# Expected mortality

The expected mortality is an option of the quality of care report, based on the mortalities of procedures performed.

## Contents

## By example

Let's take two popular procedures

- “VSD repair, Patch” with 1.38% mortality
- “Arterial switch operation (ASO)” with 7.12% mortality

Let's imagine two hospitals: ABC and DEF:

- ABC performed “VSD repair, Patch” 100 times and didn't perform ASO (neither any other procedures)
- DEF performed “VSD repair, Patch” 60 times and ASO 20 times (and no other procedures)

Since “VSD repair, Patch” has 1.38 mortality, you would expect that ABC's mortality will be 1.38% -- and that's how expected mortality is calculated. DEF will need a little more complex calculations.

- “VSD repair, Patch” was 75% of DEF's procedures
- “Arterial switch operation (ASO)” was 25% of DEF's procedures

The expected mortality of DEF will be:

<math>0.75 \times 1.38% + 0.25 \times 7.12% = 2.81%</math>

DEF's expected mortality is slightly higher because 25% of its procedures were the ASO procedures, which has a lot higher mortality than VSD patch.

If a hospital performed more procedures, there will be more things to add in the sum. The final formula is:

## The formula

<math>E = \sum_{p \in P} \frac{N_p \cdot m_p}{N}</math>

Where:

- <math>N</math> stands for total number of patients
- Capital <math>P</math> stands for the set of procedures (currently about 150)
- <math>p</math> stands for a single procedure (from <math>P</math>)
- <math>N_p</math> stands for number of patients who had procedure <math>p</math>
- <math>m_p</math> stands for 30-day mortality of procedure <math>p</math>
- <math>E</math> stands for the expected mortality

## Application

The expected mortality can be applied to the quality of care evaluation. The quality of care report has the expected mortality as an option for X-axis. To see how it works, go to the quality of care report

## Notes

- The expected mortality for the whole database and the actual mortality for the whole database are, by definition, equal. The <math>m_p</math> is calculated from the whole database.
- The name
*expected mortality*can be ambiguous. The mortality can be predicted in several ways. This method bases on the mortality-per-procedure estimation.