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 3B: More Multiple Regression Methods

This set of lectures extends the techniques debuted in lecture set 3 to allow for multiple predictors of a time-to-event outcome using a single, multivariable regression model.

- John McGready, PhD, MSAssociate Scientist, Biostatistics

Bloomberg School of Public Health

Hi everyone. John here again.

In this next set of lectures, net lecture nine, we're going to

extend the regression models that we've seen before to go above and

beyond just estimating the relationship between outcome and multiple predictors at

once, and hence being able to estimate adjusted associations.

We're going to look at actually incorporating the effect modification and

investigating effect modification in the context of a simple or

multiple regression model.

And we'll see, classically, we've seen some ways to actually look at

effect modification is to split our data into subgroups and do separate analyses.

So for example, if I wanted to see whether the relationship between an outcome and

a predictor differs between males and females after including other predictors

in the model for adjustment et cetera, I may actually split the data separately for

males and females into two, two separate regression analyses.

But what if I want to use all the data across males and

females to estimate the associations between the outcome and other predictors,

besides the one where effect modification is a question of interest?

Well, we're going to see there are ways to do that in the context of

a multiple regression model by introducing what's called an interaction term.

And this will allow us to estimate stratum-specific estimates of

an outcome-predictor relationship for one of the predictors, while using

the information for the other predictors across all levels of the effect modifier.

We're going to also extend this idea and

talk about the idea of non-linearity as a special case of effect modification, and

look at a method to actually handle non-linearity in the, on

the regression scale that doesn't involve categorizing our continuous predictor.

In many cases that's a reasonable and fine approach.

But in certain situations we may be interested in the dose response of

a relationship, so to speak.

The change in the outcome per unit change in the predictor.

And we won't get that if we categorize a continuous predictor into several groups,

even if it's ordinal categorical.

So we're going to look at a method that allows for the estimation of

the outcome exposure relationship per unit of the continuous predictor, but allows

that association to change at different points across the predictor range.

And we're going to introduce the idea of something called a linear spline.

One way to conceptualize it is, is looking at a situation where

the predictor itself modifies the relationship between itself and

the outcome in otherwise, in other words the relationship of

the outcome predictor relationship is modified by the predictor itself.

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