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# Copyright 2017-2020 Spotify AB 

# 

# Licensed under the Apache License, Version 2.0 (the "License"); 

# you may not use this file except in compliance with the License. 

# You may obtain a copy of the License at 

# 

# http://www.apache.org/licenses/LICENSE-2.0 

# 

# Unless required by applicable law or agreed to in writing, software 

# distributed under the License is distributed on an "AS IS" BASIS, 

# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 

# See the License for the specific language governing permissions and 

# limitations under the License. 

 

from pandas import DataFrame, Series 

import numpy as np 

import scipy.stats as st 

from statsmodels.stats.proportion import ( 

proportions_chisquare, proportion_confint, confint_proportions_2indep) 

from statsmodels.stats.weightstats import ( 

_zstat_generic, _zconfint_generic, _tstat_generic, _tconfint_generic) 

from typing import (Union, Iterable, List, Tuple, Dict) 

from abc import abstractmethod 

 

from ..abstract_base_classes.confidence_computer_abc import \ 

ConfidenceComputerABC 

from .sequential_bound_solver import bounds 

from ..constants import (POINT_ESTIMATE, VARIANCE, CI_LOWER, CI_UPPER, 

DIFFERENCE, P_VALUE, SFX1, SFX2, STD_ERR, ALPHA, 

ADJUSTED_ALPHA, ADJUSTED_P, ADJUSTED_LOWER, ADJUSTED_UPPER, 

NULL_HYPOTHESIS, NIM, PREFERENCE, TWO_SIDED, 

PREFERENCE_DICT, NIM_TYPE, BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED) 

from ..confidence_utils import (get_remaning_groups, validate_levels, 

level2str, listify, get_all_group_columns, 

power_calculation, validate_nims, signed_nims) 

 

 

def sequential_bounds(t: np.array, alpha: float, sides: int): 

return bounds(t, alpha, rho=2, ztrun=8, sides=sides, max_nints=1000) 

 

 

class StatsmodelsComputer(ConfidenceComputerABC): 

 

def __init__(self, data_frame: DataFrame, numerator_column: str, 

numerator_sum_squares_column: str, denominator_column: str, 

categorical_group_columns: Union[str, Iterable], 

ordinal_group_column: str, interval_size: float, 

correction_method: str): 

 

self._df = data_frame 

self._numerator = numerator_column 

self._numerator_sumsq = numerator_sum_squares_column 

if self._numerator_sumsq is None or \ 

self._numerator_sumsq == self._numerator: 

if (data_frame[numerator_column] <= 

data_frame[denominator_column]).all(): 

# Treat as binomial data 

self._numerator_sumsq = self._numerator 

else: 

raise ValueError( 

f'numerator_sum_squares_column missing or same as ' 

f'numerator_column, but since {numerator_column} is not ' 

f'always smaller than {denominator_column} it can\'t be ' 

f'binomial data. Please check your data.') 

 

self._denominator = denominator_column 

self._categorical_group_columns = categorical_group_columns 

self._ordinal_group_column = ordinal_group_column 

self._interval_size = interval_size 

 

correction_methods = [BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED] 

if correction_method.lower() not in correction_methods: 

raise ValueError(f'Use one of the correction methods ' + 

f'in {correction_methods}') 

self._correction_method = correction_method 

 

self._all_group_columns = get_all_group_columns( 

self._categorical_group_columns, self._ordinal_group_column) 

self._sufficient = None 

 

def compute_summary(self) -> DataFrame: 

return self._sufficient_statistics[ 

self._all_group_columns + 

[self._numerator, self._denominator, 

POINT_ESTIMATE, CI_LOWER, CI_UPPER]] 

 

@property 

def _sufficient_statistics(self) -> DataFrame: 

if self._sufficient is None: 

self._sufficient = ( 

self._df 

.assign(**{POINT_ESTIMATE: self._point_estimate}) 

.assign(**{VARIANCE: self._variance}) 

.pipe(self._add_point_estimate_ci) 

) 

return self._sufficient 

 

def _point_estimate(self, df: DataFrame) -> Series: 

if (df[self._denominator] == 0).any(): 

raise ValueError('''Can't compute point estimate: 

denominator is 0''') 

return df[self._numerator] / df[self._denominator] 

 

def compute_difference(self, 

level_1: Union[str, Iterable], 

level_2: Union[str, Iterable], 

absolute: bool, 

groupby: str, 

nims: NIM_TYPE, 

final_expected_sample_size: float 

) -> DataFrame: 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

difference_df = self._compute_differences(level_columns, 

level_1, 

[level_2], 

absolute, 

groupby, 

level_as_reference=True, 

nims=nims, 

final_expected_sample_size=final_expected_sample_size) 

return difference_df[listify(groupby) + 

['level_1', 'level_2', 'absolute_difference', 

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P] + 

([NIM, NULL_HYPOTHESIS, PREFERENCE] 

if nims is not None else [])] 

