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	-2.115673	0.071127	0.171063	0.262630	1	3	4.554272	22.843009	-797.082267
1	-1.974123	0.428260	-0.158586	0.312502	0	0	0.387135	-1.039225	-3.322797
2	-0.964893	0.305667	0.010051	0.281290	1	1	3.966772	8.323577	21.883266
3	-0.182383	1.015889	-0.440182	-0.422360	2	3	-0.265820	16.728035	157.233057
4	-0.399723	0.564200	-2.529025	1.728209	3	3	0.139306	21.722602	235.103613

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

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

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

## Estimate
Mean value: -9.360849851964446

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

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

## Estimate
Mean value: -9.360849851964446

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.