In my last article, I showed how to use M and Z statistics to benchmark your trauma center’s outcomes. M and Z scores allow you to measure patient outcomes against a national comparison group, the Major Trauma Outcomes Study (MTOS).

However, M and Z scores do have disadvantages. The main issue: If your patient population is *dissimilar* to the MTOS group, you cannot use this method to benchmark performance.

So what do you do if your patients do not match the MTOS comparison group — or if you simply want a more versatile benchmarking system? *The answer is the W score.*

Essentially, a W score describes the number of unexpected outcomes per 100 patients. It is not tied to any external comparison group, so it can be used by any trauma center to analyze any aspect of program performance.

In addition, a W score is typically a hand-calculated formula. That means trauma registrars, PI coordinators and other program leaders can use W values to compare any two patient groups. You are not limited to the built-in reports in your registry software.

## How to calculate a W score

To calculate a W score for any subset of your trauma patient population, you need two data fields:

- Probability of survival (Ps), which is automatically calculated by all trauma registry systems
- Outcome, in terms of death versus survival

First, run a registry report to capture these data fields for the subset of patients you want to evaluate. (For example, you might want to look at outcomes for patients with penetrating injuries.) Second, output the data into a spreadsheet file. Third, data-sort the file based on Ps. This will group your data for easy formulas.

The formula for the W score is: **W = (A – B) ÷ C/100**

**A**= the total number of patients with all data components necessary to calculate Ps*minus*the number of those patients who died**B**= the sum of all of the Ps values for this group of patients**C**= the total number of patients with all data components necessary to calculate Ps

A positive value indicates that the number of patients who survived was *higher* than expected. For example, a W value of +2 means that for every 100 patients, 2 more patients survived than were expected to. A negative value indicates that survivals were *lower* than expected.

Here’s an example of how to use the formula. Say your registry report finds 780 patients who had a penetrating injury and who also have a calculated Ps. Within this population, 30 patients died. The sum of all the Ps values for this population is 742.368. The W score calculation would be:

**W = (A – B) ÷ C/100**

W = ([780 – 30] – 742.368) ÷ 780/100

W = (750 – 742.368) ÷ 7.8

W = 7.632 ÷ 7.8

W = 0.9785

In this example, the W score is a positive number so the interpretation is that 0.9785 patients survived who were statistically expected to die. Overall, your trauma center is performing well for patients with penetrating injuries.

## How to use W scores in trauma PI

W scores play a useful role in trauma performance improvement (PI). For example, say the W score for penetrating injuries was *negative*, indicating unexpectedly high deaths among this subset of patients. This unexpected outcome is a prime candidate for review by your PI committee.

Using the W score as a starting point, the committee could identify any system-wide failures and develop recommendations for future management or guideline revisions. This would help close the loop for your PI committee, and the W score would function as a sound benchmarking method for monitoring performance.

You can use W scores to evaluate any aspect of the care your trauma program provides:

**Mechanisms of injury:**What is your W score for blunt versus penetrating injury? What does that say about your care processes?**Patient populations:**What is your W score for geriatric patients versus other adult patients? If your geriatric W is negative, what can you do to improve care for older adults?**Providers:**What is the W score for each of your trauma attendings for different injuries? Do these results highlight any opportunities for improvement?**Care continuum:**What is the W score for patients with ICU length of stay greater than 2 days? If it is negative, what can your program do to improve outcomes in intensive care?**Systems:**What is your W score for patients who receive different levels of trauma activation? What does that say about your systems of care?

Overall, W scores allow your PI initiatives to be data-driven and benchmarked.

## One caution: Check your data validity

As I noted above, the W score formula excludes patients for whom you do not have enough data to calculate a probability of survival (Ps). That allows you to evaluate outcomes even if your data is not perfect. The flip side, however, is that if the number of missing Ps calculations is elevated, the W score will be falsely affected.

Remember that the Ps is based on:

- Patient age
- Mechanism of injury — blunt versus penetrating
- Revised Trauma Score (RTS) — which consists of systolic blood pressure (SBP), respiratory rate (RR) and Glasgow Coma Scale (GC)
- Injury Severity Score (ISS)

If any of these data components are missing for a patient, the Ps will not be calculated for that patient. In general, the higher the number of missing Ps calculations, the greater the chance that your W scores will be inaccurate.

A high rate of missing Ps calculations is a caution flag that there are issues with your data. In most cases, the problem is provider documentation and/or trauma registrar abstraction. Taking steps to improve these processes will help ensure that the W score is a versatile and effective tool to measure trauma center performance.

Need help calculating W scores and other trauma risk scores?Bookmark the Trauma Calculators available from Pomphrey Consulting. This calculator page also includes several resources for understanding trauma scores and using them to improve trauma center performance.