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	-1.407332	-0.056173	0.524682	0.735251	0	0	4.864141	5.273716	79.835212
1	-0.581832	-1.617002	0.804786	-0.065007	0	1	5.247939	5.010679	-61.788236
2	-0.958478	-0.847614	2.261130	0.798190	1	3	20.445784	24.276125	-1361.010758
3	-1.818551	-0.238508	-1.883856	0.881209	1	3	6.979215	2.579859	73.519319
4	-0.695539	-1.463729	0.008912	0.891629	3	2	18.415539	22.080640	-1976.234657

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

## Estimate
Mean value: -44.172959204905396

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

## Estimate
Mean value: -44.172959204905396
### Conditional Estimates
__categorical__X0              __categorical__X1
(-4.6450000000000005, -1.569]  (-4.336, -1.407]    -156.138500
                               (-1.407, -0.825]     -93.005413
                               (-0.825, -0.331]     -55.673786
                               (-0.331, 0.258]      -19.729158
                               (0.258, 3.309]        43.037638
(-1.569, -0.978]               (-4.336, -1.407]    -144.685377
                               (-1.407, -0.825]     -86.368464
                               (-0.825, -0.331]     -48.578420
                               (-0.331, 0.258]      -11.070802
                               (0.258, 3.309]        48.415747
(-0.978, -0.468]               (-4.336, -1.407]    -143.716956
                               (-1.407, -0.825]     -80.413600
                               (-0.825, -0.331]     -43.731527
                               (-0.331, 0.258]       -7.003184
                               (0.258, 3.309]        53.984016
(-0.468, 0.11]                 (-4.336, -1.407]    -136.701641
                               (-1.407, -0.825]     -75.036007
                               (-0.825, -0.331]     -39.548946
                               (-0.331, 0.258]       -1.861913
                               (0.258, 3.309]        53.733867
(0.11, 3.119]                  (-4.336, -1.407]    -129.153329
                               (-1.407, -0.825]     -67.579358
                               (-0.825, -0.331]     -31.259031
                               (-0.331, 0.258]        3.842395
                               (0.258, 3.309]        63.560552
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.