Association for Academic Surgery
A Mathematical Model to Predict Length of Stay in Pediatric ATV Accident Victims

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Background

Children under age 12 y represent 15% of all-terrain vehicle (ATV)-related deaths, and those under 16 y old represent >36% of deaths nationwide. In recent years, this has accounted for an increasing proportion of pediatric trauma victims and longer hospitalizations secondary to worsened injuries. We believe it is possible to create a simple mathematical model that can be used to predict hospital length of stay.

Methods

A retrospective review of the trauma registry was performed for all pediatric patients who were involved in ATV accidents from January 2000 to December 2009. Four hundred twenty pediatric patients were identified. A model to predict for total LOS in pediatric patients involved in ATV accidents was constructed. SPSS ver. 17 (SPSS Inc., Chicago, IL) was utilized to conduct all statistical analyses. Statistical significance of regression coefficients was assumed at a P < 0.05 level.

Results

We performed a hierarchical multiple regression analysis to build a model that would predict for total length of stay (LOS). A logarithmic transformation was employed on LOS as a dependent variable due to skewness. In Step 1, ISS accounted for a 25% increase in shared variance in LOS (P < 0.001). In Step 2, Glasgow Coma Score (GCS) accounted for 4.3% more variance in LOS (P < 0.001). Finally, in Step 3, the presence of a closed head injury further increased (3.6%) the amount of shared variance in the model (P < 0.001). The final model accounts for 32.9% of the shared variance in total LOS. When using the logarithmic transformation, the final model is: Total LOS = 1.00 + 0.05 injury severity score (ISS) − 0.06 (GCS) + 0.35 closed head injury (CHI).

Conclusion

Based on our data and statistical analysis, we found it was possible to create a mathematical model that could predict hospital LOS in pediatric ATV accident victims.

Introduction

All-terrain vehicles (ATVs) are three- or four-wheeled vehicles with gasoline powered engines driven primarily on venues other than paved roads. They are known to have a high center of gravity and narrow wheelbase, which makes them particularly dangerous in the context of a high speed accident. Current estimates of ATVs in use in the United States are in excess of 7 million, and newer models can attain weights over 600 pounds and reach speeds of greater than 75 miles per hour [1].

The US Consumer Product Safety Commission (CPSC) collects data related to ATV injuries and deaths in the United States and helps in making recommendations to manufacturers and distributors as well as the public on safe ATV practices. They found that from January 1, 1982 to December 31, 2008 there were a total of 9633 ATV-related fatalities and 2588 of these were found to be in people younger than age 16 y [2]. Additionally, the CPSC looked at emergency department (ED) admissions for ATV-related accidents in 2008 for this age group and found that 37,700 injuries occurred in patients under the age of 16 y. This accounted for approximately 30% of all ATV-related injuries in the United States during the year of 2008 [2].

We also know from prior works that almost 80% of the deaths that occur from ATV-related accidents in the pediatric population occur in patients under the age of 16 y [3]. According to the CPSC’s National Electronic Injury Surveillance System (NEISS) data highlights from 2009 ATVs accidents resulted in 28,383 hospitalizations or deaths on arrival to the ED [4]. For hospitalized pediatric ATV accident victims, this translates into an average annual cost of $5.2 million and then $1.4 billion in ED visit costs for these patients [5].

Works looking at ATV use in the pediatric population found that of all hospitalizations during an 11-y period at a pediatric trauma center, 34% of the patients were admitted to the intensive care unit (ICU) secondary to severity of injuries [6]. They also reported that in the more recent years of their study, there were a higher proportions of patients going to the ICU than in earlier years, presumably for worse injuries. This increase in ICU admissions can be said to put a greater strain on healthcare resources.

With cost of care increasing, availability of healthcare workers decreasing, and increase in the number of ATV-related accidents in children, we felt it would be beneficial to attempt to find a way to predict total hospital length of stay in these patients. Herein, we propose a novel mathematical model to help predict hospital length of stay in the pediatric ATV accident victim.

Section snippets

Methods

After obtaining institutional review board (IRB) approval, we performed a retrospective review of the trauma registry for all pediatric patients who were involved in ATV accidents from January 1, 2000 to December 31, 2009. Pediatric patients were defined as those under the age of 18 y old. This resulted in a population of 420 subjects. We analyzed parameters of age, Glasgow Coma Score (GCS), presence of helmet, presence of closed head injury (CHI), injury severity score (ISS), systolic blood

Results

Collinearity diagnostics found acceptable tolerance levels at or above 0.8 for ISS (0.80), GCS (0.81), and CHI (0.85). The Durbin-Watson statistic yielded was 0.65, which is expected due to the use of a higher-order logarithmic transformation and thus does not warrant a possible violation [7]. The standardized residuals were normally distributed, the P-P plot of standardized residuals was acceptable, and there was no violation of the assumption of homoscedasticity.

Before the hierarchical

Discussion

According to the Health Resources and Services Administration report to Congress, there will be a 35% shortage of intensivists by the year 2020 [8]. As stated earlier, there is an overall decline in the number of primary care physicians and healthcare workers in recent years and, thus, less available resources to help in patient care. Between 1993 and 2001, ATV-related injuries in children in the U.S. increased by 94%. Children younger than 16 y of age account for 14% of ATV riders nationally,

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