Descriptive means for all model variables are given in . We present these means in three ways: for the entire population; by transfer destination (level I and level II); and for patients transferred from centers that were relatively close, or relatively far from the nearest level I center. Of the 542 patients in our analysis, 270 (49.8%) were transferred to 1 of 12 level II centers and 272 (50.2%) were transferred to 1 of 3 level I centers. Thirty-six (13.3%) patients transferred to level II centers and 42 patients transferred to level I centers (15.4%) died during hospitalization or within 30 days of hospital discharge. In general, more severely injured patients were transferred to level I centers.
Patient Characteristics, by Total Sample; Transfer Destination; and Relative Proximity to Level I Trauma Center
The last two columns in were created by dividing the patient populations into two groups of roughly equal size, based on the median differential distance of 39.4 miles. A comparison of these two groups, patients relatively close to level I centers compared with patients relatively close to level II centers, provides some insight into the instrumental variables mechanism. The groups appear to be approximately comparable in terms of demographics and measures of injury severity. They differ primarily in the distance from level I trauma centers and in the likelihood of transfer to level I trauma centers, with 80.4% of patients relatively close to level I centers transferred to level I centers, and only 21.3% of patients closer to level II centers transferred to level I centers. Despite the other similarities between the two groups, the patients closer to level I trauma centers have a lower mortality rate. If grouping by proximity to level I trauma centers is an effective randomization, a simple measure provides some insight into the mortality benefits of transfer to level I centers. With a 59.1% increase in the percentage of patients taken to level I centers, there is an approximate 3.1% decline in mortality. The full instrumental variables model aims at developing a more detailed statistical estimation of the mortality benefits of level I centers.
In order to compare the results of the instrumental variables model to a standard, single-equation model, we show the coefficients of the two contrasting models in . The results of the standard, single-equation probit model are shown in columns 2 and 3 of . Variables that are significantly associated with increased mortality (i.e., positive coefficients) include: age >55 years, log (ISS), head AIS of 5 (the most severe head injury), hypotension in the emergency department, and initial neurologic status other than alert (AVPU score of V, P, or U). The AVPU is clearly related to mortality in our sample, showing increasing significance and generally increasing magnitude with the progression from A (alert) to U (unresponsive). In this model, the coefficient for transfer to level I centers is negative (beneficial) but not statistically significant. However, these estimates may be biased if, after adjusting for observed characteristics, more severely injured patients are more likely to be transferred to a level I center. To develop an unbiased estimate of the effect of care at level I centers, we use the instrumental variables approach.
Multivariable Model Results for 30-Day Mortality, Adjusted for Clustering by Transferring–Receiving Center Pairs
Using differential distance as an instrumental variable, the bivariate probit model results are displayed in the last two columns of . In essence, we jointly estimate the decision about where to send the patient and the outcome based on that transfer decision. The coefficient estimates of the first equation, with 30-day mortality as the outcome, are shown here. In contrast to the standard probit model, the instrumental variables estimation finds a mortality benefit of transfer to a level I center relative to a level II center (p=.017). Coefficients on the other variables are qualitatively similar for the single-equation probit model and the instrumental variables, bivariate probit model.
To aid in interpretation of these coefficients, we calculated the predicted mortality for all patients in our sample both as treated at a level I and at a level II center, and then computed the relative impact of level I treatment on mean mortality. Using estimates from the bivariate probit model, we estimated the mean absolute mortality benefit of transfer to a level I trauma center to be 10.1% (95% CI: 0.3%, 22.1%).
An important assumption of our model is that differential distance is a significant predictor of transfer destination. A Wald test confirmed that differential distance is a very strong predictor of transfer destination (Wald test=26.6, p
<.001). We also conducted a Hausman test to determine whether the instrumental variables model was appropriate; that is, if there were unobserved factors that influenced mortality and the decision to transfer to a level I or level II trauma center. Despite the use of detailed data and validated measures of injury severity, a Hausman test rejects at the 5% level our single-equation model (Knapp and Seakes 1998
). This suggests that, even after adjusting for observed patient characteristics, transfer destination is still confounded by mortality risk and that an approach using instrumental variables may provide a less biased estimate.
