Greetings. In this next section,

we'll look at a very famous actually and relatively

modern regression technique for dealing with time to event outcomes,

when we actually have individual level timed to event or sensoring data.

This is called Cox proportional hazards regression named after Sir David Cox who is not

only a member of the round table in England but still a

practicing and productive statistician.

His method is so revolutionary because it allows researchers to

estimate relative hazards between groups over an entire followup period.

When we have things that unfold over time,

without having to worry about encapsulating the time element on their own,

trying to figure out what the relationship between the risk of

an outcome and an event looks like as it unfolds over time.

They can let the model handle that piece and focus on group differences across the time.

The only thing they have to give up in this processes they have to be willing to assume

that the group differences and when expodentiate the ratio of these events,

the incidence rate ratios are relatively constant over the follow up time period.

That's why it's called the Cox proportional hazards regression model,

hazard is a synonym for incidence.

So, proportional hazards or proportional incidence pretty much mean the same thing.

So we'll get into all this in this lecture.

So we'll define proportional hazards in more detail,

we'll talk about what the researcher has to give up by doing that,

but also the potential benefits they get and we'll show that the end result gives

us not only incidence rate ratios or hazard ratios with

confidence limits for any group comparison we make but

the results of this when we incorporate the behind

the scenes piece the Cox regression is estimated with

regards to the risk of the event unfolding over time.

These results can be translated back into predictive timed to

event or survival curves for different groups defined by different X values.