Before proceeding further, three clarifications need to be made:
Although it may be helpful to think of the hazard as the instantaneous probability of an event at time t, it’s not really a probability because the hazard can be greater than 1.0. This can happen because of the division by Δt in equation (2.1). Although the hazard has no upper bound, it cannot be less than 0.
Because the hazard is defined in terms of a probability (which is never directly observed), it is itself an unobserved quantity. We may estimate the hazard with data, but that’s only an estimate.
It’s most useful to think of the hazard as a characteristic of individuals, not of populations or samples (unless everyone in the population is ...