Fitting Smooth-in-Time Prognostic Risk Functions via Logistic Regression

When considering treatment options, a physician ideally has access to prognoses for various spans of prospective time, meaning known risks specific for these and also for both treatment and the profile of the patient. Accordingly, investigators ideally would report estimates of such risks from clinical trials and their non-experimental counterparts. To the extent that such risk estimates have been reported at all, they have mainly been based on the semi-parametric regression model of Cox. We focus on a family of fully-parametric hazard models of an attractive, versatile form that readily allows for non-proportionality, yet models that have not been easy to fit with standard statistical software. We elaborate an approach, recently proposed, to fitting such hazard functions via logistic regression. From the fitted hazard function, cumulative incidence and, thus, risk functions of time, treatment and profile can be derived. This approach accommodates any log-linear hazard function of prognostic time, treatment, and the prognostic indicators defining the patient's prognostic profile.