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Cox regression can be collapsible and Aalen regression can be non-collapsible

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  • Sven Ove Samuelsen

    (University of Oslo)

Abstract

It is well-known that the additive hazards model is collapsible, in the sense that when omitting one covariate from a model with two independent covariates, the marginal model is still an additive hazards model with the same regression coefficient or function for the remaining covariate. In contrast, for the proportional hazards model under the same covariate assumption, the marginal model is no longer a proportional hazards model and is not collapsible. These results, however, relate to the model specification and not to the regression parameter estimators. We point out that if covariates in risk sets at all event times are independent then both Cox and Aalen regression estimators are collapsible, in the sense that the parameter estimators in the full and marginal models are consistent for the same value. Vice-versa, if this assumption fails, then the estimates will change systematically both for Cox and Aalen regression. In particular, if the data are generated by an Aalen model with censoring independent of covariates both Cox and Aalen regression is collapsible, but if generated by a proportional hazards model neither estimators are. We will also discuss settings where survival times are generated by proportional hazards models with censoring patterns providing uncorrelated covariates and hence collapsible Cox and Aalen regression estimates. Furthermore, possible consequences for instrumental variable analyses are discussed.

Suggested Citation

  • Sven Ove Samuelsen, 2023. "Cox regression can be collapsible and Aalen regression can be non-collapsible," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 403-419, April.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:2:d:10.1007_s10985-022-09578-0
    DOI: 10.1007/s10985-022-09578-0
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    References listed on IDEAS

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    1. Robin Henderson & Alvin Milner, 1991. "Aalen Plots Under Proportional Hazards," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(3), pages 401-409, November.
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    Cited by:

    1. Yiming Chen & Paul J. Smith & Mei-Ling Ting Lee, 2023. "Causal Inference in Threshold Regression and the Neural Network Extension (TRNN)," Stats, MDPI, vol. 6(2), pages 1-24, April.

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