Demystifying the Bias from Selective Inference: a Revisit to Dawid's Treatment Selection Problem

TL;DR

This paper derives a closed-form expression for the bias caused by selective inference in treatment selection problems, providing theoretical insights and illustrating them with numerical and simulated examples.

Contribution

It introduces a new theoretical derivation of the selection bias in treatment choice, extending previous heuristic discussions and offering a clearer understanding of the bias.

Findings

Derived a closed-form expression for selection bias.

Demonstrated the theoretical results with numerical examples.

Validated findings through simulated data analysis.

Abstract

We extend the heuristic discussion in Senn (2008) on the bias from selective inference for the treatment selection problem (Dawid 1994), by deriving the closed-form expression for the selection bias. We illustrate the advantages of our theoretical results through numerical and simulated examples.