Modelling approach
We developed a lifetime patient-level decision tree, followed by a discrete event simulation to model patient flows through an English MTC system. The model estimated patient’s outcomes, costs incurred and quality adjusted life years (QALYs) accrued for patients with suspected severe injuries. Conceptual modelling, informed by a previously published model by Newgard et al and consultation with subject experts informed the final model design.[9] We have taken a patient-level approach for two reasons. Firstly, we can accurately predict the risk of death using a validated 30-day probability of survival equation, developed by the Trauma Audit and Research Network (TARN), in an English population.[10, 11] Secondly, when actual tools are assessed in English populations, this model can be easily adapted to include any correlations that exist between triage tool outcomes and the patient’s probability of survival predicted by the TARN survival equation.
Patient Population
Our model considered patients who were injured outside of the MTC’s local area for two reasons. Firstly, patients who live closest to an MTC will usually go to the MTC regardless of the severity of their injury. However, if a patient is thought to be severely injured, the MTC will be pre-alerted. Secondly, the available effectiveness evidence appears to treat all patients who live closest to an MTC as having been treated at an MTC regardless of whether the trauma team were pre-alerted. Consequently, there is no trade-off between cost and effectiveness that can be assessed in our analyses.
The model was populated with simulated patients’ representative of injured patients presenting to an English trauma system. To generate these characteristics we obtained access to baseline demographic and clinical data from a recent prehospital major trauma triage study by van Rein et al, using the data collected in the Central Netherlands region.[12] This provided a high quality data set, which should be representative of developed world patient. This data is summarised in Table 1. Means, standard deviations and covariances between all parameters were obtained from the van Rein et al data for patients with complete data for Age, Gender, ISS, Glasgow Coma Scale (GCS) and trauma type.[12] Simulated patients were sampled using correlated draws from these distributions, further details are provided in the appendix.
Table 1: A summary of the simulated characteristics of the patients included in the model
Characteristic
|
Mean
|
SD / n/N
|
Source
|
Age
|
46.8
|
21.3
|
Patients with complete Age, Gender, ISS, GCS and trauma type data in Van Rein et al.[12]
|
Percentage Male
|
58.3%
|
2887/4720
|
ISS
|
5.2
|
7.2
|
Percentage with an ISS ≥ 16
|
9.1%
|
428/4720
|
GCS
|
14.4
|
1.9
|
Percentage with blunt trauma
|
98.2%
|
4637/4720
|
SD, standard deviation; ISS, injury severity score; GCS, Glasgow Coma Scale
|
Interventions
Nine triage tools were examined, based on Newgard et al in which triage tools were derived by statistically analysing a retrospective cohort study conducted at 6 sites in the Western US between January 2006 and December 2008.[13] This study was selected as it fit nine triage tools to one dataset, so represented feasible trade-offs between sensitivity and specificity for any new rule. These analyses produced nine triage tools for which, the reported sensitivities and specificities for each tool were:
- Sensitivity 99.8%, Specificity 2.5%
- Sensitivity 94.8%, Specificity 18.7%
- Sensitivity 90.4%, Specificity 58.4%
- Sensitivity 87.5%, Specificity 62.8%
- Sensitivity 74.6%, Specificity 65.7%
- Sensitivity 69.8%, Specificity 70.1%
- Sensitivity 64.2%, Specificity 76.1%
- Sensitivity 57.0%, Specificity 80.0%
- Sensitivity 99.8%, Specificity 88.6%
We assumed that the sensitivity and specificity values for each triage tool represented the final triage decision, combining the diagnostic accuracy of the triage tool and the application of judgement by the on-scene paramedics. A recent analysis of a Dutch triage tool in an English data set produced a received-operator curve that would result in similar triage tool sensitivity and specificity as observed by Newgard et al.[14]
Perspective
In line with guidance from the English and Welsh decision maker, the National Institute for Health and Care Excellence (NICE): we undertook a cost-utility analysis; our analyses had a lifetime horizon; an NHS and personal social services perspective was taken; and, future costs and QALYs were discounted at 3.5%.[15]
Outcome measures
The primary outcome measure of the model was the incremental cost-effectiveness ratio (ICER). Key secondary outcomes of the model included: life expectancy; discounted costs; discounted QALYs; the number of patients who died prior to discharge; the number of patients who died between discharge and one-year post-injury; and, the number of patients sent to an MTC.