 

def compute_multiple_difference(self, 

level: Union[str, Iterable], 

absolute: bool, 

groupby: Union[str, Iterable], 

level_as_reference: bool, 

nims: NIM_TYPE, 

final_expected_sample_size: float 

) -> DataFrame: 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

other_levels = [other for other in self._sufficient_statistics 

.groupby(level_columns).groups.keys() if other != level] 

difference_df = self._compute_differences(level_columns, 

level, 

other_levels, 

absolute, 

groupby, 

level_as_reference, 

nims, 

final_expected_sample_size) 

return difference_df[listify(groupby) + 

['level_1', 'level_2', 'absolute_difference', 

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P] + 

([NIM, NULL_HYPOTHESIS, PREFERENCE] 

if nims is not None else [])] 

 

def _compute_differences(self, 

level_columns: Iterable, 

level: Union[str, Iterable], 

other_levels: Iterable, 

absolute: bool, 

groupby: Union[str, Iterable], 

level_as_reference: bool, 

nims: NIM_TYPE, 

final_expected_sample_size: float): 

groupby = listify(groupby) 

validate_levels(self._sufficient_statistics, 

level_columns, 

[level] + other_levels) 

validate_nims(self._sufficient_statistics, groupby, nims) 

levels = [(level2str(level), level2str(other)) 

if level_as_reference 

else (level2str(other), level2str(level)) 

for other in other_levels] 

str2level = {level2str(lv): lv for lv in [level] + other_levels} 

return ( 

self._sufficient_statistics 

.assign(level=self._sufficient_statistics[level_columns] 

.agg(level2str, axis='columns')) 

.pipe(lambda df: df if groupby == [] else df.set_index(groupby)) 

.pipe(self._create_comparison_df, 

groups_to_compare=levels, 

absolute=absolute, 

nims=nims, 

final_expected_sample_size=final_expected_sample_size) 

.assign(level_1=lambda df: 

df['level_1'].map(lambda s: str2level[s])) 

.assign(level_2=lambda df: 

df['level_2'].map(lambda s: str2level[s])) 

.reset_index() 

.sort_values(by=groupby + ['level_1', 'level_2']) 

) 

 

def _create_comparison_df(self, 

df: DataFrame, 

groups_to_compare: List[Tuple[str, str]], 

absolute: bool, 

nims: NIM_TYPE, 

final_expected_sample_size: float 

) -> DataFrame: 

 

def join(df: DataFrame) -> DataFrame: 

has_index = not all(idx is None for idx in df.index.names) 

if has_index: 

# self-join on index (the index will typically model the date, 

# i.e., rows with the same date are joined) 

return df.merge(df, 

left_index=True, 

right_index=True, 

suffixes=(SFX1, SFX2)) 

else: 

# join on dummy column, i.e. conduct a cross join 

return ( 

df.assign(dummy_join_column=1) 

.merge(right=df.assign(dummy_join_column=1), 

on='dummy_join_column', 

suffixes=(SFX1, SFX2)) 

.drop(columns='dummy_join_column') 

) 

 

comparison_df = ( 

df.pipe(join) 

.query(f'level_1 in {[l1 for l1,l2 in groups_to_compare]} and ' + 

f'level_2 in {[l2 for l1,l2 in groups_to_compare]}') 

.assign(**{DIFFERENCE: lambda df: df[POINT_ESTIMATE + SFX2] - 

df[POINT_ESTIMATE + SFX1]}) 

.assign(**{STD_ERR: self._std_err}) 

.assign(**{NIM: lambda df: self._nims_2_series(df, nims)[NIM]}) 

.assign(**{NULL_HYPOTHESIS: lambda df: 

self._nims_2_series(df, nims)[NULL_HYPOTHESIS]}) 

.assign(**{PREFERENCE: lambda df: 

self._nims_2_series(df, nims)[PREFERENCE]}) 

.pipe(self._add_p_value_and_ci, final_expected_sample_size=final_expected_sample_size) 

.pipe(self._adjust_if_absolute, absolute=absolute) 

.assign(**{PREFERENCE: lambda df: 

df[PREFERENCE].map(PREFERENCE_DICT)}) 

) 

return comparison_df 

 

