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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 warnings import warn 

 

import spotify_confidence.analysis.frequentist.confidence_computers.chi_squared_computer 

from pandas import DataFrame, Series, concat 

import numpy as np 

from statsmodels.stats.multitest import multipletests 

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

from abc import abstractmethod 

 

from spotify_confidence.analysis.abstract_base_classes.confidence_computer_abc import \ 

ConfidenceComputerABC 

from spotify_confidence.analysis.frequentist.confidence_computers.chi_squared_computer import ChiSquaredComputer 

from spotify_confidence.analysis.frequentist.confidence_computers.t_test_computer import TTestComputer 

from spotify_confidence.analysis.frequentist.confidence_computers.z_test_computer import ZTestComputer 

from spotify_confidence.analysis.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, IS_SIGNIFICANT, 

NULL_HYPOTHESIS, NIM, PREFERENCE, PREFERENCE_TEST, TWO_SIDED, 

PREFERENCE_DICT, NIM_TYPE, BONFERRONI, CORRECTION_METHODS, 

HOLM, HOMMEL, SIMES_HOCHBERG, SIDAK, HOLM_SIDAK, FDR_BH, FDR_BY, FDR_TSBH, FDR_TSBKY, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, SPOT_1_FDR_TSBKY, 

BONFERRONI_ONLY_COUNT_TWOSIDED, BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1) 

from spotify_confidence.analysis.confidence_utils import (get_remaning_groups, validate_levels, 

level2str, listify, get_all_group_columns, 

add_nim_columns, 

validate_and_rename_nims, validate_and_rename_column) 

 

 

 

 

 

class GenericComputer(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, method_column: 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 

 

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._method_column = method_column 

 

self._all_group_columns = get_all_group_columns( 

self._categorical_group_columns, self._ordinal_group_column) 

self._sufficient = None 

 

self._computers = { 

'chi-squared': ChiSquaredComputer(numerator_column, numerator_sum_squares_column, 

denominator_column, ordinal_group_column, interval_size), 

't-test': TTestComputer(numerator_column, numerator_sum_squares_column, 

denominator_column, ordinal_group_column, interval_size), 

'z-test': ZTestComputer(numerator_column, numerator_sum_squares_column, 

denominator_column, ordinal_group_column, interval_size), 

} 

 

@property 

def _confidence_computers(self): 

return self._computers 

 

def compute_summary(self, verbose: bool) -> DataFrame: 

return ( 

self._sufficient_statistics if verbose else 

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 compute_difference(self, 

level_1: Union[str, Iterable], 

level_2: Union[str, Iterable], 

absolute: bool, 

groupby: Union[str, Iterable], 

nims: NIM_TYPE, 

final_expected_sample_size_column: str, 

verbose: bool) -> 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_column=final_expected_sample_size_column) 

return (difference_df if verbose else 

difference_df[listify(groupby) + 

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

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P, IS_SIGNIFICANT] + 

([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_column: str, 

verbose: bool) -> 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] 

levels = [(level, other) for other in other_levels] 

difference_df = self._compute_differences(level_columns, 

levels, 

absolute, 

groupby, 

level_as_reference, 

nims, 

final_expected_sample_size_column) 

return (difference_df if verbose else 

difference_df[listify(groupby) + 

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

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P, IS_SIGNIFICANT] + 

([NIM, NULL_HYPOTHESIS, PREFERENCE] 

if nims is not None else [])]) 

 

def compute_differences(self, 

levels: List[Tuple], 

absolute: bool, 

groupby: Union[str, Iterable], 

nims: NIM_TYPE, 

final_expected_sample_size_column: str, 

verbose: bool 

) -> DataFrame: 

level_columns = get_remaning_groups(self._all_group_columns, groupby) 

difference_df = self._compute_differences( 

level_columns, 

[levels] if type(levels) == tuple else levels, 

absolute, 

groupby, 

level_as_reference=True, 

nims=nims, 

final_expected_sample_size_column=final_expected_sample_size_column) 

return (difference_df if verbose else 

difference_df[listify(groupby) + 

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

DIFFERENCE, CI_LOWER, CI_UPPER, P_VALUE] + 

[ADJUSTED_LOWER, ADJUSTED_UPPER, ADJUSTED_P, IS_SIGNIFICANT] + 

([NIM, NULL_HYPOTHESIS, PREFERENCE] 

if nims is not None else [])]) 

