Inverse probability weighting methods for Cox regression with right‐truncated data

• Published in: Biometrics Vol. 76; no. 2; pp. 484 - 495
• Main Authors: Vakulenko‐Lagun, Bella, Mandel, Micha, Betensky, Rebecca A.
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishing Ltd 01.06.2020
• Subjects: Computer simulation; Estimation; Hazard identification; Hazard mitigation; HIV; Human immunodeficiency virus; Latency; positivity assumption; Probabilistic methods; probability; proportional hazards; Regression analysis; retrospective ascertainment reverse time; selection bias; stabilized weights; Statistical analysis; Statistical models; Viruses; Weighting methods; selection bias; retrospective ascertainment reverse time; positivity assumption; proportional hazards; stabilized weights
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.13162

Right‐truncated data arise when observations are ascertained retrospectively, and only subjects who experience the event of interest by the time of sampling are selected. Such a selection scheme, without adjustment, leads to biased estimation of covariate effects in the Cox proportional hazards model. The existing methods for fitting the Cox model to right‐truncated data, which are based on the maximization of the likelihood or solving estimating equations with respect to both the baseline hazard function and the covariate effects, are numerically challenging. We consider two alternative simple methods based on inverse probability weighting (IPW) estimating equations, which allow consistent estimation of covariate effects under a positivity assumption and avoid estimation of baseline hazards. We discuss problems of identifiability and consistency that arise when positivity does not hold and show that although the partial tests for null effects based on these IPW methods can be used in some settings even in the absence of positivity, they are not valid in general. We propose adjusted estimating equations that incorporate the probability of observation when it is known from external sources, which results in consistent estimation. We compare the methods in simulations and apply them to the analyses of human immunodeficiency virus latency.