cluster_experiments

A Python library for end-to-end A/B testing workflows, featuring: - Experiment analysis and scorecards - Power analysis (simulation-based and normal approximation) - Variance reduction techniques (CUPED, CUPAC) - Support for complex experimental designs (cluster randomization, switchback experiments)

Key Features

1. Power Analysis

• Simulation-based: Run Monte Carlo simulations to estimate power
• Normal approximation: Fast power estimation using CLT
• Minimum Detectable Effect: Calculate required effect sizes
• Multiple designs: Support for:
• Simple randomization
• Variance reduction techniques in power analysis
• Cluster randomization
• Switchback experiments
• Dict config: Easy to configure power analysis with a dictionary

2. Experiment Analysis

• Analysis Plans: Define structured analysis plans
• Metrics:
• Simple metrics
• Ratio metrics
• Dimensions: Slice results by dimensions
• Statistical Methods:
• GEE
• Mixed Linear Models
• Clustered / regular OLS
• T-tests
• Synthetic Control
• Dict config: Easy to define analysis plans with a dictionary

3. Variance Reduction

• CUPED (Controlled-experiment Using Pre-Experiment Data):
• Use historical outcome data to reduce variance, choose any granularity
• Support for several covariates
• CUPAC (Control Using Predictors as Covariates):
• Use any scikit-learn compatible estimator to predict the outcome with pre-experiment data

Quick Start

Power Analysis Example

import numpy as np
import pandas as pd
from cluster_experiments import PowerAnalysis, NormalPowerAnalysis

# Create sample data
N = 1_000
df = pd.DataFrame({
    "target": np.random.normal(0, 1, size=N),
    "date": pd.to_datetime(
        np.random.randint(
            pd.Timestamp("2024-01-01").value,
            pd.Timestamp("2024-01-31").value,
            size=N,
        )
    ),
})

# Simulation-based power analysis with CUPED
config = {
    "analysis": "ols",
    "perturbator": "constant",
    "splitter": "non_clustered",
    "n_simulations": 50,
}
pw = PowerAnalysis.from_dict(config)
power = pw.power_analysis(df, average_effect=0.1)

# Normal approximation (faster)
npw = NormalPowerAnalysis.from_dict({
    "analysis": "ols",
    "splitter": "non_clustered",
    "n_simulations": 5,
    "time_col": "date",
})
power_normal = npw.power_analysis(df, average_effect=0.1)
power_line_normal = npw.power_line(df, average_effects=[0.1, 0.2, 0.3])


# MDE calculation
mde = npw.mde(df, power=0.8)

# MDE line with length
mde_timeline = npw.mde_time_line(
    df,
    powers=[0.8],
    experiment_length=[7, 14, 21]
)

print(power, power_line_normal, power_normal, mde, mde_timeline)

Experiment Analysis Example

import numpy as np
import pandas as pd
from cluster_experiments import AnalysisPlan, SimpleMetric, Variant, Dimension

N = 1_000
experiment_data = pd.DataFrame({
    "order_value": np.random.normal(100, 10, size=N),
    "delivery_time": np.random.normal(10, 1, size=N),
    "experiment_group": np.random.choice(["control", "treatment"], size=N),
    "city": np.random.choice(["NYC", "LA"], size=N),
    "customer_id": np.random.randint(1, 100, size=N),
    "customer_age": np.random.randint(20, 60, size=N),
})

# Define metrics
aov = SimpleMetric(alias="AOV", name="order_value")
delivery_time = SimpleMetric(alias="Delivery Time", name="delivery_time")

# Define variants and dimensions
variants = [
    Variant("control", is_control=True),
    Variant("treatment", is_control=False),
]
city_dimension = Dimension(name="city", values=["NYC", "LA"])

# Create analysis plan
plan = AnalysisPlan.from_metrics(
    metrics=[aov, delivery_time],
    variants=variants,
    variant_col="experiment_group",
    dimensions=[city_dimension],
    analysis_type="clustered_ols",
    analysis_config={
        "cluster_cols": ["customer_id"],
    },
)

# Run analysis
results = plan.analyze(experiment_data)
print(results.to_dataframe())

Variance Reduction Example

import numpy as np
import pandas as pd
from cluster_experiments import (
    AnalysisPlan,
    SimpleMetric,
    Variant,
    Dimension,
    TargetAggregation,
    HypothesisTest
)

N = 1000

experiment_data = pd.DataFrame({
    "order_value": np.random.normal(100, 10, size=N),
    "delivery_time": np.random.normal(10, 1, size=N),
    "experiment_group": np.random.choice(["control", "treatment"], size=N),
    "city": np.random.choice(["NYC", "LA"], size=N),
    "customer_id": np.random.randint(1, 100, size=N),
    "customer_age": np.random.randint(20, 60, size=N),
})

pre_experiment_data = pd.DataFrame({
    "order_value": np.random.normal(100, 10, size=N),
    "customer_id": np.random.randint(1, 100, size=N),
})

