Semiparametric Inference under Dual Positivity Boundaries:Nested Identification with Administrative Censoring and Confounded Treatment

TL;DR

This paper develops a semiparametric inference framework for causal analysis when outcomes are administratively censored and treatments are confounded, addressing dual positivity boundaries through nested identification.

Contribution

It introduces a novel nested functional approach that bypasses inverse censoring weights and characterizes the dual positivity boundaries in the efficient influence function.

Findings

The nested functional removes the censoring boundary from identification.

The dual boundaries are incorporated into the efficient influence function.

Inference theory for dual-boundary structures is established.

Abstract

When a long-term outcome is administratively censored for a substantial fraction of a study cohort while a short-term intermediate variable remains broadly available, the target causal parameter can be identified through a nested functional that integrates the outcome regression over the conditional intermediate distribution, avoiding inverse censoring weights entirely. In observational studies where treatment is also confounded, this nested identification creates a semiparametric structure with two distinct positivity boundaries -- one from the censoring mechanism and one from the treatment assignment -- that enter the efficient influence function in fundamentally different roles. The censoring boundary is removed from the identification by the nested functional but remains in the efficient score; the treatment boundary appears in both. We develop the inference theory for this dual-boundary structure. Three results are established.