  This tutorial discusses methodology for causal inference using longitudinal
modified treatment policies. This method facilitates the mathematical
formalization, identification, and estimation of many novel parameters, and
mathematically generalizes many commonly used parameters, such as the average
treatment effect. Longitudinal modified treatment policies apply to a wide
variety of exposures, including binary, multivariate, and continuous, and can
accommodate time-varying treatments and confounders, competing risks,
loss-to-follow-up, as well as survival, binary, or continuous outcomes.
Longitudinal modified treatment policies can be seen as an extension of static
and dynamic interventions to involve the natural value of treatment, and, like
dynamic interventions, can be used to define alternative estimands with a
positivity assumption that is more likely to be satisfied than estimands
corresponding to static interventions. This tutorial aims to illustrate several
practical uses of the longitudinal modified treatment policy methodology,
including describing different estimation strategies and their corresponding
advantages and disadvantages. We provide numerous examples of types of research
questions which can be answered using longitudinal modified treatment policies.
We go into more depth with one of these examples--specifically, estimating the
effect of delaying intubation on critically ill COVID-19 patients' mortality.
We demonstrate the use of the open-source R package lmtp to estimate the
effects, and we provide code on https://github.com/kathoffman/lmtp-tutorial.
