Interval estimation of the LD50 based on an up-and-down experiment

Area of Science:

• Biostatistics
• Toxicology
• Statistical Methods

Background:

• The up-and-down method is efficient for estimating the median lethal dose (LD50) of quantal response curves.
• Obtaining reliable confidence intervals for LD50 estimates from this method remains a challenge.
• Existing methods, like Dixon's maximum likelihood approach, have limited known properties.

Purpose of the Study:

• To develop and evaluate a novel confidence interval for LD50 estimation using the up-and-down method.
• To compare the performance of the new interval against Dixon's established method.
• To investigate the influence of tolerance distribution on confidence interval properties.

Main Methods:

• A new confidence interval for LD50 was derived based on turning points and phi-mixing.
• Simulation studies were conducted to assess coverage probabilities and interval characteristics.
• The proposed method was compared with Dixon's maximum likelihood confidence interval.

Main Results:

• Both the proposed and Dixon's intervals showed coverage probabilities below the nominal level for smaller sample sizes.
• The new confidence interval demonstrated superior performance in coverage, width, and stability compared to Dixon's interval when the tolerance distribution was normal.
• The advantages of the proposed method diminished with non-normal tolerance distributions.

Conclusions:

• The proposed confidence interval offers an improvement over Dixon's method for LD50 estimation with normal tolerance distributions.
• Sample size is a critical factor for the accuracy of both confidence intervals.
• Further research is needed to address non-normal tolerance distributions in LD50 estimation.