Point Estimation with Quantal Response Data: Parametric Bootstrap Estimator Beats the Corresponding MLE

• Activity Number: 547
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Amy Schrader*+ and Ishwori Dhakal and Reid D. D. Landes
• Companies: University of Arkansas for Medical Sciences and University of Arkansas for Medical Sciences and University of Arkansas for Medical Sciences
• Keywords: relative potency ; LD50 ; dose reduction factor ; mean squared error

Abstract

Maximum likelihood estimation (MLE) is often used for estimating lethal dose 50% (LD50) and dose reduction factor (DRF) in toxicity studies. We investigated two point estimators of LD50 and DRF: the MLE and the median of a parametric bootstrap distribution. In a Monte Carlo experiment, we simulated quantal response data from different experimental settings. We then compared mean squared error (MSE) between MLE and the bootstrap estimator of both LD50 and DRF. The bootstrap estimator of both LD50 and DRF generally has a lower MSE than the MLE, especially in smaller sample sizes. After investigating the variances and biases of these estimators, the differences between the MSE of the bootstrap estimator and the MSE of the MLE are attributable to the variances. We recommend using the median of the parametric bootstrap for estimating LD50 and DRF over the MLE.