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	0.152782	2.366620	0.467687	1.930517	3	1	6.768407	23.856222	2186.147887
1	-0.447605	3.691053	0.736319	0.975951	1	2	4.852149	13.671995	1260.100285
2	-0.077897	1.884326	1.728194	2.309277	0	1	6.484334	16.238016	1147.102010
3	-0.951562	0.746449	1.539181	1.504921	1	1	5.836967	18.455299	326.102074
4	0.776670	1.522993	-0.614915	-0.777967	3	1	-0.043317	7.587874	77.776876

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

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

## Estimate
Mean value: 87.13499671049453

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

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

## Estimate
Mean value: 87.13499671049453
### Conditional Estimates
__categorical__X1  __categorical__X0
(-2.964, -0.308]   (-3.5829999999999997, -0.496]    -52.444657
                   (-0.496, 0.0792]                 -18.056304
                   (0.0792, 0.589]                    0.393878
                   (0.589, 1.182]                    22.476104
                   (1.182, 3.923]                    54.373769
(-0.308, 0.28]     (-3.5829999999999997, -0.496]      2.230588
                   (-0.496, 0.0792]                  35.139766
                   (0.0792, 0.589]                   55.560245
                   (0.589, 1.182]                    74.554758
                   (1.182, 3.923]                   107.511877
(0.28, 0.783]      (-3.5829999999999997, -0.496]     32.064804
                   (-0.496, 0.0792]                  66.958371
                   (0.0792, 0.589]                   87.093783
                   (0.589, 1.182]                   107.294100
                   (1.182, 3.923]                   142.282697
(0.783, 1.357]     (-3.5829999999999997, -0.496]     64.469122
                   (-0.496, 0.0792]                  98.853483
                   (0.0792, 0.589]                  119.070601
                   (0.589, 1.182]                   139.416182
                   (1.182, 3.923]                   174.524617
(1.357, 4.616]     (-3.5829999999999997, -0.496]    120.268491
                   (-0.496, 0.0792]                 150.843577
                   (0.0792, 0.589]                  171.065307
                   (0.589, 1.182]                   194.557160
                   (1.182, 3.923]                   228.234836
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.