Estimating effect of multiple treatments

[1]:
import numpy as np
import pandas as pd
import logging

import dowhy
from dowhy import CausalModel
import dowhy.datasets

import econml
import warnings
warnings.filterwarnings('ignore')
[2]:
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()
[2]:
X0 X1 W0 W1 W2 W3 v0 v1 y
0 0.846388 0.783846 0.944644 -0.119919 3 1 6.684632 15.619628 679.274978
1 -0.382821 1.737644 -0.140717 1.156761 2 0 7.990008 10.652711 607.825673
2 0.150747 -0.409554 0.159065 1.227262 1 1 9.247153 12.982039 110.692336
3 0.662945 0.898566 -0.326534 0.329678 1 3 6.448918 16.419184 690.454111
4 0.326410 0.077312 0.238597 -0.058446 3 3 9.151193 19.622878 471.459850
[3]:
model = CausalModel(data=data["df"],
                    treatment=data["treatment_name"], outcome=data["outcome_name"],
                    graph=data["gml_graph"])
[4]:
model.view_model()
from IPython.display import Image, display
display(Image(filename="causal_model.png"))
../_images/example_notebooks_dowhy_multiple_treatments_4_0.png
[5]:
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,W0,W3,W2])
d[v₀  v₁]
Estimand assumption 1, Unconfoundedness: If U→{v0,v1} and U→y then P(y|v0,v1,W1,W0,W3,W2,U) = P(y|v0,v1,W1,W0,W3,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).

[6]:
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,W0,W3,W2])
d[v₀  v₁]
Estimand assumption 1, Unconfoundedness: If U→{v0,v1} and U→y then P(y|v0,v1,W1,W0,W3,W2,U) = P(y|v0,v1,W1,W0,W3,W2)

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

## Estimate
Mean value: 53.409694491477794

You can estimate conditional effects, based on effect modifiers.

[7]:
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,W0,W3,W2])
d[v₀  v₁]
Estimand assumption 1, Unconfoundedness: If U→{v0,v1} and U→y then P(y|v0,v1,W1,W0,W3,W2,U) = P(y|v0,v1,W1,W0,W3,W2)

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

## Estimate
Mean value: 53.409694491477794

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.