Instantaneous geometric rates via generalized linear models

The instantaneous geometric rate represents the instantaneous probability of an event of interest per unit of time. In this article, we propose a method to model the effect of covariates on the instantaneous geometric rate with two models: the proportional instantaneous geometric rate model and the proportional instantaneous geometric odds model. We show that these models can be fit within the generalized linear model framework by using two nonstandard link functions that we implement in the user-defined link programs log igr and logit igr. We illustrate how to fit these models and how to interpret the results with an example from a randomized clinical trial on survival in patients with metastatic renal carcinoma.