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	0.168032	-0.582027	-0.877777	0.580743	1	1	1.594449	6.249333	56.248186
1	1.135945	1.113098	1.651627	0.951515	3	3	19.642165	23.518580	4102.859143
2	0.189856	-0.548917	-3.208358	0.343652	2	1	-2.013081	11.659060	161.485673
3	1.197138	2.295597	-0.835399	0.970133	1	2	7.193234	13.023736	1570.680940
4	0.225148	0.284826	-0.180523	0.860278	1	1	4.144428	7.532836	187.331575

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

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

## Estimate
Mean value: 50.57316998951839

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

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

## Estimate
Mean value: 50.57316998951839
### Conditional Estimates
__categorical__X0  __categorical__X1
(-2.739, -0.134]   (-3.862, -0.646]     -93.486560
                   (-0.646, -0.0621]    -24.125216
                   (-0.0621, 0.456]      18.824671
                   (0.456, 1.051]        62.199724
                   (1.051, 3.554]       130.444222
(-0.134, 0.471]    (-3.862, -0.646]     -72.862080
                   (-0.646, -0.0621]     -4.793482
                   (-0.0621, 0.456]      38.837861
                   (0.456, 1.051]        81.778058
                   (1.051, 3.554]       152.108120
(0.471, 0.971]     (-3.862, -0.646]     -60.995027
                   (-0.646, -0.0621]      6.509509
                   (-0.0621, 0.456]      49.421424
                   (0.456, 1.051]        93.885081
                   (1.051, 3.554]       168.300456
(0.971, 1.563]     (-3.862, -0.646]     -51.037548
                   (-0.646, -0.0621]     18.556482
                   (-0.0621, 0.456]      62.254745
                   (0.456, 1.051]       105.613255
                   (1.051, 3.554]       174.771928
(1.563, 4.586]     (-3.862, -0.646]     -31.176964
                   (-0.646, -0.0621]     39.080134
                   (-0.0621, 0.456]      81.182838
                   (0.456, 1.051]       124.887844
                   (1.051, 3.554]       193.640084
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.