 

def _compute_differences(self, 

level_columns: Iterable, 

levels: Union[str, Iterable], 

absolute: bool, 

groupby: Union[str, Iterable], 

level_as_reference: bool, 

nims: NIM_TYPE, 

final_expected_sample_size_column: str): 

if type(level_as_reference) is not bool: 

raise ValueError(f'level_is_reference must be either True or False, but is {level_as_reference}.') 

groupby = listify(groupby) 

unique_levels = set([l[0] for l in levels] + [l[1] for l in levels]) 

validate_levels(self._sufficient_statistics, 

level_columns, 

unique_levels) 

str2level = {level2str(lv): lv for lv in unique_levels} 

filtered_sufficient_statistics = concat( 

[self._sufficient_statistics.groupby(level_columns).get_group(group) for group in unique_levels]) 

levels = [(level2str(l[0]), level2str(l[1])) 

if level_as_reference 

else (level2str(l[1]), level2str(l[0])) 

for l in 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_column=final_expected_sample_size_column, 

filtered_sufficient_statistics=filtered_sufficient_statistics) 

.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_column: str, 

filtered_sufficient_statistics: DataFrame 

) -> 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(add_nim_columns, nims=nims) 

.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]}' + 

'and level_1 != level_2') 

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

df[POINT_ESTIMATE + SFX1]}) 

.assign(**{STD_ERR: self._std_err}) 

.pipe(validate_and_rename_nims) 

.pipe(validate_and_rename_column, final_expected_sample_size_column) 

.pipe(validate_and_rename_column, self._method_column) 

.pipe(self._add_p_value_and_ci, 

final_expected_sample_size_column=final_expected_sample_size_column, 

filtered_sufficient_statistics=filtered_sufficient_statistics) 

.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 _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_column: str, 

filtered_sufficient_statistics: DataFrame) -> DataFrame: 

 

def set_alpha_and_adjust_preference(df: DataFrame) -> DataFrame: 

alpha_0 = 1 - self._interval_size 

return ( 

df.assign(**{ALPHA: df.apply(lambda row: 2*alpha_0 if self._correction_method == SPOT_1 

and row[PREFERENCE] != TWO_SIDED 

else alpha_0, axis=1)}) 

.assign(**{PREFERENCE_TEST: df.apply(lambda row: TWO_SIDED if self._correction_method == SPOT_1 

else row[PREFERENCE], axis=1)}) 

) 

 

def _add_adjusted_p_and_is_significant(df: DataFrame) -> DataFrame: 

if(final_expected_sample_size_column is not None): 

if self._correction_method not in [BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED, 

BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1]: 

raise ValueError(f"{self._correction_method} not supported for sequential tests. Use one of" 

f"{BONFERRONI}, {BONFERRONI_ONLY_COUNT_TWOSIDED}, " 

f"{BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY}, {SPOT_1}") 

 

df[ADJUSTED_ALPHA] = self._compute_sequential_adjusted_alpha(df, 

final_expected_sample_size_column, 

filtered_sufficient_statistics) 

df[IS_SIGNIFICANT] = df[P_VALUE] < df[ADJUSTED_ALPHA] 

df[P_VALUE] = None 

df[ADJUSTED_P] = None 

elif self._correction_method in [HOLM, HOMMEL, SIMES_HOCHBERG, 

SIDAK, HOLM_SIDAK, FDR_BH, FDR_BY, FDR_TSBH, FDR_TSBKY, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, SPOT_1_FDR_TSBKY]: 

if self._correction_method.startswith('spot-'): 

correction_method = self._correction_method[7:] 

else: 

correction_method = self._correction_method 

 

groupby = ['level_1', 'level_2'] + [column for column in df.index.names if column is not None] 

df[ADJUSTED_ALPHA] = df[ALPHA] / self._get_num_comparisons(df, self._correction_method, groupby) 

is_significant, adjusted_p, _, _ = multipletests(pvals=df[P_VALUE], 

alpha=1 - self._interval_size, 

method=correction_method) 

df[ADJUSTED_P] = adjusted_p 

df[IS_SIGNIFICANT] = is_significant 

elif self._correction_method in [BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED, 

BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1]: 

groupby = ['level_1', 'level_2'] + [column for column in df.index.names if column is not None] 

n_comparisons = self._get_num_comparisons(df, self._correction_method, groupby) 

df[ADJUSTED_ALPHA] = df[ALPHA] / n_comparisons 

df[ADJUSTED_P] = df[P_VALUE].map(lambda p: min(p * n_comparisons, 1)) 

df[IS_SIGNIFICANT] = df[P_VALUE] < df[ADJUSTED_ALPHA] 

else: 

raise ValueError("Can't figure out which correction method to use :(") 

