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	-0.614298	-1.186804	-1.224096	-2.465764	0	0	-11.985166	-3.117210	-365.334500
1	-1.815659	-0.593030	-0.942089	-1.978565	3	0	-3.185456	10.173167	408.634756
2	0.149613	-1.995628	-0.247485	-1.167555	1	0	-0.777541	2.817673	24.801607
3	-0.608667	-1.211001	1.019357	-0.172742	1	3	12.525051	20.015384	-1002.628091
4	-0.070603	-2.974622	0.061755	0.799555	1	1	8.808388	8.910479	-265.978142

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

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

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

## Estimate
Mean value: -66.74442465406742

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

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

## Estimate
Mean value: -66.74442465406742
### Conditional Estimates
__categorical__X1  __categorical__X0
(-4.729, -1.777]   (-4.679, -1.53]     -220.871781
                   (-1.53, -0.956]     -150.155692
                   (-0.956, -0.447]    -109.691028
                   (-0.447, 0.133]      -65.408004
                   (0.133, 3.604]         2.041486
(-1.777, -1.193]   (-4.679, -1.53]     -189.994985
                   (-1.53, -0.956]     -123.059891
                   (-0.956, -0.447]     -81.895146
                   (-0.447, 0.133]      -40.701964
                   (0.133, 3.604]        27.022741
(-1.193, -0.7]     (-4.679, -1.53]     -175.043669
                   (-1.53, -0.956]     -107.080577
                   (-0.956, -0.447]     -66.362576
                   (-0.447, 0.133]      -24.914318
                   (0.133, 3.604]        41.026608
(-0.7, -0.0978]    (-4.679, -1.53]     -159.866871
                   (-1.53, -0.956]      -93.306996
                   (-0.956, -0.447]     -50.013717
                   (-0.447, 0.133]      -10.095979
                   (0.133, 3.604]        56.802998
(-0.0978, 3.745]   (-4.679, -1.53]     -135.286454
                   (-1.53, -0.956]      -64.496616
                   (-0.956, -0.447]     -24.495949
                   (-0.447, 0.133]       14.385220
                   (0.133, 3.604]        82.289652
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://microsoft.github.io/dowhy/example_notebooks/dowhy-conditional-treatment-effects.html

Propensity-based methods do not support multiple treatments currently.