citest: Conditional Independence Testing for Missing Data

A hypothesis test for whether an outcome variable is independent of missingness, conditional on the observed explanatory data. The test compares classifier performance in predicting missingness with and without the outcome variable, using multiple imputation and cross-fitting to produce a valid t-statistic and p-value.

Installation

pip install citest

Quick start

import pandas as pd
from citest import CIMissTest
from citest.data import Dataset

# Load your data
data = pd.read_csv("path/to/your/data.csv")

# Define the dataset
dataset = Dataset()
dataset.make(
    data,
    y="target_variable",
    expl_vars=["expl_var1", "expl_var2", ...]
)

# Run the test
test = CIMissTest(
    dataset,
    classifier_args={"n_estimators": 20, "target_n_jobs": 8},
)
test.run()

# Print results
test.summary()

How the test works

1. Multiple imputation -- the missing data are multiply imputed (default: MIDAS denoising autoencoder).
2. Classifier comparison -- for each imputed dataset, two classifiers predict the missingness indicator R:
   • One using the outcome Y and covariates X
   • One using a permuted (uninformative) copy of Y and covariates X
3. Cross-fitting -- predictions are made out-of-fold to avoid data leakage.
4. Test statistic -- the weighted difference in binary cross-entropy between the two classifiers is combined across imputations using Rubin's rules, yielding a t-statistic and p-value.

A significant result indicates that missingness depends on the outcome even after conditioning on the covariates (i.e. the data are not missing at random with respect to Y).

Customizing the pipeline

Imputers

Class	Description
MidasImputer (default)	MIDAS denoising autoencoder (via MIDAS2)
IterativeImputer	scikit-learn iterative imputer with posterior sampling
IterativeImputer2	Robust variant with numerical guards for wide/sparse data

Classifiers

Class	Description
RFClassifier (default)	Random forest with auto-tuned max_features and min_samples_leaf
ETClassifier	Extremely randomized trees
LogisticClassifier	Logistic regression

Example with custom settings

from citest.imputer import IterativeImputer
from citest.classifier import RFClassifier

test = CIMissTest(
    dataset,
    imputer=IterativeImputer,
    classifier=RFClassifier,
    n_folds=10,
    m=10,
    classifier_args={"n_estimators": 100, "target_n_jobs": 8},
    imputer_args={"max_iter": 20},
)

Key parameters

Parameter	Default	Description
m	10	Number of multiply imputed datasets
n_folds	10	Number of cross-validation folds
variance_method	"mi_crossfit"	Variance estimator
target_level	"variable"	Granularity of the missingness target: "variable" or "column"
random_state	42	Random seed for reproducibility

Interpreting results

test.summary() prints the test output:

• Mean difference in BCE -- average reduction in cross-entropy when the real outcome is included. Positive values indicate the outcome helps predict missingness.
• t / p-value -- one-sided test of H0: the outcome does not improve missingness prediction. A small p-value provides evidence against conditional independence (i.e. evidence of MNAR-type missingness).

License

MIT