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Effects of model misspecification on tests of no randomized treatment effect arising from Cox’s proportional hazards model

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  • A. G. DiRienzo
  • S. W. Lagakos

Abstract

We examine the asymptotic and small sample properties of model‐based and robust tests of the null hypothesis of no randomized treatment effect based on the partial likelihood arising from an arbitrarily misspecified Cox proportional hazards model. When the distribution of the censoring variable is either conditionally independent of the treatment group given covariates or conditionally independent of covariates given the treatment group, the numerators of the partial likelihood treatment score and Wald tests have asymptotic mean equal to 0 under the null hypothesis, regardless of whether or how the Cox model is misspecified. We show that the model‐based variance estimators used in the calculation of the model‐based tests are not, in general, consistent under model misspecification, yet using analytic considerations and simulations we show that their true sizes can be as close to the nominal value as tests calculated with robust variance estimators. As a special case, we show that the model‐based log‐rank test is asymptotically valid. When the Cox model is misspecified and the distribution of censoring depends on both treatment group and covariates, the asymptotic distributions of the resulting partial likelihood treatment score statistic and maximum partial likelihood estimator do not, in general, have a zero mean under the null hypothesis. Here neither the fully model‐based tests, including the log‐rank test, nor the robust tests will be asymptotically valid, and we show through simulations that the distortion to test size can be substantial.

Suggested Citation

  • A. G. DiRienzo & S. W. Lagakos, 2001. "Effects of model misspecification on tests of no randomized treatment effect arising from Cox’s proportional hazards model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 745-757.
  • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:745-757
    DOI: 10.1111/1467-9868.00310
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    Cited by:

    1. Clelia Di Serio & Yosef Rinott & Marco Scarsini, 2007. "Simpson’s Paradox for the Cox Model," Levine's Bibliography 321307000000000729, UCLA Department of Economics.
    2. Peng He & Frank Eriksson & Thomas H. Scheike & Mei-Jie Zhang, 2016. "A Proportional Hazards Regression Model for the Subdistribution with Covariates-adjusted Censoring Weight for Competing Risks Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 103-122, March.
    3. Clelia Di Serio & Yosef Rinott & Marco Scarsini, 2009. "Simpson's Paradox in Survival Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 463-480, September.
    4. A. G. DiRienzo, 2003. "Nonparametric Comparison of Two Survival-Time Distributions in the Presence of Dependent Censoring," Biometrics, The International Biometric Society, vol. 59(3), pages 497-504, September.
    5. Hattori, Satoshi, 2012. "Testing the no-treatment effect based on a possibly misspecified accelerated failure time model," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 371-377.
    6. Jane Paik Kim, 2013. "A Note on Using Regression Models to Analyze Randomized Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models," Biometrics, The International Biometric Society, vol. 69(1), pages 282-289, March.
    7. Hattori, Satoshi, 2006. "Some properties of misspecified additive hazards models," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1641-1646, September.
    8. Paul Gustafson, 2007. "On Robustness and Model Flexibility in Survival Analysis: Transformed Hazard Models and Average Effects," Biometrics, The International Biometric Society, vol. 63(1), pages 69-77, March.
    9. Ting Ye & Jun Shao, 2020. "Robust tests for treatment effect in survival analysis under covariate‐adaptive randomization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1301-1323, December.
    10. Paul Frédéric Blanche & Anders Holt & Thomas Scheike, 2023. "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 441-482, April.

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