Nonparametric estimation of accelerated failure-time models with unobservable confounders and random censoring

Abstract

We consider nonparametric estimation of an accelerated failure-time model when the response variable is randomly censored on the right, and regressors are not mean independent of the error component. This dependence can arise, for instance, because of measurement error. We achieve identification and conduct estimation using a vector of instrumental variables. Censoring is independent of the response variable given the instruments. We consider settings in which regressors are continuously distributed. However, the instruments may or may not be continuous, and we show how various independence restrictions allow us to identify and estimate the unknown function of interest depending on the nature of instruments. We provide rates of convergence of our estimator and showcase its finite sample properties in simulations.

Instrumental Variable Estimation of Dynamic Treatment Effects on a Duration Outcome

“…Moreover, Beyhum et al (2022) nonparametrically estimate the average quantile treatment effect over the whole population when both the treatment and the instrument are categorical. Also, Centorrino and Florens (2021) study nonparametric estimation when the treatment is continuous, and the model is additive. They allow the instrument to be categorical, even in this case.…”

An instrumental variable approach under dependent censoring

“…Note that Tchetgen Tchetgen et al ( 2015) also proposes a control function approach. Centorrino and Florens (2021) study nonparametric estimation with continuous regressors. Confounding has also been discussed in a competing risks framework by Richardson et al (2017), Zheng et al (2017), Martinussen and Vansteelandt (2020) and Beyhum et al (2021a).…”