 

return df 

 

def _add_ci(df: DataFrame) -> DataFrame: 

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)) 

 

if self._correction_method in [HOLM, HOMMEL, SIMES_HOCHBERG, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG] \ 

and all(df[PREFERENCE_TEST] != TWO_SIDED): 

adjusted_ci = self._ci_for_multiple_comparison_methods( 

df, 

correction_method=self._correction_method, 

alpha=1 - self._interval_size, 

) 

elif self._correction_method in [BONFERRONI, BONFERRONI_ONLY_COUNT_TWOSIDED, 

BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, SPOT_1_FDR_TSBKY]: 

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

else: 

warn(f"Confidence intervals not supported for {self._correction_method}") 

adjusted_ci = Series(index=df.index, data=[(None, None) for i in range(len(df))]) 

 

adjusted_ci_df = DataFrame(index=adjusted_ci.index, 

columns=[ADJUSTED_LOWER, ADJUSTED_UPPER], 

data=list(adjusted_ci.values)) 

 

return ( 

df.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]}) 

) 

 

return ( 

df.pipe(set_alpha_and_adjust_preference) 

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

.pipe(_add_adjusted_p_and_is_significant) 

.pipe(_add_ci) 

) 

 

def _get_num_comparisons(self, df: DataFrame, correction_method: str, groupby: Iterable) -> int: 

if correction_method == BONFERRONI: 

return max(1, df.groupby(groupby).ngroups) 

elif correction_method == BONFERRONI_ONLY_COUNT_TWOSIDED: 

return max(df.query(f'{PREFERENCE_TEST} == "{TWO_SIDED}"').groupby(groupby).ngroups, 1) 

elif correction_method in [BONFERRONI_DO_NOT_COUNT_NON_INFERIORITY, SPOT_1, 

HOLM, HOMMEL, SIMES_HOCHBERG, 

SIDAK, HOLM_SIDAK, FDR_BH, FDR_BY, FDR_TSBH, FDR_TSBKY, 

SPOT_1_HOLM, SPOT_1_HOMMEL, SPOT_1_SIMES_HOCHBERG, 

SPOT_1_SIDAK, SPOT_1_HOLM_SIDAK, SPOT_1_FDR_BH, 

SPOT_1_FDR_BY, SPOT_1_FDR_TSBH, SPOT_1_FDR_TSBKY]: 

return max(1, df[df[NIM].isnull()].groupby(groupby).ngroups) 

else: 

raise ValueError(f"Unsupported correction method: {correction_method}.") 

 

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_column=None) # TODO: IS this right? 

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

.assign(achieved_power=lambda df: df.apply(self._achieved_power, mde=mde, alpha=alpha, axis=1)) 

)[['level_1', 'level_2', 'achieved_power']] 

 

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

return df.apply(lambda row: self._confidence_computers[row[self._method_column]]._variance(row), axis=1) 

 

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

return df.apply(lambda row: self._confidence_computers[row[self._method_column]]._add_point_estimate_ci(row), 

axis=1) 

 

def _p_value(self, row) -> float: 

return self._confidence_computers[row[self._method_column]]._p_value(row) 

 

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

return self._confidence_computers[row[self._method_column]]._ci(row, alpha_column=alpha_column) 

 

def _achieved_power(self, 

row: Series, 

mde: float, 

alpha: float) -> DataFrame: 

return self._confidence_computers[row[self._method_column]]._achieved_power(row, mde, alpha) 

 

def _compute_sequential_adjusted_alpha(self, 

df: DataFrame, 

final_expected_sample_size_column: str, 

filtered_sufficient_statistics: DataFrame) -> Series: 

return df.apply(lambda row: 

self._confidence_computers[row[self._method_column]]._compute_sequential_adjusted_alpha( 

row, final_expected_sample_size_column, filtered_sufficient_statistics), 

axis=1) 

# raise NotImplementedError("Sequential tests are only supported for ZTests") 

 

def _ci_for_multiple_comparison_methods( 

self, 

df: DataFrame, 

correction_method: str, 

alpha: float, 

w: float = 1.0, 

) -> Tuple[Union[Series, float], Union[Series, float]]: 

return df.apply(lambda row: 

self._confidence_computers[row[self._method_column]]._ci_for_multiple_comparison_methods( 

row, correction_method, alpha, w), 

axis=1) 

#raise NotImplementedError(f"{self._correction_method} is only supported for ZTests")