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A Semiparametric Approach for the Two‐Sample Comparison of Survival Times with Long‐Term Survivors
Author(s) -
Broët Philippe,
Rycke Yann,
TubertBitter Pascale,
Lellouch Joseph,
Asselain Bernard,
Moreau Thierry
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.00844.x
Subject(s) - term (time) , statistics , statistic , mathematics , statistical hypothesis testing , survival analysis , test statistic , sample size determination , proportional hazards model , sample (material) , econometrics , physics , quantum mechanics , thermodynamics
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.