in causalml/optimize/pns.py [0:0]
def get_pns_bounds(data_exp, data_obs, T, Y, type="PNS"):
"""
Args
----
data_exp : DataFrame
Data from an experiment.
data_obs : DataFrame
Data from an observational study
T : str
Name of the binary treatment indicator
y : str
Name of the binary outcome indicator
'type' : str
Type of probability of causation desired. Acceptable args are:
* 'PNS': Probability of necessary and sufficient causation
* 'PS': Probability of sufficient causation
* 'PN': Probability of necessary causation
Notes
-----
Based on Equation (24) in Tian and Pearl: https://ftp.cs.ucla.edu/pub/stat_ser/r271-A.pdf
To capture the counterfactual notation, we use `1' and `0' to indicate the actual and
counterfactual values of a variable, respectively, and we use `do' to indicate the effect
of an intervention.
The experimental and observational data are either assumed to come to the same population,
or from random samples of the population. If the data are from a sample, the bounds may
be incorrectly calculated because the relevant quantities in the Tian-Pearl equations are
defined e.g. as P(YifT), not P(YifT \mid S) where S corresponds to sample selection.
Bareinboim and Pearl (https://www.pnas.org/doi/10.1073/pnas.1510507113) discuss conditions
under which P(YifT) can be recovered from P(YifT \mid S).
"""
# Probabilities calculated from observational data
Y1 = data_obs[Y].mean()
T1Y0 = (
data_obs.loc[(data_obs[T] == 1) & (data_obs[Y] == 0)].shape[0]
/ data_obs.shape[0]
)
T1Y1 = (
data_obs.loc[(data_obs[T] == 1) & (data_obs[Y] == 1)].shape[0]
/ data_obs.shape[0]
)
T0Y0 = (
data_obs.loc[(data_obs[T] == 0) & (data_obs[Y] == 0)].shape[0]
/ data_obs.shape[0]
)
T0Y1 = (
data_obs.loc[(data_obs[T] == 0) & (data_obs[Y] == 1)].shape[0]
/ data_obs.shape[0]
)
# Probabilities calculated from experimental data
Y1doT1 = data_exp.loc[data_exp[T] == 1, Y].mean()
Y1doT0 = data_exp.loc[data_exp[T] == 0, Y].mean()
Y0doT0 = 1 - Y1doT0
if type == "PNS":
lb_args = [0, Y1doT1 - Y1doT0, Y1 - Y1doT0, Y1doT1 - Y1]
ub_args = [Y1doT1, Y0doT0, T1Y1 + T0Y0, Y1doT1 - Y1doT0 + T1Y0 + T0Y1]
if type == "PN":
lb_args = [0, (Y1 - Y1doT0) / T1Y1]
ub_args = [1, (Y0doT0 - T0Y0) / T1Y1]
if type == "PS":
lb_args = [0, (Y1doT1 - Y1) / T0Y0]
ub_args = [1, (Y1doT1 - T1Y1) / T0Y0]
lower_bound = max(lb_args)
upper_bound = min(ub_args)
return lower_bound, upper_bound