We applied several different models to check the robustness of our results. In addition to the single-equation probit and bivariate probit models described above, we also estimated three additional bivariate probit models with a reduced set of covariates. In the first, we eliminated most measures of injury severity, using as covariates log (ISS), gender, dichotomous variables for children <12 years old and adults >55 years old, history of comorbid condition(s), whether the patient was transferred within Oregon (versus Washington), whether the patient was transferred to a level I or level II trauma center, and differential distance as an instrument. In the second, we eliminated most demographics, using as covariates three dichotomous variables for AVPU score, with alert (A) patients acting as the reference group, log (ISS), hypotension, head AIS of 5, whether the patient was transferred to a level I or level II trauma center, and differential distance as an instrument. In each of these reduced models, the elimination of additional variables was such that a likelihood ratio test rejected the hypothesis that the more parsimonious models were equivalent to the full model. Therefore, we also estimated a third model that retained the most significant variables: log (ISS), a dichotomous variable for AVPU score of U (unresponsive), head AIS of 5, age >55, whether the patient was transferred within Oregon, whether the patient was transferred to a level I or level II trauma center, and differential distance as an instrument. Using a likelihood ratio test, we could not reject the hypothesis that this model was equivalent to the full model. (Technically, the likelihood ratio test is not valid when used with clustering; however, since we were primarily interested in investigating the sensitivity of our finding to different models, we used this test as an indicator of substantial structural difference between models.) Estimates for the absolute reduction in mortality and 95% CIs for each of these models are displayed in . In addition, we used a two-stage, linear probability model using the original set of covariates. The results of this model are also shown in .
Mortality Benefits of Transfer to Level I Trauma Center, Comparing Different Model Specifications
Point estimates of the mortality benefit of level I trauma centers range between approximately 7% and 13% for our instrumental variables models. The estimates show some sensitivity to model specification. In particular, if measures of injury severity are removed, the 95% CI is wide enough to include zero. The two-stage, linear probability model offers results qualitatively similar to the bivariate probit model, with the mortality benefit of level I care estimated to be 7.0%, and a tighter CI around this estimate that is close to zero.
As noted above, the instrumental variables models rely on two important assumptions: (1) differential distance must be a significant predictor of whether the patient is transferred to a level I or level II trauma center; and (2) differential distance must not be correlated with mortality, except through transfer to level I or level II trauma center. The first assumption has been verified using the Wald test. The second assumption cannot be statistically validated. However, we considered three ways in which this assumption could be violated. First, greater differential distance might imply more distance traveled and thus more time required to transfer the patient. Second, hospitals with larger differential distance measures are more remote from the large metropolitan areas where most level I trauma centers are located, and care may differ at these hospitals. Finally, patients initially presenting at more remote hospitals might be more severely injured than patients initially arriving at hospitals closer to level I trauma centers. We describe the examinations of each of these possibilities below.
Differential distance is defined as: distance to the nearest level I center − distance to the nearest level II center. Thus, if differential distance is 100 miles we only know that the patient must be transported at least 100 miles to get to the level I center, but we have no information about the distance to the nearest level II center. The correlation coefficient between differential distance and actual distance traveled is 0.014, indicating a low level of correlation between the two. Furthermore, there is little evidence that distance traveled is correlated with mortality. The mean distance traveled for those patients who lived is 95.2 miles, and is 102.3 for those patients who died. This difference is not significant (Mann–Whitney test, p=.41). The correlation coefficient between differential distance and actual distance traveled for those patients who died is −0.029.
There is also the potential that time elapsed during transfer could confound our model. If so, we would expect that the transfer time interval would be longer for level II trauma centers, or perhaps that it would be longer among patients who died. The data gathered on patients contained some information on the time elapsed during transfer, although these data are less reliable than data on distance. We examined this data after excluding missing values (n=32), negative values (n=2), and outliers (i.e., transfer time intervals recorded as lasting more than 3 hours or less than 10 minutes, n=12), leaving 495 observations. The mean recorded time elapsed during transfer was 64.3 minutes, with no significant difference between times for patients who lived and patients who died (Mann–Whitney test, p=.94), and no significant difference between times of transfer for level I and level II trauma centers (Mann–Whitney test, p=.12). Among patients who died, transfer time intervals to level I trauma centers were recorded to be 5 minutes longer on average, although this was not a significant difference (Mann–Whitney test, p=.16). Thus, it seems unlikely that time is a substantial confounder in our analysis, and the data do not appear to invalidate our instrument. The fact that different modes of transportation (i.e., ground, helicopter, fixed-wing aircraft) were used for transporting patients from rural hospitals may partly explain these findings. We did not include time elapsed during transfer as an independent variable in our models because RTR personnel could not resolve several of the inconsistencies in the data. We were also concerned that, since more severely injured patients would be likely to have expedited transfers, including transfer time interval would introduce the same biases that were our intent to remove.
