Alternatives to the Cox proportional hazards model: A review of additive hazards and accelerated failure time models

The Cox proportional hazards (PH) model remains the dominant approach in survival analysis, but it has two important limitations. First, it relies on the PH assumption, asserting that covariate effects act multiplicatively and remain constant over time. This assumption is often violated in practice, which complicates interpretation and compromises predictive accuracy. Second, the model is non‐collapsible, that is, marginal and conditional effects differ even in the absence of confounding, which leads to a lack of internal consistency and to the fact that the hazard ratio does not allow a causal interpretation in the presence of unobserved heterogeneity. In this article we review two alternative regression methods, the additive hazards model and the accelerated failure time (AFT) model, that address these limitations. Both models are collapsible and internally consistent, providing effect measures that retain their interpretation across conditioning sets. The additive hazards model provides a highly flexible, nonparametric formulation that naturally accommodates time‐varying covariate effects, while recent maximum likelihood methods further improve its practical performance. The AFT model offers a more intuitive interpretation by quantifying how covariates accelerate or decelerate event times; both parametric and semi‐parametric versions are discussed. We review theoretical properties, estimation methods, extensions, possible applications, and software implementations of both models. We illustrate similarities and differences between the models through a conceptual hazard and survival comparison and through a comparative data example.