Trauma Undertriage and Overtriage Rates: Are We Using the Wrong Formulas?

To the Editor,

In the United States (U.S.), regionalized trauma systems have been developed and promoted to improve patient outcomes and optimize the use of hospital resource^1–4. Undertriage and overtriage rates are important quality indicators for trauma systems. The undertriage rate is often defined to capture the proportion of major trauma receiving suboptimal care (thus increased risk of mortality or adverse outcomes). The overtriage rate is defined to capture the proportion of unnecessary use of hospital resource on minor trauma (resource overutilization). An undertriage rate of < 5% and an overtriage rate of <35% are often considered as acceptable according to the American College of Surgeons Committee on Trauma (ACS-COT)⁵.

The Cribari matrix is the most widely used formula for calculating undertriage and overtriage rates in the U.S.⁵ Hospital trauma programs often use the Cribari matrix as a screening tool to identify trauma patients whose medical care needs further review. However, in our opinion, the Cribari formula for calculating undertriage rates is confusing. We believe that the Cribari formula for calculating undertriage rates does not measure what it intends to monitor and, under some circumstances, could create a false complacency that the trauma program functions very well so that no action is needed.

The Cribari Matrix

The Cribari matrix uses the 2×2 contingency table to determine undertriage and overtriage rates at a hospital (Table 1). The formula for calculating overtriage rates is:

$$Overtriagerate=\frac{a}{a+b}$$ (1.1)

Table 1.

The Cribari matrix: Injury severity and trauma team activation.

	Minor trauma	Major trauma	Total
Full Trauma Team Activation	a	b	a+b
Limited or No Trauma Team Activation	c	d	c+d
Total	a+c	b+d	N

Common statistical terms used in diagnostic testing:

Sensitivity= b/(b+d); Specificity= c/(a+c);

False Negative Rate (FNR)=1˗Sensitivity=d/(b+d); False Positive Rate (FPR)=1˗Specificity=a/(a+c);

Positive Predictive Value (PPV)= b/(a+b); Negative Predictive Value (NPV)= c/(c+d);

False Discovery Rate (FDR)=1˗PPV=a/(a+b); False Omission Rate (FOR)=1˗NPV=d/(c+d).

The formula for calculating undertriage rates is:

$$Undertriagerate=\frac{d}{c+d}$$ (1.2)

In the context of diagnostic testing (Table 1 footnote), the Cribari formula for calculating overtriage rate (1.1) is equivalent to 1˗ Positive Predictive Value (PPV), which is also known as the False Discovery Rate (FDR). The Cribari formula for calculating undertriage rate (1.2) is equivalent to 1˗ Negative Predictive Value (NPV), which is also known as the False Omission Rate (FOR).

The Cribari formula for calculating overtriage rates (1.1) appears reasonable. It addresses the primary concern for overtriage at a hospital: resource overutilization on minor trauma. The denominator (a+b) includes all patients who received full trauma team activation regardless of trauma severity. The numerator (a) includes patients who had a minor trauma but received full trauma team activation. The overtriage rate measures the proportion of unnecessary use of hospital resource on minor trauma.

However, the Cribari formula for calculating undertriage rates (1.2) does not address the primary concern for undertriage: increased risk of mortality or adverse outcomes in major trauma patients due to suboptimal care⁵. The denominator (c+d) used in Cribari formula includes all patients who received limited or no trauma team activation. The numerator (d) includes patients who had a major trauma but received limited or no trauma team activation. We disagree with the rationale for using (c+d) as the denominator because those with minor trauma (c) are not at risk of being undertriaged.

In our opinion, the formula for calculating undertriage rates should be:

$$Undertriagerate=\frac{d}{b+d}$$ (1.3)

This formula (1.3) has been used by other researchers to calculate undertriage rates^6–8. In the context of diagnostic testing, our formula (1.3) is equivalent to 1˗ Sensitivity, which is also known as the False Negative Rate (FNR). We include all major trauma patients (b+d) in the denominator, because all major trauma patients are at increased risk of mortality or adverse outcomes when receiving limited or no trauma team activation. We use the same numerator (d) as in the Cribari formula (1.2), because it captures patients who are potentially undertriaged and require further chart review.

The main difference between the Cribari formula (1.2) and our formula (1.3) is the choice of denominator. Using the Cribari formula (1.2), hospitals that treat many more minor trauma than major trauma (e.g. c>>d) can easily reach an acceptable rate of undertriage (commonly used <5%) even when a large proportion of major trauma patients received limited or no trauma team activation. This could create a false complacency that the trauma program performed very well so that no case review or quality improvement is needed. Our formula (1.3) addresses this issue by measuring the proportion of major trauma patients receiving limited or no trauma team activation ($\frac{d}{b+d}$). We believe that our formula (1.3) directly addresses the primary concern for undertriage.

There are multiple approaches in defining major trauma as well as variations in choosing a threshold of undertriage rate to trigger case review, however, we here only discuss how to choose a denominator for calculating undertriage rates. The rationale of our formula remains grounded when different approaches are used to define major trauma or different thresholds of undertriage rate are chosen to trigger case review.

Real World Example

We hereby use data from a level I pediatric trauma center to compare the undertriage rates calculated using the Cribari formula (1.2) and our formula (1.3). In 2015, a total of 1,932 pediatric trauma patients were treated in this pediatric trauma center (Table 2). Of these patients, 194 received full trauma team activation, and 1,738 received limited or no trauma team activation. Using the Cribari formula (1.2), the undertriage rate is calculated as:

$$Undertriagerate=\frac{d}{c+d}=\frac{64}{1738}=3.7\%$$

Table 2.

Trauma data at a level I pediatric trauma center, 2015

	Minor trauma (ISS 1-15)	Major trauma (ISS 16-75)	Total
Full Trauma Team Activation	130 (a)	64 (b)	194 (a+b)
Limited or No Trauma Team Activation	1674 (c)	64 (d)	1738 (c+d)
Total	1804 (a+c)	128 (b+d)	1932 (N)

Using our formula (1.3), the undertriage rate is calculated as:

$$Undertriagerate=\frac{d}{b+d}=\frac{64}{128}=50\%$$

Based on the Cribari formula (1.2), the above mentioned trauma program has an acceptable rate of undertriage (3.7%). As a result, this trauma program may consider its performance as satisfactory and does not take action(s). In fact, 64 out of 128 major trauma patients received limited or no trauma team activation. Using our formula (1.3), this trauma program would be alerted of a high undertriage rate (50%). As a result, this trauma program would likely conduct medical chart review among the potentially undertriaged patients (d=64).

95% Confidence Intervals

The Cribari matrix does not provide confidence intervals for undertriage and overtriage rates. If we use the data of all patients to calculate overtriage and undertriage rates, we do not need to calculate confidence intervals. However, if we use sample data, we should also calculate a confidence interval (CI) for each rate. For example, a 95% CI for overtriage and undertriage rates could be calculated as $\text{p}\pm \text{1.96}\times \sqrt{\frac{\text{p}\times (1-\text{p})}{\text{n}}}$, where $\text{p}$ is the proportion of patients that were overtriaged or undertriaged ($\frac{\text{a}}{\text{a}+\text{b}}$ or $\frac{\text{d}}{\text{b}+\text{d}}$ in Table 1), and n is the total number of patients who received full trauma team activation or have major trauma (a+b or b+d in Table 1).