Estimating effect of multiple treatments

import dowhy
dowhy.enable_notebook_rendering()

from dowhy import CausalModel
import dowhy.datasets

import warnings
warnings.filterwarnings('ignore')

data = dowhy.datasets.linear_dataset(10, num_common_causes=4, num_samples=10000,
                                     num_instruments=0, num_effect_modifiers=2,
                                     num_treatments=2,
                                     treatment_is_binary=False,
                                     num_discrete_common_causes=2,
                                     num_discrete_effect_modifiers=0,
                                     one_hot_encode=False)
df=data['df']
df.head()

	X0	X1	W0	W1	W2	W3	v0	v1	y
0	-1.311765	-1.568984	-2.546688	0.395925	0	0	-9.807547	-13.050328	-1182.114209
1	-0.724059	0.059596	0.166227	0.088218	2	0	11.394021	8.411628	-171.582040
2	-0.595318	0.621521	-1.560061	1.237462	2	0	8.885696	-1.118210	113.406636
3	-1.206896	0.251498	0.799066	-0.512244	0	0	2.394178	2.807621	8.616098
4	-1.948951	-0.612659	-1.610524	1.357947	2	0	9.447075	-0.842088	176.154450

model = CausalModel(data=data["df"],
                    treatment=data["treatment_name"], outcome=data["outcome_name"],
                    graph=data["gml_graph"])

model.view_model()
from IPython.display import Image, display
display(Image(filename="causal_model.png"))

identified_estimand= model.identify_effect(proceed_when_unidentifiable=True)
print(identified_estimand)

Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
    d
─────────(E[y|W2,W0,W3,W1])
d[v₀  v₁]
Estimand assumption 1, Unconfoundedness: If U→{v0,v1} and U→y then P(y|v0,v1,W2,W0,W3,W1,U) = P(y|v0,v1,W2,W0,W3,W1)

### Estimand : 2
Estimand name: iv
No such variable(s) found!

### Estimand : 3
Estimand name: frontdoor
No such variable(s) found!

Linear model

Let us first see an example for a linear model. The control_value and treatment_value can be provided as a tuple/list when the treatment is multi-dimensional.

The interpretation is change in y when v0 and v1 are changed from (0,0) to (1,1).

linear_estimate = model.estimate_effect(identified_estimand,
                                        method_name="backdoor.linear_regression",
                                        control_value=(0,0),
                                        treatment_value=(1,1),
                                        method_params={'need_conditional_estimates': False})
print(linear_estimate)

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
    d
─────────(E[y|W2,W0,W3,W1])
d[v₀  v₁]
Estimand assumption 1, Unconfoundedness: If U→{v0,v1} and U→y then P(y|v0,v1,W2,W0,W3,W1,U) = P(y|v0,v1,W2,W0,W3,W1)

## Realized estimand
b: y~v0+v1+W2+W0+W3+W1+v0*X1+v0*X0+v1*X1+v1*X0
Target units: ate

## Estimate
Mean value: -18.564925008337156

You can estimate conditional effects, based on effect modifiers.

linear_estimate = model.estimate_effect(identified_estimand,
                                        method_name="backdoor.linear_regression",
                                        control_value=(0,0),
                                        treatment_value=(1,1))
print(linear_estimate)

*** Causal Estimate ***

## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE

### Estimand : 1
Estimand name: backdoor
Estimand expression:
    d
─────────(E[y|W2,W0,W3,W1])
d[v₀  v₁]
Estimand assumption 1, Unconfoundedness: If U→{v0,v1} and U→y then P(y|v0,v1,W2,W0,W3,W1,U) = P(y|v0,v1,W2,W0,W3,W1)

## Realized estimand
b: y~v0+v1+W2+W0+W3+W1+v0*X1+v0*X0+v1*X1+v1*X0
Target units:

## Estimate
Mean value: -18.564925008337156
### Conditional Estimates
__categorical__X1  __categorical__X0
(-3.913, -1.025]   (-4.197, -1.517]    -116.733201
                   (-1.517, -0.919]     -57.451380
                   (-0.919, -0.433]     -20.763457
                   (-0.433, 0.166]       15.228586
                   (0.166, 2.977]        80.317656
(-1.025, -0.458]   (-4.197, -1.517]    -115.985904
                   (-1.517, -0.919]     -56.184739
                   (-0.919, -0.433]     -19.930239
                   (-0.433, 0.166]       16.547837
                   (0.166, 2.977]        76.264074
(-0.458, 0.0599]   (-4.197, -1.517]    -114.229124
                   (-1.517, -0.919]     -55.978954
                   (-0.919, -0.433]     -18.292503
                   (-0.433, 0.166]       17.296747
                   (0.166, 2.977]        80.426287
(0.0599, 0.653]    (-4.197, -1.517]    -113.502305
                   (-1.517, -0.919]     -56.126682
                   (-0.919, -0.433]     -18.553484
                   (-0.433, 0.166]       19.415950
                   (0.166, 2.977]        79.025513
(0.653, 3.382]     (-4.197, -1.517]    -114.555769
                   (-1.517, -0.919]     -53.714405
                   (-0.919, -0.433]     -17.248778
                   (-0.433, 0.166]       18.916412
                   (0.166, 2.977]        81.751067
dtype: float64

More methods

You can also use methods from EconML or CausalML libraries that support multiple treatments. You can look at examples from the conditional effect notebook: https://py-why.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html

Propensity-based methods do not support multiple treatments currently.