Estimating effect of multiple treatments

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	1.767708	0.055920	-0.240717	-0.843351	1	3	6.726900	5.318777	295.611567
1	-1.470650	-0.938818	-0.975773	-0.355186	3	3	16.839656	12.739667	-1120.844957
2	-0.342821	1.699236	2.115395	-1.886431	1	1	3.640529	6.192848	194.403694
3	0.083615	0.197779	1.158983	-2.716997	1	3	5.658150	2.749601	100.307163
4	1.376552	0.300785	-0.641883	-1.958623	3	0	12.339354	10.039195	784.314906

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

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

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

## Estimate
Mean value: 34.04612866069517

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

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

## Estimate
Mean value: 34.04612866069517
### Conditional Estimates
__categorical__X0  __categorical__X1
(-3.415, -0.17]    (-3.972, -1.109]     -70.424952
                   (-1.109, -0.514]     -33.177203
                   (-0.514, -0.0098]    -14.653352
                   (-0.0098, 0.551]       4.920673
                   (0.551, 3.39]         37.852659
(-0.17, 0.411]     (-3.972, -1.109]     -38.279800
                   (-1.109, -0.514]      -5.334605
                   (-0.514, -0.0098]     15.731057
                   (-0.0098, 0.551]      36.055460
                   (0.551, 3.39]         67.421581
(0.411, 0.919]     (-3.972, -1.109]     -20.080857
                   (-1.109, -0.514]      14.305287
                   (-0.514, -0.0098]     34.978155
                   (-0.0098, 0.551]      54.666784
                   (0.551, 3.39]         87.340856
(0.919, 1.521]     (-3.972, -1.109]      -1.487976
                   (-1.109, -0.514]      33.019920
                   (-0.514, -0.0098]     53.622393
                   (-0.0098, 0.551]      73.352510
                   (0.551, 3.39]        106.654895
(1.521, 4.496]     (-3.972, -1.109]      29.589954
                   (-1.109, -0.514]      64.460886
                   (-0.514, -0.0098]     82.707948
                   (-0.0098, 0.551]     104.178150
                   (0.551, 3.39]        133.896098
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.