Estimating effect of multiple treatments

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')

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	0.048780	-1.168705	0.542571	-0.745830	0	0	2.268239	3.145854	27.554411
1	-1.086124	1.009211	-0.788796	0.536774	2	1	4.404500	7.184804	57.884088
2	-0.312494	-0.582138	0.519299	-0.638889	0	3	10.489494	1.515061	74.968139
3	1.748224	-0.769179	0.278752	1.888858	3	0	11.828633	18.127881	1569.944097
4	0.692610	1.158256	0.601062	0.591958	1	0	6.631769	6.379249	431.997043

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: nonparametric-ate

### Estimand : 1
Estimand name: backdoor
Estimand expression:
    d
─────────(E[y|W3,W0,W1,W2])
d[v₀  v₁]
Estimand assumption 1, Unconfoundedness: If U→{v0,v1} and U→y then P(y|v0,v1,W3,W0,W1,W2,U) = P(y|v0,v1,W3,W0,W1,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: nonparametric-ate

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

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

## Estimate
Mean value: 27.598049182644683

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: nonparametric-ate

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

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

## Estimate
Mean value: 27.598049182644683
### Conditional Estimates
__categorical__X1  __categorical__X0
(-4.623, -1.514]   (-3.012, -0.311]    -115.443663
                   (-0.311, 0.273]      -65.270347
                   (0.273, 0.771]       -31.873678
                   (0.771, 1.368]         1.022828
                   (1.368, 5.019]        54.280508
(-1.514, -0.926]   (-3.012, -0.311]     -77.724619
                   (-0.311, 0.273]      -29.198328
                   (0.273, 0.771]         5.232500
                   (0.771, 1.368]        38.251000
                   (1.368, 5.019]        91.802134
(-0.926, -0.416]   (-3.012, -0.311]     -61.536709
                   (-0.311, 0.273]       -5.262257
                   (0.273, 0.771]        27.660328
                   (0.771, 1.368]        61.239789
                   (1.368, 5.019]       114.295588
(-0.416, 0.179]    (-3.012, -0.311]     -39.044539
                   (-0.311, 0.273]       16.329306
                   (0.273, 0.771]        49.838503
                   (0.771, 1.368]        82.778759
                   (1.368, 5.019]       137.403639
(0.179, 3.069]     (-3.012, -0.311]      -1.954634
                   (-0.311, 0.273]       54.155801
                   (0.273, 0.771]        86.890604
                   (0.771, 1.368]       121.662042
                   (1.368, 5.019]       174.116303
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.