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 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.

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

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

Â beyond just estimating the relationship between outcome and multiple predictors at

Â once, and hence being able to estimate adjusted associations.

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

Â investigating effect modification in the context of a simple or

Â multiple regression model.

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

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

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

Â a predictor differs between males and females after including other predictors

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

Â males and females into two, two separate regression analyses.

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

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

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

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

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

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

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

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

Â We're going to also extend this idea and

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

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

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

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

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

Â a relationship, so to speak.

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

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

Â even if it's ordinal categorical.

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

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

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

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

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

Â the predictor itself modifies the relationship between itself and

Â the outcome in otherwise, in other words the relationship of

Â the outcome predictor relationship is modified by the predictor itself.

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