Accelerated failure time vs Cox proportional hazards mixture cure models: David vs Goliath?

Motahareh Parsa () and Ingrid Van Keilegom ()
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Motahareh Parsa: Katholieke Universiteit Leuven, ORSTAT
Ingrid Van Keilegom: Katholieke Universiteit Leuven, ORSTAT

Statistical Papers, 2023, vol. 64, issue 3, No 5, 835-855

Abstract: Abstract A mixture cure model relies on a model for the cure probability and a model for the survival function of the uncured subjects. For the latter, one often uses a Cox proportional hazards model. We show the identifiability of this model under weak assumptions. The model assumes that the cure threshold is the same for all values of the covariates, which might be unrealistic in certain situations. An alternative mixture cure model is the accelerated failure time (AFT) model. We also show the identifiability of this model under minimal assumptions. The cure threshold in this model depends on the covariates, which often leads to a better fit of the data. This is especially true when the follow-up period is insufficient for certain values of the covariates. We study these two models via simulations both when the follow-up is sufficient and when it is insufficient. Moreover, the two models are applied to data coming from a breast cancer clinical trial. We show that the AFT and the Cox model both fit the data well in the region of sufficient follow-up, but differ drastically outside that region.

Keywords: Accelerated failure time model; Cox proportional hazards model; Identifiability; Insufficient follow-up; Mixture cure models (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01345-5

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