As shown in , hospitals with greater differential distance are further away from the nearest level I center, which were major university centers. If care differed at more remote hospitals in a way that resulted in increased mortality, then our instrument would not be valid. One possibility might be that more remote hospitals were less likely to be level III trauma centers and more likely to be level IV or V trauma centers. We found that, in general, more remote hospitals are slightly more likely to be level IV or V hospitals, but this correlation was not statistically significant (Kendall's τ-b=0.23; p=.13) We also checked for the potential for more remote hospitals to be less likely to have a physician present when the patient arrived at the ED. We found a similar result, with more remote hospitals slightly less likely to have a physician present when the patient arrived, although this too was not statistically significant (Cochran–Armitage test; p=.14).
The geographical distance from the nearest level I center was strongly associated with transfer patterns. Some hospitals in our sample always transferred patients to level I centers (six hospitals transferring 79 patients), and others always transferred to level II centers (11 hospitals transferring 142 patients). There were two hospitals that were closer to level I centers than level II centers that occasionally made transfers to level II centers, for a total of five observations (all five patients survived). We do not know the motivating factors for these decisions; the lack of bed availability or similar factors may have affected the final destination of these patients. In addition, there were five hospitals that were relatively closer to level II centers but always transferred to level I (for a total of 60 observations). Because differences in outcomes might be due to preexisting transfer patterns at certain hospitals (i.e., always transferring to a certain trauma center), we estimated our model on the 14 hospitals (transferring 321 patients) that did not exclusively transfer patients to either a level I or level II center (i.e., each of these hospitals sent patients to both level I and level II centers). When we estimated our model on this subset of 321 patients (59% of the original sample), we found that the mortality benefit of transfer to level I centers was not significant (estimated benefit: 3.3%, 95% CI: −6.6%, 22.1%). However, the coefficients on many other variables also lost significance. We estimated a more parsimonious model that included whether the patient was transferred to a level I center; a dichotomous variable for unresponsive patient (AVPU=U); log (ISS); a dichotomous variable for patient age>55; and differential distance as the instrument. A likelihood ratio test did not reject the hypothesis that this more parsimonious model was significantly different from the full model (p=.11). In this restricted model, estimated mortality benefit of transfer to level I centers was significant at the 10% level (estimated benefit: 9.4%, 90% CI: 0.7%, 26.4%). The lack of strong significance may reflect differences in care that exist at the originating hospital, or may be because of the relatively small sample size, as the estimates based on this restricted sample otherwise qualitatively support our model.
Previous studies have shown that more rural areas have progressively higher mortality rates from motor vehicle trauma (Baker, Whitfield, and O'Neill 1987
). If more severely injured patients present to more remote hospitals, then our instrument would be invalid. To test for the potential for more severe injuries in more remote areas, we looked for trends in our variables included in the model and in a number of additional variables, including AIS score for head, face, chest, abdomen, extremities, and external (soft-tissue) injuries, the presence of a penetrating (versus blunt) injury, and the presence of unequal dilated pupils. We looked for trends by dividing hospitals into 10 groups based on increasing levels of differential distance, and by separating patients based on differential distance and the originating hospital (31 groups). Most variables showed no significant trend that suggested increasing injury severity with more remote hospitals, with two exceptions. Thirty-three patients were recorded as hypotensive, and this was more frequent at more remote hospitals (Cochran–Armitage test, p
=.004). In addition, there was a slight increase in the prevalence of patients with chest injuries (Cochran–Armitage test, p
=.08), although these injuries were not progressively more severe at more remote locations. Thus, although most variables suggested that patients did not vary in substantially different ways across hospitals, we did find limited evidence that patients presenting to more remote hospitals are injured in ways related to geographical location.