@staticmethod 

def _adjust_if_absolute(df: DataFrame, absolute: bool) -> DataFrame: 

if absolute: 

return df.assign(absolute_difference=absolute) 

else: 

return ( 

df.assign(absolute_difference=absolute) 

.assign(**{DIFFERENCE: 

df[DIFFERENCE] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{CI_LOWER: 

df[CI_LOWER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{CI_UPPER: 

df[CI_UPPER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{ADJUSTED_LOWER: 

df[ADJUSTED_LOWER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{ADJUSTED_UPPER: 

df[ADJUSTED_UPPER] / df[POINT_ESTIMATE + SFX1]}) 

.assign(**{NULL_HYPOTHESIS: 

df[NULL_HYPOTHESIS] / df[POINT_ESTIMATE + SFX1]}) 

) 

 

def _nims_2_series(self, 

df: DataFrame, 

nims: NIM_TYPE 

) -> Union[DataFrame, Dict[float, str]]: 

 

sgnd_nims = signed_nims(nims) 

if nims is None or type(nims) is tuple: 

return {NIM: sgnd_nims[0], 

NULL_HYPOTHESIS: df[POINT_ESTIMATE + SFX1]*sgnd_nims[1], 

PREFERENCE: np.repeat(sgnd_nims[2], len(df))} 

else: 

return ( 

DataFrame(index=df.index, 

columns=[NIM, NULL_HYPOTHESIS, PREFERENCE], 

data=list(df.index.to_series().map(sgnd_nims))) 

.assign(**{NULL_HYPOTHESIS: lambda d: 

d[NULL_HYPOTHESIS]*df[POINT_ESTIMATE + SFX1]}) 

) 

 

def _std_err(self, df: DataFrame) -> Series: 

return np.sqrt(df[VARIANCE + SFX1] / df[self._denominator + SFX1] + 

df[VARIANCE + SFX2] / df[self._denominator + SFX2]) 

 

def _add_p_value_and_ci(self, df: DataFrame, final_expected_sample_size: float) -> DataFrame: 

df[ALPHA] = 1 - self._interval_size 

 

if(final_expected_sample_size is None): 

df[ADJUSTED_ALPHA] = (1-self._interval_size)/len(df) 

else: 

df[ADJUSTED_ALPHA] = self._compute_sequential_adjusted_alpha(df, final_expected_sample_size) 

 

ci = df.apply(self._ci, axis=1, alpha_column=ALPHA) 

ci_df = DataFrame(index=ci.index, 

columns=[CI_LOWER, CI_UPPER], 

data=list(ci.values)) 

adjusted_ci = df.apply(self._ci, axis=1, alpha_column=ADJUSTED_ALPHA) 

adjusted_ci_df = DataFrame(index=adjusted_ci.index, 

columns=[ADJUSTED_LOWER, ADJUSTED_UPPER], 

data=list(adjusted_ci.values)) 

 

return ( 

df.assign(**{P_VALUE: df.apply(self._p_value, axis=1)}) 

.assign(**{ADJUSTED_P: lambda df: 

df[P_VALUE].map(lambda p: min(p * len(df), 1))}) 

.assign(**{CI_LOWER: ci_df[CI_LOWER]}) 

.assign(**{CI_UPPER: ci_df[CI_UPPER]}) 

.assign(**{ADJUSTED_LOWER: adjusted_ci_df[ADJUSTED_LOWER]}) 

.assign(**{ADJUSTED_UPPER: adjusted_ci_df[ADJUSTED_UPPER]}) 

) 

 

def _compute_sequential_adjusted_alpha(self, df, final_expected_sample_size): 

sample_size_by_ordinal = ( 

df[self._denominator + SFX1].groupby(self._ordinal_group_column).sum() + 

df[self._denominator + SFX2].groupby(self._ordinal_group_column).sum() 

) 

final_expected_sample_size = max(final_expected_sample_size, sample_size_by_ordinal.max()) 

sample_size_proportions = sample_size_by_ordinal / final_expected_sample_size 

 

def get_num_comparisons(df): 

if self._correction_method == BONFERRONI: 

return len(df) 

elif self._correction_method == BONFERRONI_ONLY_COUNT_TWOSIDED: 

return max(1, len(df.query(f'{PREFERENCE} == "{TWO_SIDED}"'))) 

else: 

raise ValueError("Unsupported correction method") 

 

alpha = (1 - self._interval_size) / (get_num_comparisons(df) / len(sample_size_proportions)) 

 

z_crit_one_sided = ( 

sequential_bounds( 

t=sample_size_proportions.values, alpha=alpha, sides=1 

).df.set_index(sample_size_proportions.index)['zb'] 

