/
detect_paradox.py
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/
detect_paradox.py
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# detect simpson's paradox
import numpy as np
import pandas as pd
def aggregate_data(df, conversion_col, treatment_col, segment_col):
"""
takes table of individual level data and aggregates it for simpsons paradox detection.
conversion_col is 1 if success, 0 else.
ex:
pd.DataFrame([
['small', 'A', 1],
['small', 'B', 0],
['large', 'A', 1],
['small', 'A', 1],
['large', 'B', 0],
['large', 'B', 0],
], columns=['kidney_stone_size', 'treatment', 'recovery'])
"""
df_ = df[[conversion_col, treatment_col, segment_col]]
gb = df_.groupby([segment_col, treatment_col]).agg(
[np.sum, lambda x: len(x)])
gb.columns = [conversion_col, "total"]
return gb.reset_index()
def simpsons_paradox(df, conversion_col, total_col, treatment_col, segment_col):
"""
given a dataframe like:
pd.DataFrame([
['small', 'A', 81, 87],
['small', 'B', 234, 270],
['large', 'A', 192, 263],
['large', 'B', 55, 80],
], columns=['kidney_stone_size', 'treatment', 'recovery', 'total'])
will determine if simpsons paradox exists. Non Bayesian!
> simpsons_paradox( df, 'recovery', 'total', 'treatment', 'kidney_stone_size' )
"""
# find global optimal:
gbs = df.groupby(treatment_col).sum()
print "## Global rates: "
print (gbs[conversion_col] / gbs[total_col])
print
global_optimal = (gbs[conversion_col] / gbs[total_col]).argmax()
# check optimal via segments
df_ = df.set_index([segment_col, treatment_col])
rates = (df_[conversion_col] / df_[total_col]).unstack(-1)
print "## Local rates:"
print rates
print
# find the local optimals
local_optimals = rates.apply(lambda x: x.argmax(), 1)
if local_optimals.unique().shape[0] > 1:
print "## Simpsons paradox not detected."
print "## Segmented rates do not have a consistent optimal choice"
print "## Local optimals:"
print local_optimals
print "## Global optimal: ", global_optimal
return False
local_optimal = local_optimals.unique()[0]
print "## Global optimal: ", global_optimal
print "## Local optimal: ", local_optimal
if local_optimal != global_optimal:
print "## Simpsons Paradox detected."
return True
else:
print "## Simpsons paradox not detected."
return False
if __name__ == "__main__":
# create some data, indentical to the data at
# http://en.wikipedia.org/wiki/Simpsons_paradox
d = []
d += ([('A', 'small', 1)] * 81)
d += ([('A', 'small', 0)] * (87 - 81))
d += ([('B', 'small', 0)] * (270 - 234))
d += ([('B', 'small', 1)] * (234))
d += ([('B', 'large', 1)] * (55))
d += ([('B', 'large', 0)] * (80 - 55))
d += ([('A', 'large', 0)] * (263 - 192))
d += ([('A', 'large', 1)] * (192))
df = pd.DataFrame(
d, columns=['treatment', 'kidney_stone_size', 'recovery'])
gb = aggregate_data(df, 'recovery', 'treatment', 'kidney_stone_size')
simpsons_paradox(gb, 'recovery', 'total', 'treatment', 'kidney_stone_size')