# The Importance of Reporting Variation in Hospital Data

Calling attention to the neglected stepchild of hospital analytics.

Hospital metrics typically present averages front and center.  Average length of stay, average admissions per day, average surgeries per week and so on.  But unless variation is included on equal footing, these metrics are only showing half the story and can actually be misleading.

Consider two hospitals.  Both hospitals admit an average of ten patients a day and each patient stays an average of four days.  This means both hospitals have an average inpatient census of 10 x 4 = 40 beds.

Consider further the first hospital only performs routine elective procedures and admits exactly ten patients a day and they stay for exactly four days.  In this case, the hospital needs exactly 40 inpatient beds.  Not 41 beds or 42 beds but 40 beds.  And those 40 beds are 100% full.

The second hospital is a trauma center.  It may admit as few as five patients and as many as 40 patients in day.  And these patients may stay for as little as a day and as long as 8 days.  This hospital will need many more than 40 beds.  In fact, unless this hospital has 40 x 8 = 320 beds, it risks rejecting patients.  But if it actually had 320 beds, most of the beds would be unused.  This hurts the bottom line.

Modern operations science has developed mature statistical methods to characterize this variation and forecast the number of patients likely to be rejected given a set number of beds.  These methods replace qualitative words like “many” and “most” with a more precise statement such as “with 60 beds, 93% of all patients will be admitted within three hours”.  This isn’t a crystal ball into the future but it prepares hospital staff to expect that 7% of the time patients will have to wait more than three hours for a bed.  Instead of this being a crisis, it is can be an anticipated event.  If this wait time is unacceptable, the same analysis can find the number of beds required to meet hospital policy.

In this thought experiment, both hospitals have the same averages for admission and length of stay.  But for one hospital 40 beds is adequate while the other hospital needs far more beds to manage an acceptable percentage of the population.  The difference is variation.  And it matters.

This is one reason why ICU units can be harder to manage.  ICUs typically have the largest variation in length of stay of all hospital units.  A few patients with 30 days length of stay can take up half or more of an ICU’s capacity.  It is harder to find a balance between enough beds to avoid long wait times and not so many beds that they are often empty or filled with boarders from other parts of the hospital.

On the other end of the spectrum was a unit for pediatric otolaryngology in one of our client hospitals.  This unit had an average length of stay of 1.8 days with a variation in the hours.  Properly sized, this unit will rarely have an empty bed AND patients will rarely have to wait for a bed.

When looking at averages, do not assume variation is low.  Planning based on averages runs the risk of resource scarcity during peak utilization.  Given this understanding of variation, low census in pediatric otolaryngology can be a sign of overcapacity but low census in the ICU is simply an expected part of natural variation in ICU demand.

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