CRAN status R build status codecov License: GPL v3 Project Status: Active – The project has reached a stable, usable state and is being actively developed.

Non-parametric Causal Effects of Feasible Interventions Based on Modified Treatment Policies

Nick Williams and Ivan Diaz

lmtp is an R package that provides an estimation framework for the casual effects of feasible interventions based on point-treatment and longitudinal modified treatment policies as described in Diaz, Williams, Hoffman, and Schenck (2020). Two primary estimators are supported, a targeted maximum likelihood (TML) estimator and a sequentially doubly robust (SDR) estimator (a G-computation and an inverse probability of treatment weighting estimator are provided for the sake of being thorough but their use is recommended against in favor of the TML and SDR estimators). Both binary and continuous outcomes (both with censoring) are allowed. lmtp is built atop the SuperLearner package to utilize ensemble machine learning for estimation. The treatment mechanism is estimated via a density ratio classification procedure irrespective of treatment variable type providing decreased computation time when treatment is continuous. Dynamic treatment regimes are also supported.

A list of papers using lmtp is here.

For an in-depth look at the package’s functionality, please consult the accompanying vignette.


lmtp can be installed from CRAN with:


The stable, development version can be installed from GitHub with:


The sl3 compatible version can be installed from GitHub with:


A version allowing for different covariates sets for the treatment and outcome regressions:


A version allowing for different covariates sets for the treatment and outcome regressions and that uses sl3:


What even is a modified treatment policy?

Modified treatment policies (MTP) are interventions that can depend on the natural value of the treatment (the treatment value in the absence of intervention). A key assumption for causal inference is the positivity assumption which states that all observations have a non-zero probability of experiencing a treatment value. When working with continuous or multivalued treatments, violations of the positivity assumption are likely to occur. MTPs offer a solution to this problem.

Can lmtp estimate other effects?

Yes! lmtp can estimate the effects of deterministic, static treatment effects (such as the ATE) and deterministic, dynamic treatment regimes for binary, continuous, and survival outcomes.


Feature Status
Point treatment
Longitudinal treatment
Modified treatment intervention
Static intervention
Dynamic intervention
Continuous treatment
Binary treatment
Categorical treatment
Missingness in treatment
Continuous outcome
Binary outcome
Censored outcome
Survey weights
Super learner
Clustered data
Parallel processing
Progress bars



# the data: 4 treatment nodes with time varying covariates and a binary outcome
#>   ID L_1 A_1 L_2 A_2 L_3 A_3 L_4 A_4 Y
#> 1  1   2   3   0   1   1   1   1   3 0
#> 2  2   2   1   1   4   0   3   1   2 0
#> 3  3   1   0   1   3   1   2   1   1 1
#> 4  4   1   0   0   3   1   3   1   2 0
#> 5  5   3   3   1   1   0   1   1   2 0
#> 6  6   1   0   0   2   0   3   1   4 0

We’re interested in a treatment policy, d, where exposure is decreased by 1 only among subjects whose exposure won’t go below 1 if intervened upon. The true population outcome under this policy is about 0.305.

# a treatment policy function to be applied at all time points
policy <- function(data, trt) {
  (data[[trt]] - 1) * (data[[trt]] - 1 >= 1) + data[[trt]] * (data[[trt]] - 1 < 1)

In addition to specifying a treatment policy, we need to specify our treatment variables and time-varying covariates.

# treatment nodes, a character vector of length 4
A <- c("A_1", "A_2", "A_3", "A_4")
# time varying nodes, a list of length 4
L <- list(c("L_1"), c("L_2"), c("L_3"), c("L_4"))

We can now estimate the effect of our treatment policy, d. In this example, we’ll use the cross-validated TML estimator with 10 folds.

lmtp_tmle(sim_t4, A, "Y", time_vary = L, shift = policy, intervention_type = "mtp", folds = 10)
#> LMTP Estimator: TMLE
#>    Trt. Policy: (policy)
#> Population intervention effect
#>       Estimate: 0.2526
#>     Std. error: 0.0105
#>         95% CI: (0.2321, 0.2732)

Data structure

Single time point

Time-varying exposure and confounders, not survival outcome

Single exposure, survival outcome

Time-varying exposure and confounders, survival outcome

Similar Implementations

A variety of other R packages perform similar tasks as lmtp. However, lmtp is the only R package currently capable of estimating causal effects for binary, categorical, and continuous exposures in both the point treatment and longitudinal setting using traditional causal effects or modified treatment policies.


Please cite the following when using lmtp in publications. Citation should include both the R package and the paper establishing the statistical methodology.

  title = {lmtp: {Non}-parametric {Causal} {Effects} of {Feasible} {Interventions} {Based} on {Modified} {Treatment} {Policies}},
  author = {Nicholas T Williams and Iván Díaz},
  year = {2021},
  note = {R package version 1.3.1},
  doi = {10.5281/zenodo.3874931}, 
  url = {https://github.com/nt-williams/lmtp}

  author = {Iván Díaz and Nicholas Williams and Katherine L. Hoffman and Edward J. Schenck},
  title = {Non-parametric causal effects based on longitudinal modified treatment policies},
  journal = {Journal of the American Statistical Association},
  year  = {2021},
  doi = {10.1080/01621459.2021.1955691},
  URL = {https://doi.org/10.1080/01621459.2021.1955691},


Iván Díaz, Nicholas Williams, Katherine L. Hoffman & Edward J. Schenck (2021) Non-parametric causal effects based on longitudinal modified treatment policies, Journal of the American Statistical Association, DOI: 10.1080/01621459.2021.1955691