3 lung cancer treatments
Video assisted (VATS)

3 lung cancer treatments
Open thorectomy

3 lung cancer treatments
Robotic assisted

3 lung cancer treatments
Pct white |
0.808 |
0.865 |
0.873 |
Pct high income |
0.245 |
0.324 |
0.202 |
Pct Stage 3 cancer |
0.096 |
0.134 |
0.082 |
3 lung cancer treatments
Pct white |
0.808 |
0.865 |
0.873 |
Pct high income |
0.245 |
0.324 |
0.202 |
Pct Stage 3 cancer |
0.096 |
0.134 |
0.082 |
Complications |
0.308 |
0.357 |
0.303 |
3 lung cancer treatments

Issue 1: Selection bias

Issue 2: Non-overlapping distributions

Issue 3: Large weights

Notation
Consider causal effect of A∈{1,…,Z} on binary outcome Y∈{0,1}
- i=1,…,n for n total subjects
- n=n1+…+nZ
- {Yi(1),…,Yi(Z)} as potential outcomes for i
- Covariates Xi
Notation
Interest: average treatment effect among treated
- ATT1∣1,a: effect of T=1 versus T=a among those with T=1
- ATT1∣1,a = n11∑i:Ai=1(Yi(1)−Yi(a)) for a={2,…,Z}
- Ex: Z = 3, ATT1∣1,2, ATT1∣1,3, ATT1∣2,3
- ATT1∣1,2 = n11∑i:Ai=1(Yi(1)−Yi(2))
- ATT1∣1,3 = n11∑i:Ai=1(Yi(1)−Yi(3))
- ATT1∣2,3 = n11∑i:Ai=1(Yi(2)−Yi(3))
Causal inference with multiple treatments
Why not binary approaches?
- May not fully account for differences in patient characteristics
- Comparisons of disctinct cohorts with dissimilar characteristics
- Challenging to identify optimal treatment
- Main issue: matching on scalar alone insufficient
- See Lopez & Gutman, 2017 for more
Causal inference with multiple treatments
Bayesian Additive Regression Trees
Why BART for causal inference? see Hill, 2012
- Flexibly models response surface ✔️
- Large number of continuous and categorical predictors ✔️
- No ambiguity with respect to balance assessment ✔️
- Accessibility ✔️
- Accuracy ✔️
Bayesian Additive Regression Trees
Why BART for multiple treatments?
- Coherent posterior intervals ❓
- Heterogenous treatment effects ❓
- Accessibility ❓
- Accuracy ❓
Simulation study
6 factorial design using dbarts
package in R
- Ratio of n1 : n2 : n3
- n
- No. of predictors
- P(A∣X)
- Predictor strength alignment
- Response surfaces (parallel?)
3 lung cancer treatments
ATT’s: generalizable to population receiving robotic treatment

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