Nonparametric analysis of dependently interval-censored failure time data
Yayuan Zhu
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
Search for more papers by this authorCorresponding Author
Jerald F. Lawless
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
Correspondence
Jerald F. Lawless, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
Email: [email protected]
Search for more papers by this authorCecilia A. Cotton
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
Search for more papers by this authorYayuan Zhu
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
Search for more papers by this authorCorresponding Author
Jerald F. Lawless
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
Correspondence
Jerald F. Lawless, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
Email: [email protected]
Search for more papers by this authorCecilia A. Cotton
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
Search for more papers by this authorAbstract
Failure time studies based on observational cohorts often have to deal with irregular intermittent observation of individuals, which produces interval-censored failure times. When the observation times depend on factors related to a person's failure time, the failure times may be dependently interval censored. Inverse-intensity-of-visit weighting methods have been developed for irregularly observed longitudinal or repeated measures data and recently extended to parametric failure time analysis. This article develops nonparametric estimation of failure time distributions using weighted generalized estimating equations and monotone smoothing techniques. Simulations are conducted for examination of the finite sample performance of proposed estimators. This research is motivated in part by the Toronto Psoriatic Arthritis Cohort Study, and the proposed methodology is applied to this study.
REFERENCES
- 1Sun J. The Statistical Analysis of Interval-Censored Failure Time Data. New York: Springer Science & Business Media; 2006.
- 2Lipsitz SR, Fitzmaurice GM, Ibrahim JG, Gelber R, Lipshultz S. Parameter estimation in longitudinal studies with outcome-dependent follow-up. Biometrics. 2002; 58(3): 621-630.
- 3Lin H, Scharfstein DO, Rosenheck RA. Analysis of longitudinal data with irregular, outcome-dependent follow-up. J R Stat Soc Ser B (Stat Methodol). 2004; 66(3): 791-813.
- 4Zhu Y, Lawless JF, Cotton CA. Estimation of parametric failure time distributions based on interval-censored data with irregular dependent follow-up. Stat Med. 2017; 36(10): 1548-1567.
- 5Gladman DD. Psoriatic arthritis. Rheum Dis Clin N Am. 1998; 24(4): 829-844.
- 6Mease P, Goffe BS. Diagnosis and treatment of psoriatic arthritis. J Am Acad Dermatol. 2005; 52(1): 1-19.
- 7Hogan JW, Roy J, Korkontzelou C. Handling drop-out in longitudinal studies. Stat Med. 2004; 23(9): 1455-1497.
- 8Robins JM, Rotnitzky A, Zhao LP. Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. J Am Stat Assoc. 1995; 90(429): 106-121.
- 9Robins JM. Information recovery and bias adjustment in proportional hazards regression analysis of randomized trials using surrogate markers. In: Proceedings of the Biopharmaceutical Section, Alexandria, VA: American Statistical Association; 1993: 24-33.
- 10Turnbull BW. The empirical distribution function with arbitrarily grouped, censored and truncated data. J R Stat Soc Ser B Methodol. 1976; 38(3): 290-295.
- 11Joly P, Commenges D, Letenneur L. A penalized likelihood approach for arbitrarily censored and truncated data: application to age-specific incidence of dementia. Biometrics. 1998; 54(1): 185-194.
- 12Betensky RA, Lindsey JC, Ryan LM, Wand MP. Local em estimation of the hazard function for interval-censored data. Biometrics. 1999; 55(1): 238-245.
- 13Braun J, Duchesne T, Stafford JE. Local likelihood density estimation for interval censored data. Can J Stat. 2005; 33(1): 39-60.
- 14Fan J. Local linear regression smoothers and their minimax efficiencies. Ann Stat. 1993; 21(1): 196-216.
- 15Fan J, Gijbels I. Local Polynomial Modelling and Its Applications: Monographs on Statistics and Applied Probability, Vol. 66. New York: CRC Press; 1996.
- 16Mammen E. Estimating a smooth monotone regression function. Ann Stat. 1991; 19(2): 724-740.
- 17Cheng K, Lin P. Nonparametric estimation of a regression function. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1981; 57(2): 223-233.
- 18Wright FT. Monotone regression estimates for grouped observations. Ann Stat. 1982; 10(1): 278-286.
- 19Friedman J, Tibshirani R. The monotone smoothing of scatterplots. Technometrics. 1984; 26(3): 243-250.
- 20Mukerjee H. Monotone nonparametric regression. Ann Stat. 1988; 16(2): 741-750.
- 21Hall P, Huang L. Nonparametric kernel regression subject to monotonicity constraints. Ann Stat. 2001; 29: 624-647.
- 22Zhang Z, Sun J. Interval censoring. Stat Methods Med Res. 2010; 19(1): 53-70.
- 23Barlow RE, Bartholomew DJ, Bremner JM, Brunk HD. Statistical Inference under Order Restrictions: The Theory and Application of Isotonic Regression: Wiley; 1972.
- 24Miles RE. The complete amalgamation into blocks, by weighted means, of a finite set of real numbers. Biometrika; 46(3/4).
- 25Young JG, Tchetgen Tchetgen EJ. Simulation from a known Cox MSM using standard parametric models for the g-formula. Stat Med. 2014; 33(6): 1001-1014.
- 26Dehghan MH, Duchesne T. A generalization of Turnbull's estimator for nonparametric estimation of the conditional survival function with interval-censored data. Lifetime Data Anal. 2011; 17(2): 234-255.
- 27Robins JM, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiol. 2000; 11(5): 550-560.
- 28Bůžková P, Lumley T. Longitudinal data analysis for generalized linear models with follow-up dependent on outcome-related variables. Can J Stat. 2007; 35(4): 485-500.
- 29Cook RJ, Lawless JF. The Statistical Analysis of Recurrent Events. New York: Springer; 2007.
- 30Lawless JF. Statistical Models and Methods for Lifetime Data. 2nd ed. Hoboken, New Jersey: John Wiley & Sons, Inc.; 2003.
- 31Royston JP. An extension of Shapiro and Wilk's w test for normality to large samples. Appl Stat. 1982; 31(2): 115-124.
- 32Pullenayegum EM, Lim LS. Longitudinal data subject to irregular observation: a review of methods with a focus on visit processes, assumptions, and study design. Stat Methods Med Res. 2016; 25(6): 2992-3014.
- 33Zhang J, Heitjan DF. A simple local sensitivity analysis tool for nonignorable coarsening: application to dependent censoring. Biometrics. 2006; 62(4): 1260-1268.
- 34Scharfstein DO, Rotnitzky A, Robins JM. Adjusting for nonignorable drop-out using semiparametric nonresponse models. J Am Stat Assoc. 1999; 94(448): 1096-1120.
- 35Bang H, Robins JM. Doubly robust estimation in missing data and causal inference models. Biometrics. 2005; 61(4): 962-973.
- 36van der Vaart AW. Asymptotic Statistics. Cambridge, UK: Cambridge University Press; 2000.
