Shrinkage estimation in two-stage adaptive designs with midtrial treatment selection

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Adaptive two-stage designs are crucial for efficient clinical trials, allowing for early selection of promising treatments.
• The standard maximum-likelihood estimator (MLE) for treatment selection in these designs is known to be biased.
• This bias is particularly pronounced when treatment effects are similar and the leading candidate is chosen.

Purpose of the Study:

• To investigate and quantify the selection bias in maximum-likelihood estimation for adaptive two-stage designs.
• To propose and evaluate shrinkage estimation methods as a solution to mitigate this selection bias.
• To compare the performance of shrinkage estimators against MLE and other bias-adjusted estimators.

Main Methods:

• Theoretical analysis to determine conditions for maximal selection bias of the MLE.
• Extension of Lindley's (empirical Bayes) estimator to a two-stage adaptive design framework.
• Development of a two-stage version of the best linear unbiased predictor (BLUP) for smaller trial designs (2-3 arms).
• Extensive simulation studies to assess performance metrics.

Main Results:

• Selection bias of the MLE is maximal when all treatment effects are equal and the most promising treatment is selected.
• A two-stage Lindley's estimator demonstrates uniformly smaller Bayes risk than the MLE under an empirical Bayesian framework.
• Shrinkage estimators exhibit favorable performance regarding selection bias and mean squared error compared to MLE and existing bias-adjusted methods.

Conclusions:

• Shrinkage estimation provides a robust approach to address selection bias in adaptive two-stage designs.
• The proposed two-stage Lindley's and BLUP-based estimators offer significant improvements over standard MLE.
• These findings have important implications for the efficient and accurate selection of treatments in clinical trials.