Statistics for Maintenance Modelling: Regression Modelling

# Proportional Odds Models¤

In probability theory, the odds of a particular event, T < t occurring is given by the ratio P{T < t} / P{T t}. In the proportional odds model the survival function satisfies:

= x

The proportional odds model says that the odds under explanatory variables x is x times the baseline odds (first used by Bennett (1983)). As x increases so does the probability of a shorter lifetime. By differentiating the above equation we can obtain an equation which holds for the hazard function in the proportional odds model.

Differentiating with respect to t: = x
Rearranging, the hazard function ratio thus satisfies: = x
and then, using the original equation we get: =
As S(0,x) = S0(0), at t = 0 the hazard ratio is x and tends to 1 as t . I.e. x has less effect on the hazard as time goes on.