  Longitudinal modified treatment policies (LMTP) have been recently developed
as a novel method to define and estimate causal parameters that depend on the
natural value of treatment. LMTPs represent an important advancement in causal
inference for longitudinal studies as they allow the non-parametric definition
and estimation of the joint effect of multiple categorical, numerical, or
continuous exposures measured at several time points. We extend the LMTP
methodology to problems in which the outcome is a time-to-event variable
subject to right-censoring and competing risks. We present identification
results and non-parametric locally efficient estimators that use flexible
data-adaptive regression techniques to alleviate model misspecification bias,
while retaining important asymptotic properties such as $\sqrt{n}$-consistency.
We present an application to the estimation of the effect of the
time-to-intubation on acute kidney injury amongst COVID-19 hospitalized
patients, where death by other causes is taken to be the competing event.
