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.

When ANCOVA is taken to mean a parametric model such as the linear regression model, a very impactful assumption of ANCOVA is that $Y$ has been nearly perfectly transformed so as to achieve Gaussian residuals and equal variability in $Y$ across levels of $X$.  An efficient alternative is a semiparametric ordinal regression model such as the proportional odds or proportional hazards models.  These are $Y$-transformation invariant and are discussed in BBR and RMS.  I don't have experience with PSA as an outcome but many lab measurements (HbA1c and serum creatinine being two examples) do not work well either untransformed or log transformed.
