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	-1.947532	-0.143575	-2.940761	0.704417	0	3	12.615346	-10.967185	1061.216087
1	0.219675	0.799437	-1.001001	-0.267116	1	0	1.063260	-1.713651	-14.117716
2	-0.674332	-0.715546	-1.210202	2.808832	3	1	21.176604	3.769456	-189.314365
3	-1.699811	-1.295508	-0.719221	1.067491	0	1	8.191641	-4.385406	482.126100
4	0.401843	-1.189490	-1.047737	0.839477	2	0	10.354018	0.019731	113.643012

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

## Estimate
Mean value: -24.80072189007089

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

## Estimate
Mean value: -24.80072189007089
### Conditional Estimates
__categorical__X0  __categorical__X1
(-4.591, -1.463]   (-3.915, -1.091]    -165.322384
                   (-1.091, -0.505]    -112.225705
                   (-0.505, -0.012]     -83.089046
                   (-0.012, 0.575]      -52.532390
                   (0.575, 3.402]        -1.444389
(-1.463, -0.878]   (-3.915, -1.091]    -131.403753
                   (-1.091, -0.505]     -77.727965
                   (-0.505, -0.012]     -46.798463
                   (-0.012, 0.575]      -16.150495
                   (0.575, 3.402]        35.717876
(-0.878, -0.379]   (-3.915, -1.091]    -104.854708
                   (-1.091, -0.505]     -55.463743
                   (-0.505, -0.012]     -24.275616
                   (-0.012, 0.575]        6.391078
                   (0.575, 3.402]        55.999218
(-0.379, 0.199]    (-3.915, -1.091]     -85.122556
                   (-1.091, -0.505]     -33.753638
                   (-0.505, -0.012]      -2.727838
                   (-0.012, 0.575]       28.903051
                   (0.575, 3.402]        79.552718
(0.199, 2.751]     (-3.915, -1.091]     -49.609912
                   (-1.091, -0.505]       3.774281
                   (-0.505, -0.012]      34.161021
                   (-0.012, 0.575]       64.765615
                   (0.575, 3.402]       112.691732
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.