Sample-constrained partial identification with application to selection bias

Matt J Tudball*, Kate M Tilling, Rach Hughes

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Many partial identification problems can be characterized by the optimal value of a func- 20
tion over a set where both the function and set need to be estimated by empirical data. Despite
some progress for convex problems, statistical inference in this general setting remains to be
developed. To address this, we derive an asymptotically valid confidence interval for the optimal
value through an appropriate relaxation of the estimated set. We then apply this general result
to the problem of selection bias in population-based cohort studies. We show that existing sen- 25
sitivity analyses, which are often conservative and difficult to implement, can be formulated in
our framework and made significantly more informative via auxiliary information on the population. We conduct a simulation study to evaluate the finite sample performance of our inference
procedure and conclude with a substantive motivating example on the causal effect of education
on income in the highly-selected UK Biobank cohort. We demonstrate that our method can pro- 30
duce informative bounds using plausible population-level auxiliary constraints. We implement
this method in the R package
Original languageEnglish
Article numberasac042
JournalBiometrika
Publication statusPublished - 25 Jul 2022

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