Estimating effect of multiple treatments

import dowhy
dowhy.enable_notebook_rendering()

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	-0.913387	1.350759	-1.741192	-1.197867	3	2	6.281050	8.143206	415.956375
1	-0.627155	2.262886	-0.941252	-0.021577	1	3	3.836674	8.691055	494.893179
2	-1.366484	0.777586	-2.617007	0.358667	3	1	0.848869	3.912431	46.309863
3	-0.735154	-0.160323	-1.723268	-0.726777	1	0	-0.537654	-2.018717	-36.205988
4	-0.466044	-0.428775	0.198858	1.204649	0	3	6.158671	10.895653	-44.393282

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

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

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

## Estimate
Mean value: 35.41641181173637

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

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

## Estimate
Mean value: 35.41641181173637
### Conditional Estimates
__categorical__X1   __categorical__X0
(-3.846, -0.617]    (-3.542, -0.882]     -95.322032
                    (-0.882, -0.305]     -73.417985
                    (-0.305, 0.218]      -56.003902
                    (0.218, 0.798]       -41.784637
                    (0.798, 3.663]       -15.013376
(-0.617, -0.00412]  (-3.542, -0.882]     -37.667395
                    (-0.882, -0.305]     -14.898568
                    (-0.305, 0.218]        0.154082
                    (0.218, 0.798]        15.500249
                    (0.798, 3.663]        38.931031
(-0.00412, 0.512]   (-3.542, -0.882]      -2.252417
                    (-0.882, -0.305]      20.823320
                    (-0.305, 0.218]       35.235357
                    (0.218, 0.798]        49.615928
                    (0.798, 3.663]        73.363719
(0.512, 1.1]        (-3.542, -0.882]      32.694632
                    (-0.882, -0.305]      55.084251
                    (-0.305, 0.218]       70.247163
                    (0.218, 0.798]        85.253466
                    (0.798, 3.663]       110.031058
(1.1, 3.878]        (-3.542, -0.882]      88.590825
                    (-0.882, -0.305]     113.278576
                    (-0.305, 0.218]      125.425530
                    (0.218, 0.798]       141.243135
                    (0.798, 3.663]       166.348320
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.