README.md
In crumble: Flexible and General Mediation Analysis Using Riesz Representers

crumble (verb): break or fall apart into small fragments

crumble

crumble implements a modern, unified estimation strategy (Liu et al. 2024) for common mediation estimands: natural effects (Pearl 2022), organic effects (Lok 2015), interventional effects (Vansteelandt and Daniel 2017), recanting twins (Vo et al. 2024), in causal inference in combination with modified treatment policies. It makes use of recent advancements in “Riesz-learning” to estimate a set of required nuisance parameters using deep learning. The result is a software package that is capable of estimating mediation effects with binary, categorical, continuous, or multivariate exposures with high-dimensional mediators and mediator-outcome confounders using machine learning.

This work was supported by the National Institute on Drug Abuse [R00DA042127].

remotes::install_github("nt-williams/crumble")

| Feature | Status | |---------------------------|:-------:| | Recanting twins | ✓ | | Natural effects | ✓ | | Organic effects | ✓ | | Interventional effects | ✓ | | Modified treatment Policy | ✓ | | Static intervention | ✓ | | Dynamic intervention | ✓ | | Continuous treatment | ✓ | | Binary treatment | ✓ | | Categorical treatment | ✓ | | Multivariate treatment | ✓ | | Missingness in treatment | | | Continuous outcome | ✓ | | Binary outcome | ✓ | | Censored outcome | ✓ | | Survey weights | Planned | | Super learner | ✓ | | Clustered data | Planned | | Parallel processing | ✓ | | GPU support | ✓ | | Progress bars | ✓ |

library(crumble)
library(mlr3extralearners)

data(weight_behavior, package = "mma")

weight_behavior <- na.omit(weight_behavior)

set.seed(2345)

Recanting twins

crumble(
    data = weight_behavior,
    trt = "sports", 
    outcome = "bmi",
    covar = c("age", "sex", "tvhours"),
    mediators = c("exercises", "overweigh"),
    moc = "snack",
    d0 = \(data, trt) factor(rep(1, nrow(data)), levels = c("1", "2")), 
    d1 = \(data, trt) factor(rep(2, nrow(data)), levels = c("1", "2")), 
    effect = "RT",
    learners = c("mean", "glm", "earth", "ranger"), 
    nn_module = sequential_module(),
    control = crumble_control(crossfit_folds = 1L, epochs = 20L)
)
#> ✔ Permuting Z-prime variables... 1/1 tasks [2.5s]
#> ✔ Fitting outcome regressions... 1/1 folds [25.6s]             
#> ✔ Computing alpha n density ratios... 1/1 folds [39.7s]        
#> ✔ Computing alpha r density ratios... 1/1 folds [41.6s]        
#> 
#> ══ Results `crumble()` ═════════════════════════════════════════
#> 
#> ── E[Y(d1) - Y(d0)] 
#>       Estimate: 1.0537
#>     Std. error: 0.3009
#>         95% CI: (0.4639, 1.6435)
#> 
#> ── Path: A -> Y 
#>       Estimate: 0.0366
#>     Std. error: 0.1842
#>         95% CI: (-0.3245, 0.3976)
#> 
#> ── Path: A -> Z -> Y 
#>       Estimate: -0.0202
#>     Std. error: 0.0238
#>         95% CI: (-0.0668, 0.0264)
#> 
#> ── Path: A -> Z -> M -> Y 
#>       Estimate: -6e-04
#>     Std. error: 0.0099
#>         95% CI: (-0.02, 0.0189)
#> 
#> ── Path: A -> M -> Y 
#>       Estimate: 1.0506
#>     Std. error: 0.2162
#>         95% CI: (0.627, 1.4743)
#> 
#> ── Intermediate Confounding 
#>       Estimate: -0.0127
#>     Std. error: 0.0261
#>         95% CI: (-0.0638, 0.0384)

