Bootstrap estimation of benchmark doses and confidence limits with clustered quantal data.

Area of Science:

• Toxicology and Risk Assessment
• Biostatistics
• Environmental Health

Background:

• The benchmark dose (BMD) approach is valuable for noncancer risk assessment, utilizing dose-response data effectively.
• Quantifying the statistical uncertainty of BMD estimates often involves the benchmark dose lower confidence limit (BMDL).
• The conventional delta method for BMDL calculation can be unreliable with small sample sizes or nonlinear model parameters.

Purpose of the Study:

• To propose and evaluate a novel bootstrap method for estimating the BMDL.
• To compare the performance of the bootstrap BMDL with the traditional delta method BMDL.
• To assess the statistical uncertainty quantification and conservatism of the bootstrap method.

Main Methods:

• A bootstrap resampling of residuals after model fitting was employed.
• A one-step formula was used for parameter estimation within the bootstrap scheme.
• The proposed method was illustrated using clustered binary data from developmental toxicity experiments.

Main Results:

• The bootstrap BMDL estimates were, on average, smaller than delta method BMDLs for moderately elevated dose-response data, indicating more conservative risk quantification.
• The bootstrap BMDL demonstrated better statistical performance, with coverage probabilities closer to the nominal level than the delta method BMDL.
• BMD and BMDL estimates were found to be relatively insensitive to model choice when models fit the data comparably near the BMD region.

Conclusions:

• The bootstrap method offers a more statistically honest and conservative approach to quantifying uncertainty in BMDL estimation.
• This method is particularly advantageous for analyzing developmental toxicity data, especially with dose-response relationships.
• Standard developmental toxicity experiments support dose-response assessment at a 5% benchmark risk level (BMR) and 95% confidence level for BMDL.