A Semiparametric Approach for the Two-Sample Comparison of Survival Times with Long-Term Survivors

Authors

  • Philippe Broët,

    Corresponding author
    1. National Institute for Health and Medical Research (U 472) and Department of Public Health, Hopital Paul Brousse, 16 Avenue Paul Vaillant Couturier, 94807 Villejuif Cedex, France
    2. Department of Biostatistics, Institut Curie, 26 rue d'Ulm, 75231 Paris Cedex, France
      *email:broet@vjf.inserm.fr
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  • Yann De Rycke,

    1. Department of Biostatistics, Institut Curie, 26 rue d'Ulm, 75231 Paris Cedex, France
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  • Pascale Tubert-Bitter,

    1. National Institute for Health and Medical Research (U 472) and Department of Public Health, Hopital Paul Brousse, 16 Avenue Paul Vaillant Couturier, 94807 Villejuif Cedex, France
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  • Joseph Lellouch,

    1. National Institute for Health and Medical Research (U 472) and Department of Public Health, Hopital Paul Brousse, 16 Avenue Paul Vaillant Couturier, 94807 Villejuif Cedex, France
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  • Bernard Asselain,

    1. Department of Biostatistics, Institut Curie, 26 rue d'Ulm, 75231 Paris Cedex, France
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  • Thierry Moreau

    1. National Institute for Health and Medical Research (U 472) and Department of Public Health, Hopital Paul Brousse, 16 Avenue Paul Vaillant Couturier, 94807 Villejuif Cedex, France
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*email:broet@vjf.inserm.fr

Abstract

Summary. In the two-sample comparison of survival times with long-term survivors, the overall difference between the two distributions reflects differences occurring in early follow-up for susceptible subjects and in long-term follow-up for nonsusceptible subjects. In this setting, we propose statistics for testing (i) no overall, (ii) no short-term, and (iii) no long-term difference between the two distributions to be compared. The statistics are derived as follows. A semiparametric model is defined that characterizes a short-term effect and a long-term effect. By approximating this model about no difference in early survival, a time-dependent proportional hazards model is obtained. The statistics are obtained from this working model. The asymptotic distributions of the statistics for testing no overall or no short-term effects are ascertained, while that of the statistic for testing no long-term effect is valid only when the short-term effect is small. Simulation studies investigate the power properties of the proposed tests for different configurations. The results show the interesting behavior of the proposed tests for situations where a short-term effect is expected. An example investigating the impact of progesterone receptors status on local tumor relapse for patients with early breast cancer illustrates the use of the proposed tests.

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