A class of tests of proportional hazards assumption for left-truncated and right-censored data

References

• P.K. Andersen, Comparing survival distributions via hazard ratio estimates, Scand. J. Statist. 10 (1983), pp. 77–85.
   Web of Science ®Google Scholar
• P.K. Andersen and R.D. Gill, Cox's regression model for counting processes: A large sample study, Ann. Statist. 10 (1982), pp. 1100–1120. doi: 10.1214/aos/1176345976
   Web of Science ®Google Scholar
• E. Arjas, A graphical method for assessing goodness of fit in Cox's proportional hazards model, J. Am. Statist. Assoc. 83 (1988), pp. 204–212. doi: 10.1080/01621459.1988.10478588
   Web of Science ®Google Scholar
• V. Bagdonavičius, R. Levuliené, and M.S. Nikulin, Goodness-of-fit criteria for the Cox model from left truncated and right censored data, J. Math. Sci. 167 (2010), pp. 436–443. doi: 10.1007/s10958-010-9929-6
   Google Scholar
• D.R. Cox, Regression models and life-tables, J. R. Statist. Soc. Ser. B (Methodol.) 34 (1972), pp. 187–220.
   Web of Science ®Google Scholar
• R.D. Gill and M. Schumacher, A simple test of the proportional hazards assumption. Tech. Rep. No. MSR8504, Department of Mathematics and Statistics, Centrum voor Wiskunde en Informatica, Amsterdam, 1985.
   Google Scholar
• R.D. Gill and M. Schumacher, A simple test of the proportional hazards assumption, Biometrika. 74 (1987), pp. 289–300. doi: 10.1093/biomet/74.2.289
   Web of Science ®Google Scholar
• D.P. Harrington and T.R. Fleming, A class of rank test procedures for censored survival data, Biometrika. 69 (1982), pp. 553–566. doi: 10.1093/biomet/69.3.553
   Web of Science ®Google Scholar
• D.W. Hosmer Jr and S. Lemeshow, Applied Survival Analysis Regression Modeling of Time to Event Data, Wiley, New York, 1998.
   Google Scholar
• J. Hyde, Testing survival under right censoring and left truncation, Biometrika. 64 (1977), pp. 225–230. doi: 10.1093/biomet/64.2.225
   Web of Science ®Google Scholar
• J.D. Kalbfleisch and J.F. Lawless, Estimating the incubation time distribution and expected number of cases of transfusion-associated acquired immune deficiency syndrome, Transfusion. 29 (1989), pp. 672–676. doi: 10.1046/j.1537-2995.1989.29890020437.x
   PubMed Web of Science ®Google Scholar
• J.D. Kalbfleisch and R.L. Prentice, The Statistical Analysis of Failure Time Data, Wiley, New York, 2002.
   Google Scholar
• J.P. Klein and M.L. Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data, Springer, New York, 2003.
   Google Scholar
• S.W. Lagakos, L.M. Barraj, and V. De Gruttola, Nonparametric analysis of truncated survival data, with application to AIDS, Biometrika. 75 (1988), pp. 515–523. doi: 10.1093/biomet/75.3.515
   Web of Science ®Google Scholar
• T.L. Lai and Z. Ying, Rank regression methods for left-truncated and right-censored data, Ann. Statist. 19 (1991), pp. 531–556. doi: 10.1214/aos/1176348110
   Web of Science ®Google Scholar
• D.Y. Lin, Goodness-of-fit analysis for the Cox regression model based on a class of parameter estimators, J. Am. Statist. Assoc. 86 (1991), pp. 725–728. doi: 10.1080/01621459.1991.10475101
   Web of Science ®Google Scholar
• D.Y. Lin, L.J. Wei, and Z. Ying, Checking the Cox model with cumulative sums of martingale-based residuals, Biometrika. 80 (1993), pp. 557–572. doi: 10.1093/biomet/80.3.557
   Web of Science ®Google Scholar
• I.W. McKeague and K.J. Utikal, Goodness-of-fit tests for additive hazards and proportional hazards models, Scand. J. Statist. 18 (1991), pp. 177–195.
   Web of Science ®Google Scholar
• J.-J. Ren and B. He, Estimation and goodness-of-fit for the Cox model with various types of censored data, J. Statist. Plann. Infer. 141 (2011), pp. 961–971. doi: 10.1016/j.jspi.2010.09.006
   Web of Science ®Google Scholar
• D. Schoenfeld, Chi-squared goodness-of-fit tests for the proportional hazards regression model, Biometrika. 67 (1980), pp. 145–153. doi: 10.1093/biomet/67.1.145
   Web of Science ®Google Scholar
• D. Schoenfeld, Partial residuals for the proportional hazards regression model, Biometrika. 69 (1982), pp. 239–241. doi: 10.1093/biomet/69.1.239
   Web of Science ®Google Scholar
• D. Sengupta, A. Bhattacharjee, and B. Rajeev, Testing for the proportionality of hazards in two samples against the increasing cumulative hazard ratio alternative, Scand. J. Statist. 25 (1998), pp. 637–647. doi: 10.1111/1467-9469.00126
   Web of Science ®Google Scholar
• P.-S. Shen, A class of rank-based test for left-truncated and right-censored data, Ann. Inst. Statist. Math. 61 (2009), pp. 461–476. doi: 10.1007/s10463-007-0151-3
   Web of Science ®Google Scholar
• W.-Y. Tsai, N.P. Jewell, and M.-C. Wang, A note on the product-limit estimator under right censoring and left truncation, Biometrika. 74 (1987), pp. 883–886. doi: 10.1093/biomet/74.4.883
   Web of Science ®Google Scholar
• M.C. Wang, Product limit estimates: A generalized maximum likelihood study, Commun. Statist. Theory Methods. 16 (1987), pp. 3117–3132. doi: 10.1080/03610928708829561
   Web of Science ®Google Scholar
• M. Woodroofe, Estimating a distribution function with truncated data, Ann. Statist. 13 (1985), pp. 163–177. doi: 10.1214/aos/1176346584
   Web of Science ®Google Scholar