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	-0.257775	-1.816821	-0.677777	-0.192001	2	1	6.428839	6.021733	13.954816
1	-1.988337	0.075061	2.273270	0.394716	0	3	3.158980	24.866780	-271.960235
2	-1.408438	0.344126	1.738955	-0.559022	2	2	9.934381	19.971147	-638.621666
3	-0.992839	-1.070089	-0.718630	-0.987752	3	1	7.781446	4.494957	-44.571483
4	-1.335100	0.422100	1.008882	0.087580	1	2	5.762307	15.015311	-166.633190

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

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

## Estimate
Mean value: -54.18984219940326

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

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

## Estimate
Mean value: -54.18984219940326
### Conditional Estimates
__categorical__X1  __categorical__X0
(-4.567, -1.725]   (-4.399, -1.75]     -151.096277
                   (-1.75, -1.164]     -105.384299
                   (-1.164, -0.662]     -76.732256
                   (-0.662, -0.0572]    -47.937022
                   (-0.0572, 3.238]       1.314341
(-1.725, -1.147]   (-4.399, -1.75]     -138.476042
                   (-1.75, -1.164]      -91.807058
                   (-1.164, -0.662]     -62.519469
                   (-0.662, -0.0572]    -33.528966
                   (-0.0572, 3.238]      14.827062
(-1.147, -0.637]   (-4.399, -1.75]     -128.769920
                   (-1.75, -1.164]      -83.709891
                   (-1.164, -0.662]     -54.501820
                   (-0.662, -0.0572]    -25.566340
                   (-0.0572, 3.238]      22.731651
(-0.637, -0.0533]  (-4.399, -1.75]     -124.400697
                   (-1.75, -1.164]      -74.202575
                   (-1.164, -0.662]     -46.237349
                   (-0.662, -0.0572]    -16.780231
                   (-0.0572, 3.238]      32.365639
(-0.0533, 2.942]   (-4.399, -1.75]     -109.477877
                   (-1.75, -1.164]      -62.530083
                   (-1.164, -0.662]     -32.608161
                   (-0.662, -0.0572]     -3.345889
                   (-0.0572, 3.238]      43.630256
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.