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Md Hasinur Rahaman Khan and JEH Shaw

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 (Stute, 1993, 1994), when the largest observation (Y +(n)) is censored, it is natural to apply the redistribution to the right algorithm of Efron (1967). However, Efron’s redistribution algorithm can lead to bias and inefficiency in estimation. This study explains the issues and proposes alternative ways of treating Y +(n). The new schemes use penalized weighted least squares that is optimized by a quadratic programming approach, applied to the log-normal accelerated failure time model. The proposed approaches generally outperform Efron’s redistribution approach and lead to considerably smaller mean squared error and bias estimates.

Keywords: Accelerated failure time (AFT) model and Efron’s tail correction and Imputation and Right censoring and Weighted least squares.