Business Context

MediPulse is preparing a patient-risk dataset for a hospital readmission model. Before any imputation or modeling, the analytics team wants to understand whether missing values are random, concentrated in certain fields, or associated with patient outcomes.

Problem Statement

You are given summary statistics from a 5,000-row dataset. Your task is to quantify the missingness pattern and recommend the most informative visualizations. Also test whether missingness in one key variable appears related to the target outcome.

Given Data

Additional joint missingness and outcome data:

Requirements

1. Compute the missingness rate for each variable and identify the most problematic fields.
2. Quantify whether Income and Cholesterol missingness co-occur more than expected under independence.
3. Test whether Income missingness is associated with 30-day readmission using a two-proportion z-test.
4. Recommend 3 specific visualizations, explain what each would show, and state which one you would start with.
5. Briefly explain what the results imply about whether missingness may be MCAR versus systematically related to other variables.

Assumptions

• Each row represents one unique patient encounter.
• Missing means the value is unavailable, not structurally inapplicable.
• The normal approximation is acceptable for the proportion test because group sizes are large.