A practical and example filled tour of simple and multiple regression techniques (linear, logistic, and Cox PH) for estimation, adjustment and prediction.

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From the course by Johns Hopkins University

Statistical Reasoning for Public Health 2: Regression Methods

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A practical and example filled tour of simple and multiple regression techniques (linear, logistic, and Cox PH) for estimation, adjustment and prediction.

From the lesson

Module 1B: More Simple Regression Methods

In this model, more detail is given regarding Cox regression, and it's similarities and differences from the other two regression models from module 1A. The basic structure of the model is detailed, as well as its assumptions, and multiple examples are presented.

- John McGready, PhD, MSAssociate Scientist, Biostatistics

Bloomberg School of Public Health

So in this next section, we're going to take on the case of simple regression for

time to event outcomes when there may be censoring.

And what we're going to see is that the method we're going to talk about,

which is most commonly used among the choices for different methods of

modeling time to event outcomes as a function of predictors, is called Cox's

proportional hazards regression, named after its founder, Sir David Cox.

Yes, that's right, Sir David Cox.

He's been knighted in England for his statistical achievements, and

he's a still living, practicing statistician who is based in England.

Luckily, he's come overseas a couple of times, and

I've had the chance to see him speak twice at Hopkins and meet him.

So by virtue of the fact that you're watching this video now, and

have me as your instructor, you have two degrees of separation from Sir David Cox.

That's pretty cool?

In any case, this is a huge contribution to being able to handle regression for

time to event analysis because, remember, the complication that comes in

with time to event data, is, well, the element of time.

We have these events unfolding over time, and we want to

compare the relative hazard of risk of the events between different groups.

For example, those who are treated versus those who get the placebo, or

those with stage four of the disease versus stage three, etc.

And so what the genius of the Cox proportional hazards regression method is,

is it says if you grant me one wish,

which that you are willing to assume that the relative relationship between

the risk between any two groups over time is the same across the entire time period.

That's the assumption of proportional hazards,

which we'll go into more detail on in the lecture set.

Then I'll take care, I the model,

will take care of the changing risk over time behind the scenes.

And so, what we get is actually a rather complex model,

where we don't have to worry about the most complex part,

the risk profile changing over time, as long as we're willing to assume the shape

of risks unfolding over time are similar in the different groups we're comparing.

And what the Cox model gives us is a pretty straightforward way to

estimate a relative comparison of the risk

at any time point in the follow-up period between any two groups we can compare.

So, hopefully you'll appreciate the genius of this method and

get a sense of why it makes our lives easier.

And you'll see all we have to do at the end of the results coming out

the computer are interpret things in terms of incidence rate ratios.

And then with this method we'll be able to estimate incident rate ratios,

create confidence intervals, and do hypothesis tests on these.

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