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

• Published in: Biometrics Vol. 57; no. 3; pp. 844 - 852
• Main Authors: Broët, Philippe, Rycke, Yann, Tubert‐Bitter, Pascale, Lellouch, Joseph, Asselain, Bernard, Moreau, Thierry
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.09.2001; International Biometric Society
• Subjects: Biometrics; Biometry; Breast cancer; breast neoplasms; Breast Neoplasms - metabolism; Censored data; Censorship; Cure model; Disease-Free Survival; Estimators; Female; Humans; Improper distribution; long term effects; Long-term survivors; Medical cures; Neoplasm Recurrence, Local - metabolism; Null hypothesis; Parametric models; patients; Progesterone receptors; Proportional hazards model; Proportional Hazards Models; Prospective Studies; Receptors, Progesterone - metabolism; Relapse; Semiparametric model; Statistical Distributions; statistics; Survival Analysis; Survival data; Tumors; Two-sample test
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.0006-341X.2001.00844.x

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.