How AI and ML Will Save Lives in Healthcare, Episode 4

Ep 4 Hospital Capacity and Patient Flow

Some of the deadliest delays in a hospital happen after the diagnosis. The doctors have decided a patient needs a bed, and the patient waits in the emergency department for one to open. In a study of more than 5 million admissions in England, the risk of dying within 30 days began to rise after about five hours in the emergency department. For every 72 patients delayed eight to twelve hours, there was one extra death.

This is the fourth episode of a series on where AI and machine learning actually save lives in healthcare, one clinical area at a time. This article gives you the ideas and the math. The full deep dive, with the code, a hospital simulation and the economics, is on Substack.

Boarding is now routine

A 2025 study of about 46 million US admissions found that in ordinary months more than a quarter of admitted emergency patients waited four hours or more for a bed, and closer to 35% in winter. By 2024, nearly 5% waited a full day or longer in peak months. This is no longer a winter problem. It is expensive too: a 2024 study put a day boarded in the emergency department at $1,856, against $993 on an inpatient unit.

Occupancy is a cliff

A hospital is a queue with beds as servers. Little’s law gives occupancy: admissions per day times length of stay, divided by beds. The Erlang C formula gives the chance a new patient finds every bed full.

occupied beds = admissions per day × length of stay

For a 300-bed hospital, the chance of waiting for a bed is 0.4% at 85% occupancy, 4.6% at 90% and 27.9% at 95%. A 1999 BMJ modeling study reached the same conclusion: periodic shortages above 85%, regular crises above 90%. The full article includes the calculator for your own beds.

Discharges, not admissions, are the lever

The best-documented use of machine learning in patient flow is predicting who will leave in the next day or two. At Hartford HealthCare, units that used morning discharge predictions saw stays 0.67 days shorter than units that did not. At a Johns Hopkins community hospital, stays fell by more than 12 hours on two of four units. Neither study was randomized.

The model is not the hard part. Calibrated probabilities add up to a forecast: a unit’s expected discharges tomorrow are just the sum of its patients’ probabilities. In my synthetic test, that forecast missed by 1.67 discharges on a 30-bed unit, enough to decide at 7:30 am whether to open surge beds or move an elective case.

What a simulated hospital says

I simulated a 300-bed hospital at 94.9% occupancy, where 21.6% of admitted emergency patients board four hours or more. Using the England figures, the waits cost about 52.1 excess deaths a year.

Requesting beds at triage for predicted admissions changed almost nothing, because a full hospital has no bed to give earlier. Moving discharges two hours earlier helped a little. Shortening the average stay by 0.3 days, less than half of Hartford’s result, cut excess deaths to 9.3 a year. Near the cliff, small changes in length of stay remove most of the harm.

What’s in the Full Article

• The Erlang bed calculator, in code, for your own census
• A discharge model and the unit forecast that turns its probabilities into free beds
• A simulation of a 300-bed hospital, with every assumption stated
• The economics: about $4.55 million a year in freed bed-days and avoided boarding, and the cost per death averted
• How to prove it: why 3,603 admissions per arm can prove the change and 150,569 would be needed for mortality
• An executive brief with three questions for your operations and nursing leaders

It is written for hospital executives, patient flow and nursing leaders, and the analytics teams who support them.

Read the full deep dive on Substack → HERE

Paid subscribers get the full article and key code. Team Licensing members get the complete code, implementation plan and reference architecture for running this inside a health system.

About the Author

Brian James Curry is a Kansas City AI researcher, applied scientist and data scientist working in machine learning, causal inference and healthcare intelligence. He is the founder of Vector1 Labs, an independent applied AI research lab, where his Causal Care series applies causal machine learning to health system decisions: which programs work, for whom, and what they are worth. He also founded KC AI Lab, which began in 2016 as the Kansas City Machine Learning Group and has grown to more than 1,500 members.

He has more than twenty years of experience leading analytics, data science and machine learning at Hallmark, Garmin, Koch Industries, Tractor Supply Company and Vail Resorts. His open-source research tools on GitHub include PyCausalSim (causal discovery through simulation), Papilon (marketing mix modeling and complex systems) and tincast (forecasting for AI-critical commodities), along with MeaningFlow and Daedalus. A Kansas State University alum from a small Kansas farming town, he writes about agentic AI, causal inference, healthcare AI and the economics of AI on Medium and Substack. Contact: brian@vector1.ai.