Small-sample confidence sets for the MTD in a phase I clinical trial

Area of Science:

• Biostatistics
• Clinical Trial Design
• Pharmacometrics

Background:

• Phase I clinical trials aim to determine the maximum tolerable dose (MTD).
• Accurate estimation of MTD is essential for patient safety and subsequent trial phases.
• Existing interval estimation methods may lack precision under specific sampling schemes.

Purpose of the Study:

• To evaluate interval estimation procedures for MTD in Phase I trials.
• To investigate the performance of a two-stage stochastic sampling scheme.
• To develop methods for constructing confidence intervals with correct coverage probabilities.

Main Methods:

• Utilized a two-stage stochastic sampling scheme (Storer, 1989).
• Examined likelihood functions and large-sample statistics under conditional binomial and true stochastic sampling.
• Employed Monte Carlo simulation for evaluating confidence set membership.
• Assessed intervals based on a likelihood ratio criterion.

Main Results:

• Intervals based on conditional binomial assumptions showed no improvement over unadjusted intervals.
• Methods considering the true stochastic sampling scheme yielded intervals with correct coverage probabilities.
• Confidence intervals frequently included infinite MTD values in small-sample settings, particularly with shallow dose-response curves.
• Likelihood ratio-based intervals demonstrated superior performance in handling MTD estimation.

Conclusions:

• Stochastic sampling schemes can lead to improved MTD interval estimation in Phase I trials.
• Likelihood ratio criteria offer a robust approach for constructing accurate MTD confidence intervals.
• Careful consideration of sampling schemes is vital for reliable dose-finding studies.