) if not (df[PREFERENCE] == TWO_SIDED).all() else None 

 

z_crit_two_sided = ( 

sequential_bounds( 

t=sample_size_proportions.values, alpha=alpha, sides=2 

).df.set_index(sample_size_proportions.index)['zb'] 

) if not (df[PREFERENCE] != TWO_SIDED).all() else None 

 

def z_crit(row): 

has_multi_index = len(df.index.names) > 1 

ordinal = row.name[df.index.names.index(self._ordinal_group_column)] if has_multi_index else row.name 

return z_crit_two_sided.loc[ordinal] if row[PREFERENCE] == TWO_SIDED else z_crit_one_sided.loc[ordinal] 

 

def alpha_from_z_crit(row): 

return 2 * (1 - st.norm.cdf(z_crit(row))) if row[PREFERENCE] == TWO_SIDED else 1 - st.norm.cdf(z_crit(row)) 

 

return df.apply(alpha_from_z_crit, axis=1) 

 

def achieved_power(self, level_1, level_2, mde, alpha, groupby): 

"""Calculated the achieved power of test of differences between 

level 1 and level 2 given a targeted MDE. 

 

Args: 

level_1 (str, tuple of str): Name of first level. 

level_2 (str, tuple of str): Name of second level. 

mde (float): Absolute minimal detectable effect size. 

alpha (float): Type I error rate, cutoff value for determining 

statistical significance. 

groupby (str): Name of column. 

If specified, will return the difference for each level 

of the grouped dimension. 

 

Returns: 

Pandas DataFrame with the following columns: 

- level_1: Name of level 1. 

- level_2: Name of level 2. 

- power: 1 - B, where B is the likelihood of a Type II (false 

negative) error. 

 

""" 

groupby = listify(groupby) 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

return ( 

self._compute_differences(level_columns, 

level_1, 

[level_2], 

True, 

groupby, 

level_as_reference=True, 

nims=None, # TODO: IS this right? 

final_expected_sample_size=None) # TODO: IS this right? 

.pipe(lambda df: df if groupby == [] else df.set_index(groupby)) 

.pipe(self._achieved_power, mde=mde, alpha=alpha) 

) 

 

@staticmethod 

def _variance(self, df: DataFrame) -> Series: 

pass 

 

@abstractmethod 

def _add_point_estimate_ci(self, df: DataFrame) -> DataFrame: 

pass 

 

@abstractmethod 

def _p_value(self, row) -> float: 

pass 

 

@abstractmethod 

def _ci(self, row, alpha_column: str) -> Tuple[float, float]: 

pass 

 

@abstractmethod 

def _achieved_power(self, 

df: DataFrame, 

mde: float, 

alpha: float) -> DataFrame: 

pass 

 

 

class ChiSquaredComputer(StatsmodelsComputer): 

def _variance(self, df: DataFrame) -> Series: 

variance = df[POINT_ESTIMATE] * (1 - df[POINT_ESTIMATE]) 

if (variance < 0).any(): 

raise ValueError('Computed variance is negative. ' 

'Please check your inputs.') 

return variance 

 

def _add_point_estimate_ci(self, df: DataFrame): 

df[CI_LOWER], df[CI_UPPER] = proportion_confint( 

count=df[self._numerator], 

nobs=df[self._denominator], 

alpha=1-self._interval_size, 

) 

return df 

 

def _p_value(self, row): 

_, p_value, _ = ( 

proportions_chisquare(count=[row[self._numerator + SFX1], 

row[self._numerator + SFX2]], 

nobs=[row[self._denominator + SFX1], 

row[self._denominator + SFX2]]) 

) 

return p_value 

 

def _ci(self, row, alpha_column: str) -> Tuple[float, float]: 

return confint_proportions_2indep( 

count1=row[self._numerator + SFX2], 

nobs1=row[self._denominator + SFX2], 

count2=row[self._numerator + SFX1], 

nobs2=row[self._denominator + SFX1], 

alpha=row[alpha_column], 

compare='diff', 

method='wald' 

) 

 

def _achieved_power(self, 

df: DataFrame, 

mde: float, 

alpha: float) -> DataFrame: 

s1, s2 = df[self._numerator + SFX1], df[self._numerator + SFX2] 

n1, n2 = df[self._denominator + SFX1], df[self._denominator + SFX2] 

 

pooled_prop = (s1 + s2) / (n1 + n2) 

var_pooled = pooled_prop * (1 - pooled_prop) 

 

power = power_calculation(mde, var_pooled, alpha, n1, n2) 

 

return ( 

df.assign(achieved_power=power) 

.loc[:, ['level_1', 'level_2', 'achieved_power']] 

