided by the ratio on the control and

the risk or proportion or probability depending on the study design.

Is expressed as the a, the number event divided by the marginal total,

which is the total number in the testing intervention group.

So you can use that formula to get the risk ratio.

Odds ratio says it is the ratio of the odds on the treatment,

divided by the odds on the control.

Again, you can use the formula to get the odds ratio.

Risk difference is the risk on the treatment minus the risk on the control.

And the number needed to treat is the inverse of the risk difference.

So there are the measure we typically use for dichotomous data and this is really

not new to you, because you have used this multiple times in different classworks.

Some features for the risk ratio.

It's easy to interpret and

easy to explain, because you can say the probability of having the event

In the treatment group comparing to the control group is this.

But it's not typically the effect measure reported in multivariate analysis.

For example, if you run a multiple adjustic regression,

you're more likely to get odds ratio out of it, instead of risk ratio.

If there's no event in the control group or in your denominator for

the risk ratio, you cannot really calculate the risk ratio.

And what about odds ratio?

Well, it has the best developed statistical methodology,

particularly for For adjusting for covariance.

And you can calculate odds ratio from some study design that do not

allow calculation of absolute risks or rates.

For example, in case control study where you actually select

how many controls to be included in your study by design.

There you cannot calculate the absolute risk, but

you can still use odds ratio to measure the strength of association.

It can be difficult to interpret, particularly when the baseline rate is

above 20%, and I will come back to this point why that's a problem.

Relative ratio and odds ratio are not the same.

Because, if you remember from the formula I showed you,

one is using the marginal total in the denominator.

One is using the number of null value in the denominator.

So there are calculated using different formula, even for the same 2x2 table,

you're going to get two different numbers.

So let's say, based on a 2x2 table, you get the relative risk of .8.

And then you will find a different odds ratio,

because odds ratio is calculated using a different formula.

And both relative ratio and

odds ratio are entirely valid ways of describing an intervention effect.

Problem may arise if the odds ratio is misinterpreted as relative risk.

So here's the question for you.

Based on a two by two table, if I get a relative risk of 0.8,

what would be the odds ratio?

Is the odds ration more likely to be less than 0.8 or greater than 0.8?

Well, as a matter of effect,

odds ratio is always more extreme than the relative risk.

Meaning a way from the now value of one.

So let's say the relative ratio is point eight.

The odds ratio will be less than point eight away from the now value of one.