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Prognostic score matching methods for estimating the average effect of a non-reversible binary time-dependent treatment on the survival function

Author

Listed:
  • Kevin He

    (University of Michigan)

  • Yun Li

    (University of Pennsylvania Perelman School of Medicine)

  • Panduranga S. Rao

    (University of Michigan)

  • Randall S. Sung

    (University of Michigan)

  • Douglas E. Schaubel

    (University of Pennsylvania Perelman School of Medicine)

Abstract

In evaluating the benefit of a treatment on survival, it is often of interest to compare post-treatment survival with the survival function that would have been observed in the absence of treatment. In many practical settings, treatment is time-dependent in the sense that subjects typically begin follow-up untreated, with some going on to receive treatment at some later time point. In observational studies, treatment is not assigned at random and, therefore, may depend on various patient characteristics. We have developed semi-parametric matching methods to estimate the average treatment effect on the treated (ATT) with respect to survival probability and restricted mean survival time. Matching is based on a prognostic score which reflects each patient’s death hazard in the absence of treatment. Specifically, each treated patient is matched with multiple as-yet-untreated patients with similar prognostic scores. The matched sets do not need to be of equal size, since each matched control is weighted in order to preserve risk score balancing across treated and untreated groups. After matching, we estimate the ATT non-parametrically by contrasting pre- and post-treatment weighted Nelson–Aalen survival curves. A closed-form variance is proposed and shown to work well in simulation studies. The proposed methods are applied to national organ transplant registry data.

Suggested Citation

  • Kevin He & Yun Li & Panduranga S. Rao & Randall S. Sung & Douglas E. Schaubel, 2020. "Prognostic score matching methods for estimating the average effect of a non-reversible binary time-dependent treatment on the survival function," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 451-470, July.
  • Handle: RePEc:spr:lifeda:v:26:y:2020:i:3:d:10.1007_s10985-019-09485-x
    DOI: 10.1007/s10985-019-09485-x
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    References listed on IDEAS

    as
    1. Bo Lu, 2005. "Propensity Score Matching with Time-Dependent Covariates," Biometrics, The International Biometric Society, vol. 61(3), pages 721-728, September.
    2. Douglas E. Schaubel, 2004. "Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data," Biometrika, Biometrika Trust, vol. 91(2), pages 291-303, June.
    3. Judith Lok & Richard Gill & Aad Van Der Vaart & James Robins, 2004. "Estimating the causal effect of a time‐varying treatment on time‐to‐event using structural nested failure time models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(3), pages 271-295, August.
    4. David M. Vock & Anastasios A. Tsiatis & Marie Davidian & Eric B. Laber & Wayne M. Tsuang & C. Ashley Finlen Copeland & Scott M. Palmer, 2013. "Assessing the Causal Effect of Organ Transplantation on the Distribution of Residual Lifetime," Biometrics, The International Biometric Society, vol. 69(4), pages 820-829, December.
    5. Ben B. Hansen, 2008. "The prognostic analogue of the propensity score," Biometrika, Biometrika Trust, vol. 95(2), pages 481-488.
    6. Schaubel, Douglas E. & Wolfe, Robert A. & Sima, Camelia S. & Merion, Robert M., 2009. "Estimating the Effect of a Time-Dependent Treatment by Levels of an Internal Time-Dependent Covariate: Application to the Contrast Between Liver Wait-List and Posttransplant Mortality," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 49-59.
    7. Guanghui Wei & Douglas E. Schaubel, 2008. "Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards," Biometrics, The International Biometric Society, vol. 64(3), pages 724-732, September.
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