Accelerated Failure-Time Models › Disadvantages

The main disadvantage is the distributional assumption. The parametric AFT models studied here require us to choose the distribution of the error term $W$ in the log-time equation. If that distribution is wrong, coefficient estimates can be biased, standard errors can be misleading, and predicted survival curves can be systematically off. Cox regression avoids this specific assumption, although it imposes proportional hazards. In practice, the choice between Cox and AFT is a choice about which assumption is more defensible for the problem at hand.

AFT models also impose a strong structural assumption: covariates multiply the event time by a constant factor. Equivalently, the effect of a covariate is the same at every quantile of the event-time distribution. If a treatment changes conditional time ratios only for the highest-risk subjects, or if those ratios differ across event-time quantiles, a single time ratio may be too simple. AFT models can include interactions, and generalized formulations can handle time-varying covariates with an explicit event-time model. The static model below does not acquire that ability by inserting measurements obtained after baseline. A single time ratio is not a universal description of heterogeneous treatment effects.

Parametric extrapolation is both an advantage and a risk. Once we fit a distribution, we can predict survival beyond the largest observed time. That extrapolation is only as credible as the distributional assumption. A log-normal model and a Weibull model can agree near the middle of the observed data and diverge sharply in the tail. If the scientific decision depends on long-term survival, we should check whether the data inform that region.

There are also practical identifiability and numerical issues. The scale parameter $\sigma$ must be positive, so the implementation below optimizes over $\log \sigma$. With heavy censoring, small samples, or extreme covariate values, the likelihood can be flat or poorly behaved. The likelihood also assumes independent censoring: if censoring is related to unobserved prognosis after conditioning on covariates, these reduced contributions are not generally justified without addressing the observation mechanism. We should also avoid comparing AIC values from a Cox partial likelihood directly with AIC values from a full AFT likelihood, because the two likelihoods are not on the same footing.