Best statistical test for biological experiment with ordinal independent variable and binary outcomes over a time course

Question

I am analysing a dataset with the following characteristics:

1. We have three different groups. The difference between them lies in different levels of expression of a specific gene (no expression, medium expression, high expression). This could then be thought of as an ordinal variable.
2. The response variable is a purely binary outcomes, yes/no.
3. The measurements are taken over the course of three time points.
4. The sample measured for each group is measured at each time point is different.

From what I've read, ordinal logistic regression or proportional odds regression may be appropriate, but these are not methods I am familiar with and I am unsure their assumptions are met here. What would be the best approaches to study the magnitude of the effect size and the significance of the difference between groups?

Answer 1

The type of model depends first on the outcome variable. As your outcome is binary, what you need is a type of binomial regression, such as logistic regression. That's pretty standard.

The coding of the ordinal predictor is a separate issue. With only 3 levels, it's simplest to ignore its ordinal nature and just code it as a 3-level categorical predictor with the no-expression group as the reference level. In a logistic regression you will get 2 regression coefficients representing the log-odds difference between each of the gene-expression groups and the no-expression group in terms of the binary outcome. That would provide the same information as trying to code the gene-expression predictor as ordinal.

If you have continuous values for the gene expression, you probably would be better off using them directly with a flexible fit (regression spline or other generalized additive model). It's generally poor practice to categorize a continuous predictor.

If you are making measurements on different individuals at the 3 time points then you are all set. If there are repeated measurements on individuals you will need to take the within-individual correlations into account, typically with a mixed model.