Predicting 7-Day Purchase After Email Send

Context

You are given a CSV where each row is a user–email send (or scheduled send/control), with columns:

• user_id, send_ts, treatment_flag (1=sent, 0=control/holdout)
• opened, clicked, purchased_within_7d (label)
• user_region, device_type, tenure_days
• prior_sessions_28d, prior_purchases_180d, avg_cart_value_180d, categories_viewed_28d
• email_personalization_score, deliverability_score
• plus other anonymized features

Goal: Build a model that, at send time, predicts whether a user will purchase within 7 days of the email send, then decide whom to send to in order to maximize incremental revenue.

Assume purchased_within_7d is defined as a purchase occurring within [send_ts, send_ts + 7d). For control rows (treatment_flag=0), the window is anchored on the scheduled send_ts.

Tasks

1. EDA and Leakage Control

• Identify potential target leakage and ensure all features are computable at send_ts. Avoid using post-send behaviors (e.g., opened, clicked) unless modeling a multi-stage chain with predicted intermediates.
• Explore class imbalance, missingness, outliers, and high-cardinality categoricals. Propose concrete data quality checks.

2. Modeling

• Train two models to predict purchased_within_7d at send time: a baseline logistic regression and a gradient-boosted tree.
• Use time-based splits: train = 2025-06, valid = 2025-07, test = 2025-08.
• Within the train month, use time-aware cross-validation and tune hyperparameters. Apply monotonic constraints and/or regularization where appropriate.

3. Evaluation

• Report ROC AUC, PR AUC, calibration (reliability curve, Brier score), and incremental lift at the top 10% scored users versus control.
• Provide 95% confidence intervals via bootstrap and assess stability by user_region and device_type.

4. Deployment

• Choose a decision rule that maximizes expected incremental revenue given an email cost of $0.003 and an estimated treatment effect from a calibration experiment.
• Describe monitoring (data drift, performance drift, alerting), retraining cadence, and next steps (feature engineering, causal uplift modeling, de-biasing via IPS/DR estimators).