# Define test
cupac_model = TargetAggregation(
    agg_col="customer_id",
    target_col="order_value"
)

hypothesis_test = HypothesisTest(
    metric=SimpleMetric(alias="AOV", name="order_value"),
    analysis_type="clustered_ols",
    analysis_config={
        "cluster_cols": ["customer_id"],
        "covariates": ["customer_age", "estimate_order_value"],
    },
    cupac_config={
        "cupac_model": cupac_model,
        "target_col": "order_value",
    },
)

# Create analysis plan
plan = AnalysisPlan(
    tests=[hypothesis_test],
    variants=[
        Variant("control", is_control=True),
        Variant("treatment", is_control=False),
    ],
    variant_col="experiment_group",
)

# Run analysis
results = plan.analyze(experiment_data, pre_experiment_data)
print(results.to_dataframe())

Installation

You can install this package via pip.

pip install cluster-experiments

For detailed documentation and examples, visit our documentation site.

Features

The library offers the following classes:

• Regarding power analysis:
  • PowerAnalysis: to run power analysis on any experiment design, using simulation
  • PowerAnalysisWithPreExperimentData: to run power analysis on a clustered/switchback design, but adding pre-experiment df during split and perturbation (especially useful for Synthetic Control)
  • NormalPowerAnalysis: to run power analysis on any experiment design using the central limit theorem for the distribution of the estimator. It can be used to compute the minimum detectable effect (MDE) for a given power level.
  • ConstantPerturbator: to artificially perturb treated group with constant perturbations
  • BinaryPerturbator: to artificially perturb treated group for binary outcomes
  • RelativePositivePerturbator: to artificially perturb treated group with relative positive perturbations
  • RelativeMixedPerturbator: to artificially perturb treated group with relative perturbations for positive and negative targets
  • NormalPerturbator: to artificially perturb treated group with normal distribution perturbations
  • BetaRelativePositivePerturbator: to artificially perturb treated group with relative positive beta distribution perturbations
  • BetaRelativePerturbator: to artificially perturb treated group with relative beta distribution perturbations in a specified support interval
  • SegmentedBetaRelativePerturbator: to artificially perturb treated group with relative beta distribution perturbations in a specified support interval, but using clusters
• Regarding splitting data:
  • ClusteredSplitter: to split data based on clusters
  • FixedSizeClusteredSplitter: to split data based on clusters with a fixed size (example: only 1 treatment cluster and the rest in control)
  • BalancedClusteredSplitter: to split data based on clusters in a balanced way
  • NonClusteredSplitter: Regular data splitting, no clusters
  • StratifiedClusteredSplitter: to split based on clusters and strata, balancing the number of clusters in each stratus
  • RepeatedSampler: for backtests where we have access to counterfactuals, does not split the data, just duplicates the data for all groups
  • Switchback splitters (the same can be done with clustered splitters, but there is a convenient way to define switchback splitters using switch frequency):
    • SwitchbackSplitter: to split data based on clusters and dates, for switchback experiments
    • BalancedSwitchbackSplitter: to split data based on clusters and dates, for switchback experiments, balancing treatment and control among all clusters
    • StratifiedSwitchbackSplitter: to split data based on clusters and dates, for switchback experiments, balancing the number of clusters in each stratus
    • Washover for switchback experiments:
      • EmptyWashover: no washover done at all.
      • ConstantWashover: accepts a timedelta parameter and removes the data when we switch from A to B for the timedelta interval.
• Regarding analysis methods:
  • GeeExperimentAnalysis: to run GEE analysis on the results of a clustered design
  • MLMExperimentAnalysis: to run Mixed Linear Model analysis on the results of a clustered design
  • TTestClusteredAnalysis: to run a t-test on aggregated data for clusters
  • PairedTTestClusteredAnalysis: to run a paired t-test on aggregated data for clusters
  • ClusteredOLSAnalysis: to run OLS analysis on the results of a clustered design
  • OLSAnalysis: to run OLS analysis for non-clustered data
  • TargetAggregation: to add pre-experimental data of the outcome to reduce variance
  • SyntheticControlAnalysis: to run synthetic control analysis
• Regarding experiment analysis workflow:
  • Metric: abstract class to define a metric to be used in the analysis
  • SimpleMetric: to create a metric defined at the same level of the data used for the analysis
  • RatioMetric: to create a metric defined at a lower level than the data used for the analysis
  • Variant: to define a variant of the experiment
  • Dimension: to define a dimension to slice the results of the experiment
  • HypothesisTest: to define a Hypothesis Test with a metric, analysis method, optional analysis configuration, and optional dimensions
  • AnalysisPlan: to define a plan of analysis with a list of Hypothesis Tests for a dataset and the experiment variants. The analyze() method runs the analysis and returns the results
  • AnalysisResults: to store the results of the analysis
• Other:
  • PowerConfig: to conveniently configure PowerAnalysis class
  • ConfidenceInterval: to store the data representation of a confidence interval
  • InferenceResults: to store the structure of complete statistical analysis results