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

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  • Bella Vakulenko‐Lagun
  • Micha Mandel
  • Rebecca A. Betensky

Abstract

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.

Suggested Citation

  • Bella Vakulenko‐Lagun & Micha Mandel & Rebecca A. Betensky, 2020. "Inverse probability weighting methods for Cox regression with right‐truncated data," Biometrics, The International Biometric Society, vol. 76(2), pages 484-495, June.
  • Handle: RePEc:bla:biomet:v:76:y:2020:i:2:p:484-495
    DOI: 10.1111/biom.13162
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    References listed on IDEAS

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    1. Micha Mandel & Jacobo de Uña†à lvarez & David K. Simon & Rebecca A. Betensky, 2018. "Inverse probability weighted Cox regression for doubly truncated data," Biometrics, The International Biometric Society, vol. 74(2), pages 481-487, June.
    2. Lior Rennert & Sharon X. Xie, 2018. "Cox regression model with doubly truncated data," Biometrics, The International Biometric Society, vol. 74(2), pages 725-733, June.
    3. Jing Qin & Yu Shen, 2010. "Statistical Methods for Analyzing Right-Censored Length-Biased Data under Cox Model," Biometrics, The International Biometric Society, vol. 66(2), pages 382-392, June.
    4. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
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    1. Peng Liu & Kwun Chuen Gary Chan & Ying Qing Chen, 2023. "On a simple estimation of the proportional odds model under right truncation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 537-554, July.

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