Electronic Journal of Statistics

A nonparametric analysis of waiting times from a multistate model using a novel linear hazards model approach

Douglas J. Lorenz and Somnath Datta

Full-text: Open access

Abstract

Traditional methods for the analysis of failure time data are often employed in the analysis of waiting times of transient states from multistate models. However, such methods can exhibit bias when waiting times among model states are dependent, even when censoring is random. Furthermore, right-censoring can occur prior to entry into the transient state of interest, preventing the observation of transitions from the state and providing another potential source of bias. We introduce a nonparametric linear hazards model for waiting times from multistate models, analogous to Aalen’s linear hazards model for failure time data, where proper estimation can be carried out via reweighting, a method flexible enough to incorporate general forms of induced and other dependent censoring. We illustrate the approximate unbiasedness of the proposed regression coefficient estimators through a simulation study, while also demonstrating the bias arising from traditional Aalen’s linear hazards model estimators obtained from correlated waiting time data. Theoretical results for the parameter estimators are provided. The reweighted estimators are used in the analysis of two data sets, to identify predictors of ambulatory recovery in a data set of spinal cord injury patients receiving activity-based rehabilitation and to identify prognostic indicators for patients receiving bone marrow transplant.

Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 419-443.

Dates
Received: January 2014
First available in Project Euclid: 17 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1426611769

Digital Object Identifier
doi:10.1214/15-EJS1003

Mathematical Reviews number (MathSciNet)
MR3323205

Zentralblatt MATH identifier
1308.62192

Subjects
Primary: 62N02: Estimation 62N01: Censored data models
Secondary: 62G05: Estimation

Keywords
Inverse probability weighting Aalen’s linear model multivariate survival data

Citation

Lorenz, Douglas J.; Datta, Somnath. A nonparametric analysis of waiting times from a multistate model using a novel linear hazards model approach. Electron. J. Statist. 9 (2015), no. 1, 419--443. doi:10.1214/15-EJS1003. https://projecteuclid.org/euclid.ejs/1426611769


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References

  • [1] Harkema, S.J., Schmidt-Read, M., Behrman, A.L., Bratta, A., Sisto, S.A., Edgerton, V.R., Establishing the NeuroRecovery Network: Multisite rehabilitation centers that provide activity-based therapies and assessments for neurologic disorders., Archives of Physical Medicine and Rehabilitation 2012; 93(9): 1498–1507.
  • [2] Harkema, S.J., Schmidt-Read, M., Lorenz, D., Edgerton, V.R., Behrman, A.L., Balance and ambulation improvements in individuals with chronic incomplete spinal cord injury using locomotor training-based rehabilitation., Archives of Physical Medicine and Rehabilitation 2012; 93(9): 1508–1517.
  • [3] van Hedel, H.J., Dietz, V., Rehabilitation of locomotion after spinal cord injury., Restorative Neurology and Neuroscience 2010; 28: 123–134.
  • [4] Lorenz, D.J., Datta, S., Comparing waiting times in a multi-stage model: A log-rank approach., Journal of Statistical Planning and Inference 2012; 142: 2832–2843.
  • [5] Aalen, O.O., A model for nonparametric regression analysis of counting processes. In, Lecture Notes on Mathematical Statistics and Probability, 2, Klonecki, W., Kozek, A., Rosiski, J. (eds.), New York: Springer-Verlag, 1980: 1–25.
  • [6] Aalen, O.O., A linear regression model for the analysis of lifetimes., Statistics in Medicine 1989; 8: 907–925.
  • [7] Aalen, O.O., Further results on the non-parametric linear regression model in survival analysis., Statistics in Medicine 1993; 12: 1569–1588.
  • [8] Huang, Y., Censored regression with the multistate accelerated sojourn times model., Journal of the Royal Statistical Society Series B 2002; 64: 17–29.
  • [9] Schaubel, D.E., Cai, J., Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data., Biometrika 2004; 91: 291–303.
  • [10] Copelan, E.A., Biggs, J.C., Thompson, J.M., Crilley, P., Szer, J., Klein, J.P. et al., Treatment for acute myelocytic leukemia with allogeneic bone marrow transplantation following preparation with BuCy2., Blood 1991; 78: 838–843.
  • [11] Andersen, P.K., Borgan, Ø., Gill, R.D., Keiding, N., Statistical Models Based on Counting Processes. New York: Springer-Verlag, 1993.
  • [12] Robins, J.M., Rotnitsky, A., Recovery of information and adjustment for dependent censoring using surrogate markers. In, AIDS Epidemiology – Methodological Issues, Jewell, N., Dietz, K., Farewell, V. (eds.), 1993; 297–331. Boston: Birkhauser.
  • [13] Robins, J.M., Rotnitsky, A., Semiparametric regression estimation in the presence of dependent censoring., Biometrika 1995; 82: 805–820.
  • [14] Satten, G.A., Datta, S., Marginal estimation for multi-stage models: Waiting time distributions and competing risks analyses., Statistics in Medicine 2002; 21: 3–19.
  • [15] Satten, G.A., Datta, S., Robins, J.M., Estimating the marginal survival function in the presence of time dependent covariates., Statistics and Probability Letters 2001; 54: 397–403.
  • [16] R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria 2012. Available at, http://www.R-project.org/.
  • [17] Lorenz D.J., Datta, S., Supplement to “A nonparametric analysis of waiting times from a multistate model using a novel linear hazards model approach”. 2015; DOI:, 10.1214/15-EJS1003SUPP.
  • [18] Behrman, A.L., Ardolino, E.A., VanHiel, L., Kern, M., Atkinson, D., Lorenz D., et al., Assessment of functional improvement without compensation reduces variability of outcome measures after human spinal cord injury., Archives of Physical Medicine and Rehabilitation 2012; 93(9): 1518–1529.
  • [19] Klein, J.P., Moeschberger, M.L., Survival Analysis: Techniques for Censored and Truncated Data. New York: Springer Verlag, 1997.
  • [20] Klein, J.P., Moeschberger, M.L., Modified by Yan J., Data sets from Klein and Moeschberger (1997), Survival Analysis 2003; R package version, 0.1-3.
  • [21] Hosmer, D.W., Royston, P., Using Aalen’s linear hazards model to investigate time-varying effects in the proportional hazards regression model., The Stata Journal 2002; 2(4): 331–350.
  • [22] McKeague, I.W., Asymptotic theory for weighted least squares estimation in Aalen’s additive risk model., Contemporary Mathematics 1988; 80: 139–152.
  • [23] Huffer, F.W., McKeague, I.W., Weighted least squares estimation for Aalen’s additive risk model., Journal of the American Statistical Association 1991; 86: 114–129.
  • [24] Cong, X.J., Yin, G., Shen, Y., Marginal analysis of correlated failure time data with informative cluster sizes., Biometrics 2007; 63: 663–672.
  • [25] Williamson, J.M., Kim, H.Y., Manatunga, A., Addiss, D.G., Modeling survival data with informative cluster size., Statistics in Medicine 2008; 27: 543–555.

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