A hazard function can be approximated using a piecewise constant (PC) function (https://en.wikipedia.org/wiki/Step_function). The parameters of a PC function are *jump points, *at which the value of the hazard can change, and hazard *levels, *which remain constant between consecutive jump points.

PC functions have attractive features in building intensity models.

- They can be
**added and multiplied**together, and the resulting function is still a PC function, thus*multiplicative and additive hazard models*can be easily constructed. - They can be
**shifted**by adding or subtracting a constant from the jump point values, thus*different time scales*can be incorporated in the model by selecting the constant appropriately, for example, the time of birth, diagnosis of a disease and onset of a treatment. - They can also be
**integrated**easily, thus calculation of the*Poisson likelihood*is computationally simple and efficient. - If the “true” hazard function has a
**strict changepoint**, at which the*hazard function increases/decreases*considerably during a short time interval, a PC function can fit to these changes accurately.