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Flexible semi-parametric regression of state occupational probabilities in a multistate model with right-censored data. (English) Zbl 1468.62406

Summary: 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62M05 Markov processes: estimation; hidden Markov models
62N02 Estimation in survival analysis and censored data

Software:

isotone; cmprsk
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Full Text: DOI Link

References:

[1] Aalen, OO, Non-parametric inference in connection with multiple decrement models, Scan J Stat, 3, 15-27, (1976) · Zbl 0331.62030
[2] Aalen, OO, Non-parametric inference for a family of counting processes, Ann Stat, 6, 701-726, (1978) · Zbl 0389.62025 · doi:10.1214/aos/1176344247
[3] Aalen, OO; Klonecki, W (ed.); Kozek, A (ed.); Rosiski, J (ed.), A model for non-parametric regression analysis of counting processes, No. 2, 1-25, (1980), New York · Zbl 0445.62095
[4] Aalen, OO, A linear regression model for the analysis of lifetimes, Stat Med, 8, 907-925, (1989) · doi:10.1002/sim.4780080803
[5] Aalen, OO; Johansen, S, An empirical transition matrix for nonhomogeneous Markov chains based censored observations, Scand J Stat, 5, 141-150, (1978) · Zbl 0383.62058
[6] Andersen, PK; Keiding, N, Multi-state models for event history analysis, Stat Methods Med Res, 11, 91-115, (2002) · Zbl 1121.62568 · doi:10.1191/0962280202SM276ra
[7] Andersen, PK; Klein, JP, Regression analysis for multistate models based on a pseudo-value approach, with application to bone-marrow transplant studies, Scand J Stat, 34, 3-16, (2007) · Zbl 1142.62053 · doi:10.1111/j.1467-9469.2006.00526.x
[8] Barlow RE, Bartholomew DJ, Bremner JM, Brunk HD (1972) Statistical inference under order restrictions. Willey, New York · Zbl 0246.62038
[9] Breslow, NE, Discussion of the paper by D. R. Cox, J R Stat Soc Ser B, 34, 216-217, (1972)
[10] Copelan, EA; Biggs, JC; Thompson, JM; Crilley, P; Szer, J; etal., Treatment for acute myelocytic leukemia with allogeneic bone marrow transplantation following preparation with bucy2, Blood, 78, 838-843, (1991)
[11] Cox, DR, Regression model and life-tables, J R Stat Soc Ser B, 34, 187-220, (1972) · Zbl 0243.62041
[12] Datta, S; Satten, GA, Validity of the aalen-johansen estimators of state occupation probabilities and integrated transition hazards for non-Markov models, Stat Probab Lett, 55, 403-411, (2001) · Zbl 0998.62072 · doi:10.1016/S0167-7152(01)00155-9
[13] Datta, S; Satten, GA, Estimation of integrated transition hazards and stage occupation probabilities for non-Markov system under dependent censoring, Biometrics, 58, 792-802, (2002) · Zbl 1210.62115 · doi:10.1111/j.0006-341X.2002.00792.x
[14] Fine, JP; Gray, RJ, A proportional hazards model for the subdistribution of a competing risk, J Am Stat Assoc, 94, 496-509, (1999) · Zbl 0999.62077 · doi:10.1080/01621459.1999.10474144
[15] Harkema, SJ; Schmidt-Read, M; Behrman, AL; Bratta, A; Sisto, SA; etal., Establishing the neurorecovery network: multisite rehabilitation centers that provide activity-based therapies and assessments for neurologic disorders, Arch Phys Med Rehabil, 93, 1498-1507, (2012) · doi:10.1016/j.apmr.2011.01.023
[16] Ichimura, H; Hall, P; Hardle, W, Optimal smoothing in single index models, Ann Stat, 21, 157-178, (1993) · Zbl 0770.62049 · doi:10.1214/aos/1176349020
[17] Klein JP, Moeschberger ML (1997) Survival analysis: techniques for censored and truncated data. Springer, New York · Zbl 0871.62091 · doi:10.1007/978-1-4757-2728-9
[18] Klein, RW; Spady, RH, An efficient estimator for binary response models, Econometrica, 66, 387-421, (1993) · Zbl 0783.62100 · doi:10.2307/2951556
[19] Koul, H; Susarla, V; Ryzin, J, Regression analysis with randomly right censored data, Ann Stat, 9, 1276-1288, (1981) · Zbl 0477.62046 · doi:10.1214/aos/1176345644
[20] Leeuw, J; Hornik, K; Mair, P, Isotone optimization in R: pool-adjacent-violators algorithm (PAVA) and active set methods, J Stat Softw, 32, 1-24, (2009) · doi:10.18637/jss.v032.i05
[21] Li, G; Datta, S, A bootstrap approach to nonparametric regression for right censored data, Ann Inst Stat Math, 53, 708-729, (2001) · Zbl 1003.62036 · doi:10.1023/A:1014644700806
[22] Lorenz, DJ; Datta, S, A nonparametric analysis of waiting times from a multistate model using a novel linear hazards model approach, Electron J Stat, 9, 419-443, (2015) · Zbl 1308.62192 · doi:10.1214/15-EJS1003
[23] Marron, J; LePage, R (ed.); Billard, L (ed.), Bootstrap bandwidth selection, 249-262, (1992), New York · Zbl 0838.62029
[24] Mostajabi, F; Datta, S, Nonparametric regression of state occupation, entry, exit, and waiting times with multistate right-censored data, Stat Med, 32, 3006-3019, (2013) · doi:10.1002/sim.5703
[25] Pepe, MS; Cai, J, Some graphical displays and marginal regression analysis for recurrent failure times and time dependent covariates, J Am Stat Assoc, 88, 811-820, (1993) · Zbl 0794.62074 · doi:10.1080/01621459.1993.10476346
[26] Scheike, TH; Zhang, M, Direct modelling of regression effects for transition probabilities in multistate models, Scand J Stat, 34, 17-32, (2007) · Zbl 1142.62056 · doi:10.1111/j.1467-9469.2006.00544.x
[27] Hedel, HJ; Dietz, V, Rehabilitation of locomotion after spinal cord injury, Restor Neurol Neurosci, 28, 123-134, (2010)
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