GAM

In a previous post, I described some ways one might go about analyzing data from a stepped-wedge, cluster-randomized trial using a generalized additive model (a GAM), focusing on continuous outcomes. I have spent the past few weeks developing a similar model for a binary outcome, and have started to explore model comparison and methods to evaluate goodness-of-fit. The following describes some of my thought process.

Trying to simulate data with non-linear relationships can be frustrating, since there is not always an obvious mathematical expression that will give you the shape you are looking for. I’ve come up with a relatively simple solution for somewhat complex scenarios that only requires the specification of a few points that lie on or near the desired curve. (Clearly, if the relationships are straightforward, such as relationships that can easily be represented by quadratic or cubic polynomials, there is no need to go through all this trouble.) The translation from the set of points to the desired function and finally to the simulated data is done by leveraging generalized additive modelling (GAM) methods, and is described here.