Repeated measures anova or ancova ... or other!

Question

I'm working on a trial and would really like some suggestions on how to analyse my data.

The study is a randomised crossover trial. I am interested in glucose response to three different lengths of an exercise. Each invididual will undergo one of three different lengths of exercise per lab day (0, 30 and 60 minutes). There are 6 measurement periods: pre exposure, post exposure time 1, 2, 3, 4 & 5.

Data is assumed to be normal

Dependent continuous: glucose

Independent categorical: exercise length (0, 30 and 60 minutes)

I have a two questions: #1 Would repeated measures (within subjects) anova be appropriate in this case? Or is linear mixed model more appropriate?

#2 However, I also plan analysing by age (older and younger adults) as I want to know if the age of participants effects the outcome. Would this case mean that I could use age as a covariate and therefore use ANCOVA? Or maybe something else?

Thanks in advance

Answer 1

In reverse order:

Question 2. Don't get hung up on the terminology. Yes, once you add a continuous predictor like age into a model with fixed treatments you are doing ANCOVA (analysis of covariance). But it's still just a linear model, now with a continuous predictor added to the categorical treatment predictor. In R, at least, you can just specify the predictors without worrying about which acronym is appropriate.

Question 1. Chapter 7 of Frank Harrell's course notes and book discuss different ways to handle longitudinal data. For a simple situation like this, his suggestion to try generalized least squares would seem to be a good choice. That allows for a wider range of correlation structures than simple repeated-measures models to handle the correlations within individuals, and it doesn't require measurements at the same times for all individuals (and thus can handle missing data). Generalized least squares doesn't impose a Gaussian distribution of random effects, as a mixed model would. It's implemented, for example, by the gls() function in the R nlme package; Harrell provides a useful wrapper for gls() in the Gls() function of his rms package.

The best analysis approach (whether you choose standard repeated-measures, generalized least squares, or a mixed model) would be to use the baseline glucose as a predictor and the actual glucose measurements (rather than changes in glucose) as the outcomes. You might also consider flexible continuous modeling of time, depending on your experimental design.