A semi-parametric regression model for analysis of middle censored lifetime data

Authors

  • Sreenivasa Rao Jammalamadaka University of California, Santa Barbara
  • Sundaresan Nair Prasad Cochin University of Science and Technology, Kerala
  • Paduthol Godan Sankaran Cochin University of Science and Technology

DOI:

https://doi.org/10.6092/issn.1973-2201/6281

Keywords:

Middle censoring, Proportional Hazards model, Self consistent estimator

Abstract

Middle censoring introduced by Jammalamadaka and Mangalam (2003), refers to data arising in situations where the exact lifetime becomes unobservable if it falls within a random censoring interval, otherwise it is observable.
In the present paper we propose a semi-parametric regression model for such lifetime data, arising from an unknown population and subject to middle censoring.
We provide an algorithm to find the nonparametric maximum likelihood estimator (NPMLE) for regression parameters and the survival function. The consistency of the estimators are established.
We report simulation studies to assess the finite sample properties of the estimators.
We then analyze a real life data on survival times for diabetic patients studied by Lee et al. (1988).

References

A. ABUZAID, M. ABU EL-QUMSAN, A. EL-HABIL (2015). On the robustness of right and middle censoring schemes in parametric survival models. Communications in Statistics-Simulation and Computation, , no. To appear.

N. DAVARZANI, A. PARSIAN (2011). Statistical inference for discrete middlecensored data. Journal of Statistical Planning and Inference, 141, no. 4, pp. 1455–1462.

C. R. DAVID (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, 34, pp. 187–220.

A. P. DEMPSTER, N. M. LAIRD, D. B. RUBIN (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the royal statistical society. Series B (methodological), pp. 1–38.

B. EFRON (1967). The two sample problem with censored data. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability. vol. 4, pp. 831–853.

J. HUANG, J. A. WELLNER (1995). Efficient estimation for the proportional hazards model with” case 2” interval censoring. Technical Report No. 290, Department of Statistics, University of Washington, Seattle, USA.

S. K. IYER, S. R. JAMMALAMADAKA, D. KUNDU (2008). Analysis of middlecensored data with exponential lifetime distributions. Journal of Statistical Planning and Inference, 138, no. 11, pp. 3550–3560.

S. R. JAMMALAMADAKA, S. K. IYER (2004). Approximate self consistency for middle-censored data. Journal of statistical planning and inference, 124, no. 1, pp. 75–86.

S. R. JAMMALAMADAKA, E. LEONG (2015). Analysis of discrete lifetime data under middle-censoring and in the presence of covariates. Journal of Applied Statistics, 42, no. 4, pp. 905–913.

S. R. JAMMALAMADAKA, V. MANGALAM (2003). Nonparametric estimation for middle-censored data. Journal of nonparametric statistics, 15, no. 2, pp. 253–265.

S. R. JAMMALAMADAKA, V. MANGALAM (2009). A general censoring scheme for circular data. Statistical Methodology, 6, no. 3, pp. 280–289.

J. D. KALBFLEISCH, R. L. PRENTICE (2011). The statistical analysis of failure time data, vol. 360. John Wiley & Sons.

J. P. KLEIN, M. L. MOESCHBERGER (2005). Survival analysis: techniques for censored and truncated data. Springer Science & Business Media.

J. F. LAWLESS (2011). Statistical models and methods for lifetime data, vol. 362. John Wiley & Sons.

E. T. LEE, J. WANG (2003). Statistical methods for survival data analysis, vol. 476. John Wiley & Sons.

E. T. LEE, M. A. YEH, J. L. CLEVES, D. SHAFER (1988). Vascular complications in noninsulin dependent diabetic oklahoma indians. Diabetes, 37,(Suppl. 1).

V. MANGALAM, G. M. NAIR, Y. ZHAO (2008). On computation of npmle for middle-censored data. Statistics & Probability Letters, 78, no. 12, pp. 1452–1458.

P. G. SANKARAN, S. PRASAD (2014). Weibull regression model for analysis of middle-censored lifetime data. Journal of Statistics and Management Systems, 17, no. 5-6, pp. 433–443.

P.-S. SHEN (2010). An inverse-probability-weighted approach to the estimation of distribution function with middle-censored data. Journal of Statistical Planning and Inference, 140, no. 7, pp. 1844–1851.

P.-S. SHEN (2011). The nonparametric maximum likelihood estimator for middlecensored data. Journal of Statistical Planning and Inference, 141, no. 7, pp. 2494–2499.

J. SUN (2006). The statistical analysis of interval-censored failure time data. Springer Science & Business Media.

T. TARPEY, B. FLURY (1996). Self-consistency: a fundamental concept in statistics. Statistical Science, pp. 229–243.

W.-Y. TSAI, J. CROWLEY (1985). A large sample study of generalized maximum likelihood estimators from incomplete data via self-consistency. The Annals of Statistics, pp. 1317–1334.

B. W. TURNBULL (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. Journal of the Royal Statistical Society. Series B (Methodological), pp. 290–295.

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Published

2016-03-31

How to Cite

Jammalamadaka, S. R., Prasad, S. N., & Sankaran, P. G. (2016). A semi-parametric regression model for analysis of middle censored lifetime data. Statistica, 76(1), 27–40. https://doi.org/10.6092/issn.1973-2201/6281

Issue

Vol. 76 No. 1 (2016)

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Articles

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