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	3.478355	0.950201	-1.283866	0.702492	2	2	15.825919	4.221690	969.126674
1	0.111915	0.533298	1.928152	0.362418	2	0	17.018736	10.067362	502.977712
2	1.028958	0.553118	3.040734	1.852888	0	2	24.175454	17.575311	2084.692456
3	0.761331	0.986196	1.466116	0.484399	0	1	13.621585	6.120504	534.611529
4	0.565970	-0.298851	1.782537	0.553373	1	3	25.190648	10.968219	673.748567

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

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

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

## Estimate
Mean value: 130.27662853752327

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

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

## Estimate
Mean value: 130.27662853752327
### Conditional Estimates
__categorical__X1  __categorical__X0
(-4.093, 0.0588]   (-3.53, 0.0899]        2.090685
                   (0.0899, 0.665]       51.194647
                   (0.665, 1.173]        78.741560
                   (1.173, 1.753]       107.293791
                   (1.753, 4.508]       155.951323
(0.0588, 0.64]     (-3.53, 0.0899]       33.311782
                   (0.0899, 0.665]       81.214917
                   (0.665, 1.173]       110.623183
                   (1.173, 1.753]       140.540786
                   (1.753, 4.508]       190.205985
(0.64, 1.162]      (-3.53, 0.0899]       51.899674
                   (0.0899, 0.665]      100.666380
                   (0.665, 1.173]       131.176068
                   (1.173, 1.753]       160.418091
                   (1.753, 4.508]       209.396845
(1.162, 1.749]     (-3.53, 0.0899]       70.789839
                   (0.0899, 0.665]      119.822565
                   (0.665, 1.173]       149.082664
                   (1.173, 1.753]       178.997122
                   (1.753, 4.508]       230.296951
(1.749, 4.594]     (-3.53, 0.0899]      102.942682
                   (0.0899, 0.665]      150.433502
                   (0.665, 1.173]       179.368204
                   (1.173, 1.753]       211.821964
                   (1.753, 4.508]       258.463569
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.