Abstract
The location shift model is commonly used to quantify the difference between groups in a two-arm study. Nonparametric inference procedures for the location shift parameter with censored observations have recently been extensively studied. However, the validity of these procedures depends heavily on the model assumption. In this article, a class of graphical and numerical methods are proposed for checking the adequacy of the location shift model. Our graphical procedures are much less subjective than the eye-ball method based on the standard Q-Q plot. The proposed methods are illustrated with real-life examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersen P.K. (1982), “Testing Goodness of Fit of Cox's Regression and Life Model,” Biometrics, 38, 67–77.
Bickel P.J. and Wichura M.J. (1971), “Convergence Criterion for Multiparameter Stochastic Processes and Some Applications,” The Annals of Mathematical Statistics, 42, 1656–1670.
Billingsley P. (1968), Convergence of Probability Measures, New York: Wiley.
Cox D.R. (1972), “Regression Models and Life Tables” (with discussion), Journal of Royal Statistical Society B, 34, 187–220.
Cox D.R. and Oakes D.O. (1984), Analysis of Survival Data, London: Chapman Hall.
Fischl M.A., Parker C.B., Pettinelli C., Wulfsohn M., Hirsch M.S., Collier A.C., Antoniskis D., Ho M., Richman D.D., Fuchs E., Merigan T.C., Reichman R.C., Gold J., Steigbigel N., Leoung G.S., Rasheed S., Tsiatis A. and The AIDS Clinical Trials Group (1990), “A Randomized Controlled Trial of a Reduced Daily Dose of Zidovudine in Patients with the Acquired Immunodeficiency Syndrome,” New England Journal of Medicine, 323, 1009–1114.
Fleming T.F. and Harrington D.P. (1991), Counting Processes and Survival Analysis, New York: Wiley.
Hsieh F. (1995), “The Empirical Process Approach for Semiparametric Two-Sample Models with Heterogeneous Treatment Effect”. Journal of the Royal Statistical Society B, 57, 735–748.
Kalbfleisch J.D. and Prentice R.L. (1980), The Statistical Analysis of Failure Time Data, New York: Wiley.
Lin D.Y., Wei L.J. and Ying Z. (1993), “Checking the Cox Model with Cumulative Sums of Martingale-Based Residuals,” Biometrika, 80, 557–572.
Louis T.A. (1981), “Nonparametric Analysis of an Accelerated Failure Time Model,” Biometrika, 68, 381–390.
Meng X.L., Bassiakos Y. and Lo S.H. (1991), “Large Sample Properties for a General Estimator of the Treatment Effect in the Two-sample Problem with Right Censoring,” Annals of Statistics, 19, 1786–1812.
Schoenfeld D. (1980), “Chi-squared Goodness-of-Fit Tests for the Proportional Hazards Regression Model,” Biometrika, 67, 145–153.
Wei L.J. (1984), “Testing Goodness of Fit for Proportional Hazards Model with Censored Observations,” Journal of the American Statistical Association, 79, 649–652.
Wei L.J. and Gail M.H. (1983), “Nonparametric Estimation for a Scale-Change with Censored Observations,” Journal of the American Statistical Association, 78, 382–388.
Ying Z. (1993), “A Large Sample Study of Rank Estimation for Censored Regression Data,” The Annals of Statistics, 21, 76–99.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rossini, A.J., Wei, L.J. & Ying, Z. Checking adequacy of the semiparametric location shift model with censored data. Lifetime Data Anal 2, 145–157 (1996). https://doi.org/10.1007/BF00128572
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00128572