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Estimation of Causal Odds of Concordance using the Aalen Additive Model

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  • Torben Martinussen
  • Christian Bressen Pipper

Abstract

xml:id="sjos12004-abs-0001" type="main" xml:lang="en"> A simple summary of a treatment effect is attractive, which is part of the explanation of the success of the Cox model when analysing time-to-event data since the relative risk measure is such a convenient summary measure. In practice, however, the Cox model may fail to give a reasonable fit, very often because of time-changing treatment effect. The Aalen additive hazards model may be a good alternative as time-changing effects are easily modelled within this model, but results are then evidently more complicated to communicate. In such situations, the odds of concordance measure (OC) is a convenient way of communicating results, and recently Martinussen & Pipper (2012) showed how a variant of the OC measure may be estimated based on the Aalen additive hazards model. In this study, we propose an estimator that should be preferred in observational studies as it always estimates the causal effect on the chosen scale, only assuming that there are no un-measured confounders. The resulting estimator is shown to be consistent and asymptotically normal, and an estimator of its limiting variance is provided. Two real applications are provided.

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  • Torben Martinussen & Christian Bressen Pipper, 2014. "Estimation of Causal Odds of Concordance using the Aalen Additive Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 141-151, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:141-151
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    File URL: http://hdl.handle.net/10.1002/sjos.12004
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    References listed on IDEAS

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    1. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    2. Janez Stare & Robin Henderson & Maja Pohar, 2005. "An individual measure of relative survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 115-126, January.
    3. Murphy, S. A. & Sen, P. K., 1991. "Time-dependent coefficients in a Cox-type regression model," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 153-180, October.
    4. Torben Martinussen & Thomas H. Scheike & Ib M. Skovgaard, 2002. "Efficient Estimation of Fixed and Time‐varying Covariate Effects in Multiplicative Intensity Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 57-74, March.
    5. Li Chen & D. Y. Lin & Donglin Zeng, 2010. "Attributable fraction functions for censored event times," Biometrika, Biometrika Trust, vol. 97(3), pages 713-726.
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    Cited by:

    1. Kevin Burke & Frank Eriksson & C. B. Pipper, 2020. "Semiparametric multiparameter regression survival modeling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 555-571, June.

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