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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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.

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Module 4: Additional Topics in Regression

- John McGready, PhD, MSAssociate Scientist, Biostatistics

Bloomberg School of Public Health

Greetings everyone.

John here again.

In this next lecture set, lecture ten, we'll talk briefly about

another method that can be used when we want to control for

a lot of potential confounders, but we're not particularly interested in

their relationships with the outcome after adjustment.

What we're really interested in an observational study sense is

the relationship between the outcome and a single predictor,

like whether a person self-selected to be in an intervention group or control group,

but because of the observational nature of the study it's necessary to control for

potential differences.

And we may have a lot of potential confounders measured and collected on our

participants and non-participants in the intervention that we'd like to adjust for,

but again, we're not interested in their associations with the outcome.

With traditional regression what we do is run a multiple regression where we

included our predictor of interest plus all of the potential confounders

to adjust.

And then we may iterate and pull out some of the potential confounders that did

not appear to be associated, statistically speaking, after adjustment for

the others, et cetera, but there's a limitation as to

how many potential confounders we can include because we only have so

much data and can only estimate so many slopes in our regression.

So another approach has come along that will allow us to take the information

about confounder distributions between persons in the intervention group and

persons who self-selected to be in the control group, and

take this information across many potential confounders and

turn it into a single score, such that persons with single scores closer to

each other are more similar in their distribution of confounders.

And this approach is called creating something called a propensity score.

And then, instead of doing the traditional regression approach,

where we regress our outcome on our main predictor of interest and a bunch of

other x's to represent our potential confounders, we can reduce the information

about the confounder distributions to this single score and adjust for it alone.

And that will allow us to estimate potentially a more

precise outcome exposure relationship, because we don't have to

estimate a bunch of ancillary slopes that we're not interested in

by including each of our confounders as individual predictors in the regression.

This also will allow us in situations, and

we'll talk about reasons why you may want to do this and

sometimes its done in the literature, to match people in the intervention and

control groups based on their confounder distributions using a single score,

such again that people who are closer in their scores are more similar on their

distribution of the potential confounders.

So in this unit we'll talk about the idea of propensity scores,

generally how they're created, and these can really only be used when our

predictor of interest is either binary which is the case we'll focus on, but

the ideas can be extended to when it's categorical.

If the predictor of interest is continuous it either needs to be dichotomized or

categorized to do this.

But we'll talk about situations on how to estimate the propensity score,

what the logic is behind it.

We'll compare the results from a study where we adjust the traditional way to

adjusting using the propensity score.

And we'll look at some examples of propensity score adjustment literature,

and then we'll also talk briefly about situations where it may make sense to

take everybody who gets the intervention and match them to a subset of people in

the control group based on the propensity score distributions.

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