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	0.688028	-0.570179	-0.787887	0.479003	3	3	9.679098	6.204148	108.190491
1	-0.288296	-0.603436	0.162024	-0.651557	0	0	2.372026	-3.495385	12.209979
2	1.905892	-0.833302	1.485347	-1.040674	2	1	13.177795	-0.545013	139.956383
3	0.621439	-0.585854	1.408494	1.183161	2	0	10.331170	7.882728	95.378611
4	0.101068	-0.273072	-0.117280	-0.515313	2	3	11.525165	0.560455	127.060069

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*X0+v0*X1+v1*X0+v1*X1
Target units: ate

## Estimate
Mean value: 5.078224345610501

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*X0+v0*X1+v1*X0+v1*X1
Target units:

## Estimate
Mean value: 5.078224345610501
### Conditional Estimates
__categorical__X0  __categorical__X1
(-3.758, -0.64]    (-4.402, -1.361]    -72.578624
                   (-1.361, -0.783]    -39.306583
                   (-0.783, -0.286]    -19.224005
                   (-0.286, 0.334]       1.070074
                   (0.334, 3.166]       35.627126
(-0.64, -0.0764]   (-4.402, -1.361]    -57.395848
                   (-1.361, -0.783]    -23.361290
                   (-0.783, -0.286]     -3.911810
                   (-0.286, 0.334]      17.008063
                   (0.334, 3.166]       49.812228
(-0.0764, 0.412]   (-4.402, -1.361]    -47.951547
                   (-1.361, -0.783]    -15.183702
                   (-0.783, -0.286]      4.696040
                   (-0.286, 0.334]      25.565515
                   (0.334, 3.166]       57.882635
(0.412, 0.997]     (-4.402, -1.361]    -38.293553
                   (-1.361, -0.783]     -6.556265
                   (-0.783, -0.286]     13.596805
                   (-0.286, 0.334]      34.149412
                   (0.334, 3.166]       68.228800
(0.997, 4.057]     (-4.402, -1.361]    -24.095849
                   (-1.361, -0.783]      7.787794
                   (-0.783, -0.286]     27.864159
                   (-0.286, 0.334]      48.219762
                   (0.334, 3.166]       83.308854
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.