Lab Meeting

Different types of effect

lm(y ~ treatment + batch)
design(dds) <- ~ treatment + batch

• treatment can be one of a pre-chosen set of options
• batch takes arbitrary labels that could go on indefinitely

Random and Fixed effects

• For treatment we’re interested in expected values (of treated, and control and their difference). FIXED effect

• For batch we’re less interested in the individual expected values. We probably assume that they’re zero on average, but might be interested in their variance - how much ‘noise’ they’re introducing. RANDOM effect

Notation

lm(y ~ treatment + batch)
library(lme4)
lmer(y ~ treatment + (1|batch))

These are pretty much equivalent, the latter saying ‘allow a different intercept (constant term) for each batch’.

The former would phrase results in terms of individual treatment effects and individual batch effects.

The latter would make the ‘noise due to batch’ the primary piece of information (about batch, treatment is as usual).

Quick win

Different batches have different uptake of treatment

lm(y ~ treatment * batch)
lmer(y ~ treatment + (treatment|batch))

• First model’s treatment coefficient is treatment effect in the (arbitrary) batch₀

• Second model’s treatment coefficient is for the ‘average’ batch.

Generalises

Most experiments have same number of samples (fastq’s) and biological units (mice). But frequently this is not the case.

• Left and right half of brain

• Three arbitrary regions per tissue per mouse

• Patient follow-up visits.

We believe patients may vary (in baseline, and in response?). But we’re interested in them as a whole, not individually.

Formulae

lmer(y ~ treatment + side +  (1|mouse))
# lmer(y ~ treatment + side +  (side|mouse))
lmer(y ~ treatment +  (1|mouse))
#lmer(y ~ treatment + (1|mouse/region))
lmer(y ~ gender + time*Arm + (1|patient))
#lmer(y ~ gender + rcs(time,3)*Arm + (time|patient))

So we still need to think about how to specify the model!

But the language helps us focus on the true role of predictors.

Why bother

• Should let us auto-rephrase those nasty gender:recoded_patient + gender:visit + gender formulae that DESeq2 forces upon us.

• More ‘intelligent’ plots: we don’t need a legend with 73 patients in ‘different’ colours (but we might like to know which genes are patient-variable.)

• Don’t suggest fitting the models using lme4:: (you need lots of instances, each with lots of measurements) - but it might be a handy sanity check occasionally.

Package of the week

gt and gtsummary - like ggplot, but for tables. Static table generation in rmarkdown, with pipe-able formatting, sorting and margins.

gtsummary gives a ‘Table 1’ summary of RCT/observational data to give a quick overview of the properties of a data-frame, perhaps stratified by a subset of columns.

It also can give the much-maligned ‘Table 2’ assessing the association of each independent variable on the outcome. Don’t ‘conclude’ anything from these.