On the use of historical estimates

TL;DR

This paper reviews how historical estimates are used across fields, highlights the lack of proper uncertainty accounting, and proposes a mathematical framework with variants for better inference and study design.

Contribution

It introduces a principled methodology for incorporating uncertainty in historical estimates and compares different variants for improved statistical inference.

Findings

Derived limiting distributions for the variants

Provided a framework for future study design using historical data

Compared the proposed methods with existing practices

Abstract

The use of historical estimates in current studies is common in a wide variety of application areas. Nevertheless, despite their routine use the uncertainty associated with historical estimates is rarely properly accounted for in the analysis. In this communication we review common practices and then provide a mathematical formulation and a principled methodology for addressing the problem of drawing inferences in the presence of historical data. Three distinct variants are investigated in detail; the corresponding limiting distributions are found and compared. The design of future studies, given historical data, is also explored and relations with a variety of other well--studied statistical problems discussed.