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.

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:

The **sl3** development compatible version can be installed from GitHub with:

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.**

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 | ✓ |

Mediation | |

Survey weights | ✓ |

Super learner | ✓ |

Clustered data | ✓ |

Parallel processing | ✓ |

Progress bars | ✓ |

```
library(lmtp)
#> Major changes in lmtp 0.9.0. Consult NEWS.md for more information.
# the data: 4 treatment nodes with time varying covariates and a binary outcome
head(sim_t4)
#> 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.

```
# our 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.

```
# our treatment nodes, a character vector of length 4
a <- c("A_1", "A_2", "A_3", "A_4")
# our time varying nodes, a list of length 4
time_varying <- 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 = time_varying, k = 0, shift = policy, folds = 10)
#> LMTP Estimator: TMLE
#> Trt. Policy: (policy)
#>
#> Population intervention effect
#> Estimate: 0.2598
#> Std. error: 0.0188
#> 95% CI: (0.2228, 0.2967)
```

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.

```
@Manual{,
title = {lmtp: {Non}-parametric {Causal} {Effects} of {Feasible} {Interventions} {Based} on {Modified} {Treatment} {Policies}},
author = {Nicholas T Williams and Iván Díaz},
year = {2020},
note = {R package version 0.0.5},
doi = {10.5281/zenodo.3874931},
url = {https://github.com/nt-williams/lmtp}
}
@Article{,
journal = {arxiv},
title = {Non-parametric causal effects based on longitudinal modified treatment policies},
author = {Iván Díaz and Nicholas Williams and Katherine L Hoffman and Edward J Schneck},
year = {2020},
url = {https://arxiv.org/abs/2006.01366v2}
}
```

Diaz I, Williams N, Hoffman KL, Schenck, EJ (2020). *Non-Parametric Causal Effects Based on Longitudinal Modified Treatment Policies*. https://arxiv.org/abs/2006.01366