Natural effects

crumble(
    data = weight_behavior,
    trt = "sports", 
    outcome = "bmi",
    covar = c("age", "sex", "tvhours"),
    mediators = c("exercises", "overweigh"),
    d0 = \(data, trt) factor(rep(1, nrow(data)), levels = c("1", "2")), 
    d1 = \(data, trt) factor(rep(2, nrow(data)), levels = c("1", "2")), 
    effect = "N",
    learners = c("mean", "glm", "earth", "ranger"), 
    nn_module = sequential_module(),
    control = crumble_control(crossfit_folds = 1L, epochs = 20L)
)
#> ✔ Fitting outcome regressions... 1/1 folds [10.6s]             
#> ✔ Computing alpha n density ratios... 1/1 folds [53.1s]        
#> 
#> ══ Results `crumble()` ═════════════════════════════════════════
#> 
#> ── E[Y(d1) - Y(d0)] 
#>       Estimate: 1.0289
#>     Std. error: 0.28
#>         95% CI: (0.48, 1.5777)
#> 
#> ── Natural Direct Effect 
#>       Estimate: 0.0165
#>     Std. error: 0.1717
#>         95% CI: (-0.3201, 0.3531)
#> 
#> ── Natural Indirect Effect 
#>       Estimate: 1.0124
#>     Std. error: 0.2178
#>         95% CI: (0.5856, 1.4393)

Organic effects

crumble(
    data = weight_behavior,
    trt = "sports", 
    outcome = "bmi",
    covar = c("age", "sex", "tvhours"),
    mediators = c("exercises", "overweigh"),
    d0 = \(data, trt) factor(rep(1, nrow(data)), levels = c("1", "2")), 
    d1 = \(data, trt) factor(rep(2, nrow(data)), levels = c("1", "2")), 
    effect = "O",
    learners = c("mean", "glm", "earth", "ranger"), 
    nn_module = sequential_module(),
    control = crumble_control(crossfit_folds = 1L, epochs = 20L)
)
#> ✔ Fitting outcome regressions... 1/1 folds [10.7s]             
#> ✔ Computing alpha n density ratios... 1/1 folds [48.2s]        
#> 
#> ══ Results `crumble()` ═════════════════════════════════════════
#> 
#> ── Organic Direct Effect 
#>       Estimate: 0.011
#>     Std. error: 0.1772
#>         95% CI: (-0.3364, 0.3584)
#> 
#> ── Organic Indirect Effect 
#>       Estimate: 1.0278
#>     Std. error: 0.2231
#>         95% CI: (0.5904, 1.4651)#>

Randomized interventional effects

crumble(
    data = weight_behavior,
    trt = "sports", 
    outcome = "bmi",
    covar = c("age", "sex", "tvhours"),
    mediators = c("exercises", "overweigh"),
    moc = "snack",
    d0 = \(data, trt) factor(rep(1, nrow(data)), levels = c("1", "2")), 
    d1 = \(data, trt) factor(rep(2, nrow(data)), levels = c("1", "2")), 
    effect = "RI",
    learners = c("mean", "glm", "earth", "ranger"), 
    nn_module = sequential_module(),
    control = crumble_control(crossfit_folds = 1L, epochs = 20L)
)
#> ✔ Permuting Z-prime variables... 1/1 tasks [2s]
#> ✔ Fitting outcome regressions... 1/1 folds [14.2s]             
#> ✔ Computing alpha r density ratios... 1/1 folds [1m 23.2s]     
#> 
#> ══ Results `crumble()` ═════════════════════════════════════════
#> 
#> ── Randomized Direct Effect 
#>       Estimate: 0.0162
#>     Std. error: 0.1774
#>         95% CI: (-0.3315, 0.364)
#> 
#> ── Randomized Indirect Effect 
#>       Estimate: 1.0304
#>     Std. error: 0.2296
#>         95% CI: (0.5805, 0.4662)

References

Liu, Richard, Nicholas T Williams, Kara E Rudolph, and Iván Dı́az. 2024. “General Targeted Machine Learning for Modern Causal Mediation Analysis.” *arXiv Preprint arXiv:2408.14620*.

Lok, Judith J. 2015. “Organic Direct and Indirect Effects with Post-Treatment Common Causes of Mediator and Outcome.” .

Pearl, Judea. 2022. “Direct and Indirect Effects.” In, 373–92. ACM. .

Vansteelandt, Stijn, and Rhian M. Daniel. 2017. “Interventional Effects for Mediation Analysis with Multiple Mediators.” *Epidemiology* 28 (2): 258–65. .

Vo, Tat-Thang, Nicholas Williams, Richard Liu, Kara E. Rudolph, and Ivan Dıaz. 2024. “Recanting Twins: Addressing Intermediate Confounding in Mediation Analysis.” .