A blended distance to define "people-like-me"

TL;DR

This paper introduces a blended distance measure combining predictive and Mahalanobis distances for curve matching, analyzing its properties through simulations and highlighting the bias-variance trade-off involved.

Contribution

It proposes and evaluates a new blended distance metric for curve matching, demonstrating its effects on bias, variance, and prediction accuracy in simulation studies.

Findings

Blending towards Mahalanobis distance worsens bias, coverage, and predictive power.

More weight on Mahalanobis distance reduces variance but decreases accuracy.

High prediction accuracy relies on variability in donor profiles.

Abstract

Curve matching is a prediction technique that relies on predictive mean matching, which matches donors that are most similar to a target based on the predictive distance. Even though this approach leads to high prediction accuracy, the predictive distance may make matches look unconvincing, as the profiles of the matched donors can substantially differ from the profile of the target. To counterbalance this, similarity between the curves of the donors and the target can be taken into account by combining the predictive distance with the Mahalanobis distance into a `blended distance' measure. The properties of this measure are evaluated in two simulation studies. Simulation study I evaluates the performance of the blended distance under different data-generating conditions. The results show that blending towards the Mahalanobis distance leads to worse performance in terms of bias, coverage, and predictive power. Simulation study II evaluates the blended metric in a setting where a single value is imputed. The results show that a property of blending is the bias-variance trade off. Giving more weight to the Mahalanobis distance leads to less variance in the imputations, but less accuracy as well. The main conclusion is that the high prediction accuracy achieved with the predictive distance necessitates the variability in the profiles of donors.