Longitudinal Modified Treatment Policies (LMTPs): A unified framework for studying complex exposures

Corresponding code guide for Hoffman et al. (2023)

This repository demonstrates the use of the open-source R package lmtp to estimate the effects of delaying intubation on mortality in a cohort of hospitalized COVID-19 patients during Spring 2020, as described in Hoffman et al. (2023).

What are LMTPs?

Longitudinal Modified Treatment Policies (LMTPs) are a recently developed methodology for causal inference (Diaz et al. (2021)). LMTPs generalize many commonly used parameters for causal inference including average treatment effects, and facilitate the mathematical formalization, identification, and estimation of many novel parameters. LMTPs apply to a wide variety of exposures, including binary, multivariate, and continuous, as well as exposures that result in practical violations of the positivity assumption. LMTPs can accommodate time-varying treatments and confounders, competing risks, loss-to-follow-up, as well as survival, binary, or continuous outcomes.

About the application

Hoffman et al. provides numerous examples of types of research questions which can be answered within the proposed framework, and then goes into more depth with one of these examples---specifically, estimating the effect of delaying intubation on critically ill COVID-19 patients' mortality. The study design is retrospective and uses electronic health records of 3,059 patients hospitalized with COVID-19 at New York Presbyterian hospital between March 1 and May 15, 2020. The exposure is categorical and time-varying, and the outcome is also time-to-event with informative right-censoring. Adjustment set includes dozens of baseline and time-varying confounders. The estimator is a sequentially doubly robust (SDR) estimator which utilizes regressions for the exposure and outcome. These exposure and outcome regressions utilized a superlearner ensemble of flexible machine learning regressions.

Repository contents

Main scripts:

• R/run_lmtp.R - main analysis script. sets up exposure, confounders, outcome, and runs lmtp_sdr() for an intervention and null intervention for all time points in the study.
• R/clean_results.R - summarizes LMTP results as tibbles and creates graphs of output.

Supporting scripts:

• R/vis.R contains data visualization functions to plot incidence and incidence differences over time
• R/utils.R contains helper functions to clean results and summarize analyses (e.g. create marginal / simultaneous confidence intervals across all time points of incidence curve)
• R/assess_density_ratios.R provides code to plot the density ratios across time to assess for potential positivity violations

Additional resources

• lmtp Github and package documentation
• Williams and Diaz (2023) tutorial paper on the lmtp package
• KHstats' introductory blog post on Modified Treatment Policies
• Diaz et al. (2021)'s original Journal of the American Statistical Association statistical methodology paper on LMTPs
• Diaz et al. (2022)'s statistical methodology paper adapting LMTPs for competing risks data

Acknowledgements

Several functions in vis.R and utils.R were adapted from code written by Dr. Nima Hejazi.