Estimating effect of multiple treatments

import dowhy
dowhy.enable_notebook_rendering()

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	-1.631834	-0.732712	-1.486485	-0.115370	0	0	-8.839621	-4.979303	-523.811632
1	-1.132617	0.715087	-1.309199	0.115198	3	2	8.987890	20.536670	-544.900202
2	1.251704	-0.438323	0.241551	-0.664516	0	0	-2.685975	-2.140839	-19.369511
3	-0.171360	0.979683	0.309194	0.977418	0	1	10.036483	7.047617	201.823558
4	1.112863	1.672066	1.695142	-0.429582	1	1	10.428849	12.888579	1214.562517

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

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

## Estimate
Mean value: 32.6551274218245

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

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

## Estimate
Mean value: 32.6551274218245
### Conditional Estimates
__categorical__X0  __categorical__X1
(-3.385, -0.862]   (-3.529, -0.329]    -125.149971
                   (-0.329, 0.273]     -106.592181
                   (0.273, 0.765]       -95.176969
                   (0.765, 1.363]       -83.803876
                   (1.363, 4.247]       -64.066238
(-0.862, -0.27]    (-3.529, -0.329]     -46.822087
                   (-0.329, 0.273]      -27.579335
                   (0.273, 0.765]       -17.297589
                   (0.765, 1.363]        -5.062335
                   (1.363, 4.247]        14.255666
(-0.27, 0.23]      (-3.529, -0.329]       2.640733
                   (-0.329, 0.273]       21.474724
                   (0.273, 0.765]        32.596247
                   (0.765, 1.363]        44.018360
                   (1.363, 4.247]        63.075617
(0.23, 0.808]      (-3.529, -0.329]      51.508618
                   (-0.329, 0.273]       70.768601
                   (0.273, 0.765]        80.177867
                   (0.765, 1.363]        92.897428
                   (1.363, 4.247]       111.034967
(0.808, 4.199]     (-3.529, -0.329]     134.206907
                   (-0.329, 0.273]      149.658092
                   (0.273, 0.765]       159.859578
                   (0.765, 1.363]       172.246050
                   (1.363, 4.247]       187.855341
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.