On dealing with censored largest observations under weighted least squares

ABSTRACT

When observations are subject to right censoring, weighted least squares with appropriate weights (to adjust for censoring) is sometimes used for parameter estimation. With Stute's weighted least squares method, when the largest observation is censored ($Y_{\left(n\right)}^{+}$), it is natural to apply the redistribution to the right algorithm of Efron [The two sample problem with censored data. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4. New York: Prentice Hall; 1967. p. 831–853]. However, Efron's redistribution algorithm can lead to bias and inefficiency in estimation. This study explains the issues clearly and proposes some alternative ways of treating $Y_{\left(n\right)}^{+}$. The first four proposed approaches are based on the well known Buckley–James [Linear regression with censored data. Biometrika 1979;66:429–436] method of imputation with the Efron's tail correction and the last approach is indirectly based on a general mean imputation technique in literature. All the new schemes use penalized weighted least squares optimized by quadratic programming implemented with the accelerated failure time models. Furthermore, two novel additional imputation approaches are proposed to impute the tail tied censored observations that are often found in survival analysis with heavy censoring. Several simulation studies and real data analysis demonstrate that the proposed approaches generally outperform Efron's redistribution approach and lead to considerably smaller mean squared error and bias estimates.

KEYWORDS:

• Accelerated failure time model
• Efron's tail correction
• right censoring
• Stute's weighted least squares

AMS SUBJECT CLASSIFICATION:

• 62Nxx
• 62Fxx

Acknowledgments

The first author is grateful to the centre for research in Statistical Methodology (CRiSM), Department of Statistics, University of Warwick, UK for offering research funding for his PhD study.

Disclosure statement

No potential conflict of interest was reported by the authors.