Cox Proportional Hazards › Advantages

The Cox model leaves the baseline hazard shape unspecified. A parametric survival model instead chooses a family for that shape, which can add information if the choice is appropriate but can introduce misspecification. The Cox model trades that distributional choice for the proportional-hazards assumption and a model for the covariate effects. Its efficiency relative to a parametric fit depends on the data-generating process and censoring; there is no universal few-percent information-loss bound.

The hazard-ratio interpretation also suits many applied questions well. Clinicians want to know how much a treatment multiplies a patient's hazard at any moment; engineers want to know how much a maintenance schedule multiplies a failure rate; product managers want to know how much a pricing change multiplies a cancellation hazard. In each case, the Cox coefficient reports the log hazard ratio per unit of covariate, and its exponentiated form $\exp(\beta)$ reports the multiplicative change in hazard.

Statistical inference for the Cox model is well established. The partial likelihood behaves asymptotically like an ordinary likelihood (Andersen and Gill, 1982), so model-based standard errors, Wald intervals, likelihood-ratio tests and score tests are available under their regularity and sampling assumptions. Clustering, misspecification and sparse events can require additional methods. Time-varying covariates, stratification, and penalization all extend naturally. These tools support a familiar regression workflow, while censoring-aware risk sets, proportional-hazards diagnostics, and survival-specific evaluation remain necessary.