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	0.178007	-0.639310	-1.788712	0.246032	3	1	4.647042	3.825705	65.322247
1	1.792623	-1.013292	0.876567	-1.763037	0	2	0.107641	6.266805	70.627946
2	0.204256	-0.194886	1.185497	-2.261566	1	1	0.332344	8.690260	96.238062
3	1.508591	0.997241	-1.639269	-2.041966	2	2	-3.558085	-0.574165	-29.605238
4	-1.209755	-0.389969	-0.644132	-0.134412	2	1	6.137576	6.339628	79.985602

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

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

## Estimate
Mean value: 22.25845726793183

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

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

## Estimate
Mean value: 22.25845726793183
### Conditional Estimates
__categorical__X0  __categorical__X1
(-3.306, -0.28]    (-3.65, -0.846]     -14.213706
                   (-0.846, -0.269]      5.928376
                   (-0.269, 0.25]       18.385412
                   (0.25, 0.853]        31.043649
                   (0.853, 4.86]        51.529347
(-0.28, 0.302]     (-3.65, -0.846]     -13.082238
                   (-0.846, -0.269]      8.109030
                   (-0.269, 0.25]       20.594350
                   (0.25, 0.853]        33.728952
                   (0.853, 4.86]        53.943140
(0.302, 0.802]     (-3.65, -0.846]     -10.653578
                   (-0.846, -0.269]      9.353780
                   (-0.269, 0.25]       22.335409
                   (0.25, 0.853]        34.773520
                   (0.853, 4.86]        56.268985
(0.802, 1.379]     (-3.65, -0.846]      -9.280687
                   (-0.846, -0.269]     10.641964
                   (-0.269, 0.25]       23.494075
                   (0.25, 0.853]        36.585261
                   (0.853, 4.86]        56.801042
(1.379, 4.106]     (-3.65, -0.846]      -8.579829
                   (-0.846, -0.269]     13.522220
                   (-0.269, 0.25]       26.088410
                   (0.25, 0.853]        38.839871
                   (0.853, 4.86]        60.410755
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.