The ICERs between the strategies were calculated as difference in cost / difference in QALYs. As we have a decision problem with multiple strategies, a full incremental analysis was undertaken in line with the NICE methods guide.[15] In this approach strategies are ordered by their effectiveness (measured in QALYs). Any tools that are dominated (they produce less QALYs at a higher cost than another tool) or extendedly dominated (a combination of two other tools can produce the same QALYs at a lower cost) were removed from consideration. ICERs were then calculated comparing each remaining tool, except the least effective tool, to the next least effective remaining tool.
The maximum acceptable ICER (MAICER), is the amount of money that a decision-maker is willing to pay to gain 1 additional QALY. NICE’s MAICER is usually considered to be £20,000 per QALY, but may increase to £30,000, as detailed in the NICE methods guide.[15] In a full incremental analysis, the most effective tool with an ICER below the decision maker’s MAICER is the cost-effective tool.
Model Structure and Logic
A diagram of the model is presented in Figure 1. Patients enter the model and the sensitivity and specificity of the triage tool determines whether they go to the MTC or local hospital. For patients who go to a local hospital, there is a probability that they will undergo secondary transfer to the MTC. For patients who the triage tool suggests that they go directly to the MTC, there is a chance that they will initially go to a local hospital for urgent care after which they will undergo a secondary transfer to the MTC. Any patient who goes to the MTC will gain the full benefit from MTC care, but all patients who undergo a secondary transfer will incur costs for an additional ambulance callout. Post-admission, each patient’s probability of survival within 30 days is estimated. Patients with an ISS of 16 or more and who did not go to an MTC, have a relative risk of death applied to their 30 day survival probability to reflect the poorer outcomes we expect for these patients. Patients who survive up until 30 days post-injury, have their probability of survival up to one year post-injury estimated. Again, a relative risk of death was applied to increase the probability of death for patients with an ISS of 16 or more who did not receive MTC care. Patients who survive up to one year post-injury, enter a long-term discrete event simulation in which their life expectancy is estimated using general population mortality data, increased by a hazard ratio dependent on their ISS, to estimate their expected remaining life expectancy. This model was developed in R v4.0.2.[16]
Probability of events and effectiveness of MTCs
We used the same evidence as the previously published Newgard et al economic model for the effectiveness of MTCs on patient outcomes. These studies are analyses of large cohort studies in a North American setting.[2–4] The data on the probability of death was updated to include UK data, where this was known to exist. The 2006 TARN survival prediction model was selected for use in our base case economic model, as our patient cohort did not have information on comorbidities which is required in the 2015 TARN survival equation.[10, 11]
Table 2: A summary of the parameters used in the model.
Clinical parameters
|
Parameter
|
Value
|
Source
|
Probability of patients having a transfer from a local hospital to an MTC if:
|
They were a true positive
(ISS ≥ 16 & tool positive)
|
26.6%
|
Newgard et al 2016[32]
|
They were a false negative
(ISS ≥ 16 & tool negative)
|
32.5%
|
They were a true negative
(ISS < 16 & tool negative)
|
4.3%
|
They were a false positive
(ISS < 16 & tool positive)
|
7.4%
|
Probability of death within 30 days
|
Risk equation
|
TARN[10]
|
Relative risk of death within 30 days of hospitalisation for patients with an ISS ≥ 16 who were treated at a local hospital
|
1.25
|
Newgard et al 2013[3]
|
Relative risk of death within 30 days of hospitalisation for patients with an ISS < 16 who were treated at a local hospital
|
1
|
Assumption
|
Probability of death between 30 days post-injury and 1-year post-injury for patients with an ISS ≥ 16
|
3.6%
|
Mackenzie et al. 2006[2]
|
Relative risk of death between 30 days and 1 year post-hospitalisation for patients with an ISS ≥ 16 who were treated at an local hospital
|
1.64
|
Probability of death between 30 days post-injury and 1-year post-injury for patients with an ISS < 16
|
1.7%
|
Davidson et al 2011[33]
|
Probability of death after 1 year
|
Age and gender dependant
|
ONS[34]
|
Hazard Ratio for the risk of death if someone has a suspected major trauma case with:
|
An ISS of less than 16
|
1.38
|
Newgard et al 2016[9]
Cameron et al. 2005[4]
|
An ISS of greater than or equal to 16
|
5.19
|
Utility parameters
|
Parameter
|
Value
|
Source
|
Utility for patients with:
|
An ISS of 16 or more
|
0.65
|
Ahmed et al [17]
|
An ISS of 15 or less
|
0.65
|
General population utility
|
Constant
|
0.9508566
|
Ara and Brazier[35]
|
Age
|
-0.0002587
|
Age squared
|
-0.0000332
|
Male (1 = male, 0 = otherwise)
|
0.0212126
|
Calculations
|
Age and gender matched general population utility for the Ahmed et al population
|
0.824
|
Calculated. Mean age was 61 years and 59.1% of the analysis population was male in Ahmed et al.[17]
|
Utility multipliers, relative to the utility in the general population, for patients with:
|
An ISS of 16 or more
|
0.789
|
Calculated
|
An ISS between 15 and 9
|
0.789
|
Calculated
|
An ISS of under 9
|
1
|
We assumed that these patients would have a utility equal to that of the general population
|
Cost Parameters
|
Parameter
|
Value
|
Source
|
Admission costs – base case
|
Transfers between local hospitals and MTCs
|
£252
|
Assumed to be one additional ambulance call out. NHS improvement.[23] Currency Code ASS02.
