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	-0.610485	-0.361963	0.454827	1.298354	0	1	8.448088	6.745871	41.409778
1	-0.382653	-0.207038	0.248333	-1.312163	2	0	1.797379	3.629792	40.533986
2	-2.544719	1.385429	0.878959	-0.897343	2	1	5.830589	8.248788	97.279320
3	-1.087287	-0.360749	-1.518408	-2.218330	2	0	-10.533392	-4.248372	-291.363295
4	-0.611511	-1.514700	1.302823	-0.726144	3	2	12.254958	15.266457	-704.334604

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

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

## Estimate
Mean value: 26.688772806024613

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

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

## Estimate
Mean value: 26.688772806024613
### Conditional Estimates
__categorical__X1  __categorical__X0
(-3.26, -0.246]    (-4.732, -1.371]    -40.208441
                   (-1.371, -0.795]    -25.115264
                   (-0.795, -0.303]    -13.251766
                   (-0.303, 0.281]      -4.487960
                   (0.281, 3.645]       13.324645
(-0.246, 0.352]    (-4.732, -1.371]    -16.542026
                   (-1.371, -0.795]      1.315167
                   (-0.795, -0.303]     11.386216
                   (-0.303, 0.281]      21.408088
                   (0.281, 3.645]       38.025938
(0.352, 0.862]     (-4.732, -1.371]      0.328755
                   (-1.371, -0.795]     16.467108
                   (-0.795, -0.303]     26.378072
                   (-0.303, 0.281]      36.580765
                   (0.281, 3.645]       53.877811
(0.862, 1.453]     (-4.732, -1.371]     15.220637
                   (-1.371, -0.795]     31.770172
                   (-0.795, -0.303]     42.066948
                   (-0.303, 0.281]      52.743631
                   (0.281, 3.645]       69.495885
(1.453, 4.515]     (-4.732, -1.371]     41.171839
                   (-1.371, -0.795]     57.430537
                   (-0.795, -0.303]     67.502442
                   (-0.303, 0.281]      76.439040
                   (0.281, 3.645]       93.678987
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.