Bootstrap-calibrated estimation for progressively censored competing risks data under the Gompertz-Lindley model
Keywords:
Progressive Type-II censoring; competing risks modeling; Gompertz-Lindley lifetime model; bootstrap bias correction; BCa confidence intervals; statistical survival analysisAbstract
This paper develops a Bootstrap-Calibrated Hybrid Estimator (BCHE) for the parameters of the Gompertz-Lindley distribution (GLD) under progressive Type-II censoring in the presence of competing risks. The proposed approach combines maximum likelihood estimation via Newton-Raphson iteration with a parametric bootstrap calibration loop to correct finite-sample bias in all three model parameters simultaneously. Bias-corrected and accelerated (BCa) bootstrap confidence intervals are constructed and compared against the standard Wald-type asymptotic confidence intervals obtained from the observed Fisher information matrix. A comprehensive Monte Carlo simulation study is conducted using the heart disease dataset parameters from the literature, covering four sample-size configurations and three progressive censoring schemes. Simulation results confirm that the BCHE substantially reduces relative absolute bias and mean squared error for the GLD shape parameter, where classical maximum likelihood estimation is known to perform poorly under moderate to heavy censoring. Bootstrap BCa intervals achieve empirical coverage closer to the nominal 95% level with shorter average lengths compared to Wald-type intervals. A real data application to heart disease patient records with two competing failure causes—myocardial infarction and death from other causes—further illustrates the practical utility of the proposed methodology and demonstrates the suitability of the GLD for competing risks lifetime data.
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