|
MTC admission, if ISS is 16 or over
|
£2,819
|
NHS improvement[22]
|
MTC admission, if ISS is less than 16 and over 8
|
£1,466
|
Treatment of a patient with blunt trauma and an ISS in the range of:
|
ISS≤9
|
£6,198
|
Christensen et al[20]
|
9<ISS≤16
|
£8,989
|
16< ISS≤25
|
£14,205
|
ISS > 25
|
£21,173
|
Treatment of a patient with penetrating trauma and an ISS in the range of:
|
ISS≤9
|
£6,501
|
Christensen et al[21]
|
9<ISS≤15
|
£6,035
|
15< ISS≤24
|
£9,453
|
24< ISS≤34
|
£12,347
|
ISS > 34
|
£16,438
|
Post discharge costs
|
Cost between discharge and 6 months post treatment
|
£1,766
|
John Nichol, Personal communication
|
Relative increase in lifetime treatment costs for patients with an ISS ≥ 16 compared to the general population
|
1.45
|
Cameron et al. 2006[25]
Delgado et al 2013[24]
|
Relative increase in lifetime treatment costs for patients with an ISS < 16 compared to the general population
|
1.25
|
Cameron et al. 2006[25]
Delgado et al 2013[24]
|
Yearly costs of NHS treatment
|
Age and gender dependent
|
Asaria 2017[26]
|
NB – distributions and the standard errors around each parameter are provided in the appendix
local hospital – local hospital; MTC, major trauma centre; ISS, injury severity score
|
Utilities
The utility parameters used in the model are provided in Table 2. Our utilities are from Ahmed et al, which is a survey in which 154 patients, whose ISS was 9 or more, completed the EQ-5D-5L questionnaire at an English MTC one year post-injury.[17] There was no evidence in this study that utility varied by ISS score. For patients with an ISS of 9 or more we applied these utilities multiplicatively to age-gender matched utilities for the UK general population.[18] For patients with an ISS of less than 9 we assumed that their injury did not have long term effects on their utility.
Costs
The costs in the model reflect English practice and are provided in Table 2. All costs are in 2017/18 prices. Costs from previous years were inflated to 2017/18 prices using the HCHS Pay and Prices inflation index.[19] Other costs incurred within the first 6 months post-injury were obtained from UK based studies and sources.[20–23][John Nicholl, personal communication] After 6 months we adopt the data reported in Delgado et al, which was a cost-effectiveness analysis of helicopter versus ground transport in the US.[24] These parameters, which is that based on data from one Canadian study, are an increase in costs for patients with a history of trauma compared to the general population.[25] We used English health care costs incurred by the general population, according to their age and gender, and the data from Delgado et al to calculate the increased long term health care costs incurred by each patient in our model.[24, 26]
Scenario analyses
A base case deterministic analysis was performed, where all parameters are set to mean values. In order to account for the uncertainty in model inputs a probabilistic sensitivity analysis (PSA) was conducted using Monte Carlo simulation to randomly sample from a distribution assigned to each model parameter (see Appendix). Multiple model runs were performed, each with independent random draws from every parameter’s distribution. ICERs were calculated from the mean expected costs and effects over all model runs. We assessed the stability of our model results with respect to the number of patients (assessed visually) and number of PSA runs (assessed using the Hatswell et al method).[27] We found that 25,000 simulated patients and 2,000 PSA runs produced stable results (see Appendix).
We conducted three scenario analyses to explore the robustness of model assumptions.
In the first scenario analysis we used the 2015 TARN survival equation and assumed that the simulated patients in our model were in the same risk category as people with missing Charlson Comorbidity Index (CCI).[11]
In the second scenario analysis, we explored the benefit of MTC care to patients with an ISS between 9 and 15 inclusive, as these patients incur costs for going to an MTC in England implying there may be a belief by payers that these patients would benefit from MTC care.
In the final set of scenario analyses we varied the cost of MTC care, as the cost of MTC care in England is reviewed regularly.