ANCOVA limitations and alternative methods I was given a database with prostate cancer patients measured for PSA (continuous) at two time points, prior and after treatment, using three drugs (categorical), including information about age (continuous) and tumor size (continuous).
The task is to propose a linear model for analyzing the data using PSA as an endpoint, address its limitations and propose at least three (3) alternative methods for dealing with them.
I thought ANCOVA could be a simple method to use for modeling the three independent variables, but I'm not sure on how to describe alterantive methods for addressing its limitations like non-parallel slopes, non-linear outcome etc.

You just named two:

*

*Slopes that aren’t parallel


*Nonlinear trends
Two remedies should address these, perhaps by using an interaction term to remedy the former and a spline for the latter.
These can be combined to allow for different nonlinear behavior in each group. Instead of ANCOVA-with-interaction multiplying just the factor levels by the covariate to get different slopes, multiply the factor levels by splines of the covariate to allow one level to exhibit rise-fall-rise while another exhibits fall-rise-fall (for instance).
