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 technical paper in Observational Studies.

**lmtp** can be installed from CRAN with:

`install.packages("lmtp")`

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

`::install_github("nt-williams/lmtp@devel") devtools`

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

`::install_github("nt-williams/lmtp@separate-variable-sets") devtools`

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 | ✓ |

Incremental Propensity Score Intervention (Using the risk ratio) | ✓ |

Static intervention | ✓ |

Dynamic intervention | ✓ |

Continuous treatment | ✓ |

Binary treatment | ✓ |

Categorical treatment | ✓ |

Multivariate treatment | ✓ |

Missingness in treatment | |

Continuous outcome | ✓ |

Binary outcome | ✓ |

Censored outcome | ✓ |

Mediation | |

Survey weights | ✓ |

Super learner | ✓ |

Clustered data | ✓ |

Parallel processing | ✓ |

Progress bars | ✓ |

```
library(lmtp)
#> Loading required package: mlr3superlearner
#> Loading required package: mlr3learners
#> Warning: package 'mlr3learners' was built under R version 4.2.3
#> Loading required package: mlr3
#> Warning: package 'mlr3' was built under R version 4.2.3
# 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.

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

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

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 estimate
#> Estimate: 0.2526
#> Std. error: 0.0223
#> 95% CI: (0.2089, 0.2962)
```

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 article and the
paper establishing the statistical methodology.

```
@article{,
title = {lmtp: An R package for estimating the causal effects of modified treatment policies},
author = {Nicholas T Williams and Iván Díaz},
journal = {Observational Studies},
year = {2023},
url = {https://muse.jhu.edu/article/883479}
}
@article{
doi:10.1080/01621459.2021.1955691,
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