The distribution of the maximum likelihood estimator in up-and-down experiments for quantal dose-response data

Area of Science:

• Biostatistics
• Pharmacometrics
• Clinical Trial Design

Background:

• Up-and-down designs are common in biopharmaceutical research for dose escalation studies.
• Standard statistical methods like logistic or probit regression are typically applied for analyzing these designs.
• Previous studies have sometimes reported unexpectedly steep dose-response curves.

Purpose of the Study:

• To investigate the accuracy of standard maximum likelihood logistic or probit regression for analyzing up-and-down designs.
• To identify potential biases in parameter estimation and precision when using these conventional methods.
• To provide a probable explanation for observed steeper-than-expected dose-response curves in practice.

Main Methods:

• The study involved theoretical demonstration and simulation (implied) of maximum likelihood estimation.
• Analysis focused on the bias of the regression parameter estimator in logistic and probit models.
• The impact of this bias on the estimation of mean, median, and ED50 was examined.

Main Results:

• Maximum likelihood estimators systematically and considerably exaggerate the regression parameter in up-and-down designs, especially with moderately large sample sizes.
• This exaggeration leads to an overestimation of the steepness of the dose-response curve.
• Confidence intervals for estimated parameters, including ED50, are found to be misleadingly narrow, suggesting false precision.

Conclusions:

• Conventional logistic or probit regression analysis is not recommended for up-and-down designs due to inherent bias.
• The bias in maximum likelihood estimation offers a likely explanation for steeper-than-expected dose-response curves.
• Researchers should be cautious about the precision of estimates derived from these methods in such study designs.