.reset_index() 

) 

 

 

class TTestComputer(StatsmodelsComputer): 

def _variance(self, df: DataFrame) -> Series: 

variance = ( 

df[self._numerator_sumsq] / df[self._denominator] - 

df[POINT_ESTIMATE] ** 2) 

if (variance < 0).any(): 

raise ValueError('Computed variance is negative. ' 

'Please check your inputs.') 

return variance 

 

def _add_point_estimate_ci(self, df: DataFrame): 

df[CI_LOWER], df[CI_UPPER] = _tconfint_generic( 

mean=df[POINT_ESTIMATE], 

std_mean=np.sqrt(df[VARIANCE] / df[self._denominator]), 

dof=df[self._denominator] - 1, 

alpha=1-self._interval_size, 

alternative=TWO_SIDED 

) 

return df 

 

def _dof(self, row): 

v1, v2 = row[VARIANCE + SFX1], row[VARIANCE + SFX2] 

n1, n2 = row[self._denominator + SFX1], row[self._denominator + SFX2] 

return ((v1 / n1 + v2 / n2) ** 2 / 

((v1 / n1) ** 2 / (n1 - 1) + 

(v2 / n2) ** 2 / (n2 - 1))) 

 

def _p_value(self, row) -> float: 

_, p_value = _tstat_generic(value1=row[POINT_ESTIMATE + SFX2], 

value2=row[POINT_ESTIMATE + SFX1], 

std_diff=row[STD_ERR], 

dof=self._dof(row), 

alternative=row[PREFERENCE], 

diff=row[NULL_HYPOTHESIS]) 

return p_value 

 

def _ci(self, row, alpha_column: str) -> Tuple[float, float]: 

return _tconfint_generic( 

mean=row[DIFFERENCE], 

std_mean=row[STD_ERR], 

dof=self._dof(row), 

alpha=row[alpha_column], 

alternative=row[PREFERENCE]) 

 

def _achieved_power(self, 

df: DataFrame, 

mde: float, 

alpha: float) -> DataFrame: 

v1, v2 = df[VARIANCE + SFX1], df[VARIANCE + SFX2] 

n1, n2 = df[self._denominator + SFX1], df[self._denominator + SFX2] 

 

var_pooled = ((n1 - 1) * v1 + (n2 - 1) * v2) / (n1 + n2 - 2) 

 

power = power_calculation(mde, var_pooled, alpha, n1, n2) 

 

return ( 

df.assign(achieved_power=power) 

.loc[:, ['level_1', 'level_2', 'achieved_power']] 

.reset_index() 

) 

 

 

class ZTestComputer(StatsmodelsComputer): 

def _variance(self, df: DataFrame) -> Series: 

variance = ( 

df[self._numerator_sumsq] / df[self._denominator] - 

df[POINT_ESTIMATE] ** 2) 

if (variance < 0).any(): 

raise ValueError('Computed variance is negative. ' 

'Please check your inputs.') 

return variance 

 

def _add_point_estimate_ci(self, df: DataFrame): 

df[CI_LOWER], df[CI_UPPER] = _zconfint_generic( 

mean=df[POINT_ESTIMATE], 

std_mean=np.sqrt(df[VARIANCE] / df[self._denominator]), 

alpha=1-self._interval_size, 

alternative=TWO_SIDED 

) 

return df 

 

def _p_value(self, row) -> float: 

_, p_value = _zstat_generic(value1=row[POINT_ESTIMATE + SFX2], 

value2=row[POINT_ESTIMATE + SFX1], 

std_diff=row[STD_ERR], 

alternative=row[PREFERENCE], 

diff=row[NULL_HYPOTHESIS]) 

return p_value 

 

def _ci(self, row, alpha_column: str) -> Tuple[float, float]: 

return _zconfint_generic( 

mean=row[DIFFERENCE], 

std_mean=row[STD_ERR], 

alpha=row[alpha_column], 

alternative=row[PREFERENCE]) 

 

def _achieved_power(self, 

df: DataFrame, 

mde: float, 

alpha: float) -> DataFrame: 

v1, v2 = df[VARIANCE + SFX1], df[VARIANCE + SFX2] 

n1, n2 = df[self._denominator + SFX1], df[self._denominator + SFX2] 

 

var_pooled = ((n1 - 1) * v1 + (n2 - 1) * v2) / (n1 + n2 - 2) 

 

power = power_calculation(mde, var_pooled, alpha, n1, n2) 

 

return ( 

df.assign(achieved_power=power) 

.loc[:, ['level_1', 'level_2', 'achieved_power']] 

.reset_index() 

)