Identify which Modified Treatment Policies (MTPs) yield satisfactorily low bias under sparsity/positivity issues

Determine which specific Modified Treatment Policies in continuous-treatment causal inference result in satisfactorily low bias when practical positivity violations and finite-sample sparsity are present, to guide the choice of estimand in applications.

Background

The paper motivates Modified Treatment Policies (MTPs) as a flexible class of estimands that can relax strict positivity assumptions relative to static interventions, making them attractive when practical positivity violations occur.

However, the authors point out that practitioners lack guidance on which concrete MTPs will avoid large bias in finite samples with sparse data. The proposed diagnostic aims to provide data-driven insight, but the broader question of characterizing which MTPs reliably yield low bias remains unresolved.