Abstract
Inference for the state occupation probabilities, given a set of baseline covariates, is an important problem in survival analysis and time to event multistate data. We introduce an inverse censoring probability re-weighted semi-parametric single index model based approach to estimate conditional state occupation probabilities of a given individual in a multistate model under right-censoring. Besides obtaining a temporal regression function, we also test the potential time varying effect of a baseline covariate on future state occupation. We show that the proposed technique has desirable finite sample performances and its performance is competitive when compared with three other existing approaches. We illustrate the proposed methodology using two different data sets. First, we re-examine a well-known data set dealing with leukemia patients undergoing bone marrow transplant with various state transitions. Our second illustration is based on data from a study involving functional status of a set of spinal cord injured patients undergoing a rehabilitation program.
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References
Aalen OO (1976) Non-parametric inference in connection with multiple decrement models. Scan J Stat 3:15–27
Aalen OO (1978) Non-parametric inference for a family of counting processes. Ann Stat 6:701–726
Aalen OO (1980) A model for non-parametric regression analysis of counting processes. In: Klonecki W, Kozek A, Rosiski J (eds) Lecture notes on mathematical statistics and probability, vol 2. Springer, New York, pp 1–25
Aalen OO (1989) A linear regression model for the analysis of lifetimes. Stat Med 8:907–925
Aalen OO, Johansen S (1978) An empirical transition matrix for nonhomogeneous Markov chains based censored observations. Scand J Stat 5:141–150
Andersen PK, Keiding N (2002) Multi-state models for event history analysis. Stat Methods Med Res 11:91–115
Andersen PK, Klein JP (2007) Regression analysis for multistate models based on a pseudo-value approach, with application to bone-marrow transplant studies. Scand J Stat 34:3–16
Barlow RE, Bartholomew DJ, Bremner JM, Brunk HD (1972) Statistical inference under order restrictions. Willey, New York
Breslow NE (1972) Discussion of the paper by D. R. Cox. J R Stat Soc Ser B 34:216–217
Copelan EA, Biggs JC, Thompson JM, Crilley P, Szer J et al (1991) Treatment for acute myelocytic leukemia with allogeneic bone marrow transplantation following preparation with BuCy2. Blood 78:838–843
Cox DR (1972) Regression model and life-tables. J R Stat Soc Ser B 34:187–220
Datta S, Satten GA (2001) Validity of the Aalen–Johansen estimators of state occupation probabilities and integrated transition hazards for non-Markov models. Stat Probab Lett 55:403–411
Datta S, Satten GA (2002) Estimation of integrated transition hazards and stage occupation probabilities for non-Markov system under dependent censoring. Biometrics 58:792–802
Fine JP, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94:496–509
Harkema SJ, Schmidt-Read M, Behrman AL, Bratta A, Sisto SA et al (2012) Establishing the NeuroRecovery Network: multisite rehabilitation centers that provide activity-based therapies and assessments for neurologic disorders. Arch Phys Med Rehabil 93:1498–1507
Ichimura H, Hall P, Hardle W (1993) Optimal smoothing in single index models. Ann Stat 21:157–178
Klein JP, Moeschberger ML (1997) Survival analysis: techniques for censored and truncated data. Springer, New York
Klein RW, Spady RH (1993) An efficient estimator for binary response models. Econometrica 66:387–421
Koul H, Susarla V, Van Ryzin J (1981) Regression analysis with randomly right censored data. Ann Stat 9:1276–1288
Leeuw J, Hornik K, Mair P (2009) Isotone optimization in R: pool-adjacent-violators algorithm (PAVA) and active set methods. J Stat Softw 32:1–24
Li G, Datta S (2001) A bootstrap approach to nonparametric regression for right censored data. Ann Inst Stat Math 53:708–729
Lorenz DJ, Datta S (2015) A nonparametric analysis of waiting times from a multistate model using a novel linear hazards model approach. Electron J Stat 9:419–443
Marron J (1992) Bootstrap bandwidth selection. In: LePage R, Billard L (eds) Exploring the limits of bootstrap. Wiley, New York, pp 249–262
Mostajabi F, Datta S (2013) Nonparametric regression of state occupation, entry, exit, and waiting times with multistate right-censored data. Stat Med 32:3006–3019
Pepe MS, Cai J (1993) Some graphical displays and marginal regression analysis for recurrent failure times and time dependent covariates. J Am Stat Assoc 88:811–820
Scheike TH, Zhang M (2007) Direct modelling of regression effects for transition probabilities in multistate models. Scand J Stat 34:17–32
van Hedel HJ, Dietz V (2010) Rehabilitation of locomotion after spinal cord injury. Restor Neurol Neurosci 28:123–134
Acknowledgements
We thank the Christopher and Dana Reeve Foundation and all current and past members of the NeuroRecovery Network for the provision of the spinal cord injury data. Also, we thank the associate editor and two anonymous reviewers for many constructive suggestions.
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Siriwardhana, C., Kulasekera, K.B. & Datta, S. Flexible semi-parametric regression of state occupational probabilities in a multistate model with right-censored data. Lifetime Data Anal 24, 464–491 (2018). https://doi.org/10.1007/s10985-017-9403-6
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DOI: https://doi.org/10.1007/s10985-017-9403-6