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	0.921327	1.390097	0.762682	0.498981	0	1	4.025165	10.702244	521.876393
1	2.860156	0.448513	-0.614746	0.745837	3	3	6.862402	29.439688	1720.771628
2	1.098624	1.109132	0.508865	1.516299	0	0	4.056166	1.848361	122.478391
3	0.852896	-1.583007	0.769158	0.155863	1	3	9.428646	24.507579	-1250.825929
4	1.066358	-0.863283	-0.692260	0.433443	3	0	2.457265	12.994037	79.769286

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

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

## Estimate
Mean value: 86.98215448607412

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

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

## Estimate
Mean value: 86.98215448607412
### Conditional Estimates
__categorical__X1              __categorical__X0
(-3.7729999999999997, -0.505]  (-3.516, -0.208]    -130.785325
                               (-0.208, 0.383]     -100.775154
                               (0.383, 0.879]       -80.757119
                               (0.879, 1.483]       -59.751641
                               (1.483, 4.222]       -28.185272
(-0.505, 0.092]                (-3.516, -0.208]     -27.403113
                               (-0.208, 0.383]        6.185364
                               (0.383, 0.879]        22.802503
                               (0.879, 1.483]        43.753686
                               (1.483, 4.222]        76.549133
(0.092, 0.597]                 (-3.516, -0.208]      38.508392
                               (-0.208, 0.383]       69.321297
                               (0.383, 0.879]        86.952838
                               (0.879, 1.483]       107.354818
                               (1.483, 4.222]       137.803860
(0.597, 1.181]                 (-3.516, -0.208]      98.693127
                               (-0.208, 0.383]      130.652155
                               (0.383, 0.879]       151.174073
                               (0.879, 1.483]       168.625077
                               (1.483, 4.222]       202.541129
(1.181, 4.31]                  (-3.516, -0.208]     203.499012
                               (-0.208, 0.383]      234.643790
                               (0.383, 0.879]       248.317746
                               (0.879, 1.483]       272.567389
                               (1.483, 4.222]       302.347991
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.