Conditional bias of point estimates following a group sequential test

Area of Science:

• Statistics
• Sequential Analysis
• Biostatistics

Background:

• Repeated significance testing in sequential experiments inflates Type I error rates.
• Unadjusted estimators, like the maximum likelihood estimator (MLE), exhibit significant bias due to early stopping rules.
• Existing methods often have satisfactory unconditional bias but severe conditional bias upon stopping time.

Purpose of the Study:

• To investigate conditional and marginal biases in estimating the Brownian motion drift parameter in sequential trials.
• To develop new conditional estimators that minimize bias, particularly conditional bias upon stopping time.
• To evaluate the performance of proposed estimators against existing methods via simulation.

Main Methods:

• Approximation of sequential trial test statistics using Brownian motion with a drift parameter.
• Analysis of conditional bias in point estimation methods for the Brownian motion drift parameter.
• Development and Monte Carlo simulation of novel conditional estimators.

Main Results:

• Conditional bias can be substantial for existing point estimation methods, even with acceptable unconditional bias.
• Proposed conditional estimators significantly reduce conditional bias compared to unconditional estimators.
• Monte Carlo simulations demonstrate that the new estimators yield lower conditional bias and Mean Squared Error (MSE) than naive MLE and a bias-reduced estimator.

Conclusions:

• Conditional bias is a critical issue in sequential analysis parameter estimation.
• The newly proposed conditional estimators effectively mitigate conditional bias in Brownian motion drift estimation.
• These improved estimators offer better accuracy and reliability in sequential experimental settings.