An implicitly defined parametric model for censored survival data and covariates

Parametric survival functions are usually defined as explicit functions of time and covariates. However, consideration of some simple differential equations describing certain survival curves leads to a descriptive equation which cannot be explicitly solved for the survival function. Nevertheless, the resulting survival function has useful properties: it is a hybrid between the exponential and uniform distributions, it can be used computationally in the same fashion as other survival models, and the effect of covariates on model parameters can be incorporated in a straightforward manner. The derivation and an example of the use of this model are provided.