The Proportional Hazards Model

The proportional hazards model assumes that the time to event is described by a hazard function, which is a measure of the potential for the event to occur at a particular time t, given that the event did not yet occur. Larger values of the hazard function indicate greater potential for the event to occur.

The hazard function is the product of a baseline hazard function, which is independent of the covariates, and an exponential function describing the effect of the covariates. The shape of the hazard function over time is defined by the baseline hazard, for all cases. The covariates simply help to determine the overall magnitude of the function. While the baseline hazard is dependent upon time, the covariate effect is the same for all time points. Thus, the ratio of the hazards for any two cases at any time period is the ratio of their covariate effects. This is the proportional hazards assumption.

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