Estimating effect of multiple treatments

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	-0.782955	-0.117877	0.556503	0.576597	0	2	10.075403	5.888747	2.584256
1	0.533871	0.225779	1.091080	0.106325	2	2	10.368336	10.836949	496.136374
2	0.719629	0.823192	-0.619869	0.614200	1	1	4.088105	7.815383	300.441897
3	-0.596388	-0.462312	0.304888	0.076668	3	2	7.784805	14.458986	-184.907269
4	1.470431	1.013644	0.009036	-2.402029	2	3	1.394636	1.845187	55.330271

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

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

## Estimate
Mean value: 26.349570350104635

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

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

## Estimate
Mean value: 26.349570350104635
### Conditional Estimates
__categorical__X0  __categorical__X1
(-4.113, -0.663]   (-3.479, -0.833]     -97.708112
                   (-0.833, -0.255]     -52.276502
                   (-0.255, 0.251]      -22.606347
                   (0.251, 0.847]         7.788871
                   (0.847, 4.047]        54.294575
(-0.663, -0.0794]  (-3.479, -0.833]     -65.348499
                   (-0.833, -0.255]     -21.277903
                   (-0.255, 0.251]        7.985988
                   (0.251, 0.847]        35.896265
                   (0.847, 4.047]        83.248394
(-0.0794, 0.414]   (-3.479, -0.833]     -49.649198
                   (-0.833, -0.255]      -2.170874
                   (-0.255, 0.251]       26.187706
                   (0.251, 0.847]        55.797786
                   (0.847, 4.047]       100.403169
(0.414, 1.005]     (-3.479, -0.833]     -30.638770
                   (-0.833, -0.255]      15.790545
                   (-0.255, 0.251]       43.731940
                   (0.251, 0.847]        73.447815
                   (0.847, 4.047]       120.114812
(1.005, 4.298]     (-3.479, -0.833]      -1.009736
                   (-0.833, -0.255]      46.841476
                   (-0.255, 0.251]       75.184308
                   (0.251, 0.847]       103.445271
                   (0.847, 4.047]       151.322717
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.