Lecture notes. Written from the material of GTPB Psls20, licensed CC BY 4.0. These are notes, not a transcript: the material has been reorganised and rewritten. This adaptation carries the same licence, and the original is linked above.

37. Multiple Regression and Confounding: FEV¶

What this covers¶

A second worked exercise in multiple regression, set up as a self-contained analysis for the reader to carry out rather than one that is walked through. It assumes the reader already has multiple linear regression — fitting a model with several predictors, reading a coefficient as an effect "holding the other variables fixed," and the idea of a confounder, a third variable associated with both the predictor of interest and the outcome that can create or hide an association between them. The question this exercise poses is a clean instance of exactly that problem: an apparent effect of smoking on lung function that has to be checked against the other things that differ between the smokers and non-smokers in the sample.

The FEV dataset and the question¶

FEV — forced expiratory volume — is a measure of how much air a person can exhale, in litres, during a forced breath. The dataset records the FEV of 606 children aged 6 to 17, together with each child's age, height, gender, and, most importantly, whether the child is a smoker or a non-smoker.

The question the exercise sets is whether smoking has an effect on the FEV of children — but with a qualification that is the whole point of doing this as a multiple regression rather than a two-group comparison: accounting for potential confounders. Smokers and non-smokers in a sample of children are not otherwise identical groups — age and height, in particular, both affect lung volume directly and are very likely to differ between smokers and non-smokers (a child who smokes is more likely to be older) — so a raw comparison of FEV between the two groups risks attributing to smoking an effect that is really driven by age or height. Untangling that is what the regression model, with smoking status alongside the other recorded variables, is for.

Exercises¶

The dataset and goal above are the setup for the following tasks. Carry out each step and record what it shows before moving to the next.

Import the FEV dataset and tidy it as needed for analysis (in particular, make sure that categorical variables such as gender and smoking status are represented as such, not as numbers).
Explore the data: visualize the (unadjusted) association between smoking and FEV, and then examine age, height, and gender as potential confounders of that association — how does each of them relate both to smoking status and to FEV?
Fit a regression model for FEV that includes smoking status together with the variables identified as potential confounders, and interpret the coefficient on smoking status in that model.
State a conclusion: does smoking have an effect on the FEV of children once age, height, and gender are accounted for, and how does that conclusion compare with what the raw, unadjusted comparison in step 2 suggested?

Sources¶

This chapter is built entirely from the converted tutorial notes for this exercise; no slide deck or lecture transcript was supplied for it, and no worked solution is included in the source.

Dataset description ("The FEV dataset") and the stated goal: docs/omics-statistics/gtpb/psls20/tutorialScripts/excercises/08_multipleRegression/Multiple_regression_FEV_half_2.md.
The same file's section headings — Load libraries and import the data, Data tidying, Data exploration (with the instruction to "visualize the effect of smoking on the FEV" and "assess all potential confounders"), Data analysis, and Conclusion — give the structure of the exercise reproduced above; the source itself contains no code, output, or discussion under any of these headings beyond that one sentence of instruction, so no worked figures, model output, or numerical results were available to report.

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