Long-run health economic model

Background

The study described in this report included a ‘within-trial’ economic evaluation to estimate the costs and effects of craniotomy compared to DC for ASDH. This enabled data taken from UK randomised trial participants to be used to estimate whether one intervention could be considered cost-effective compared to the comparator intervention. The advantage of a within-trial evaluation is that it uses data collected from randomised individuals. It also enables appropriate data to be collected prospectively. However, one issue with a within-trial analysis is that it is limited to the follow-up period of the trial. Individuals may live for many years after the conclusion of a trial. If one intervention is associated with clinical improvements, then these improvements may persist for many years. In the case of TBI, if one treatment was more effective than another, it could lead to differences in mortality between groups. It could also mean there are differences in levels of disability and morbidity, which may mean that there are long-term implications in terms of healthcare resource use, costs borne by individuals and accrued HRQoL. And this could lead to differences in results between analyses that take a shorter time frame and ones which have looked at costs and benefits further into the future. One common tool for estimating long-term costs and consequences is the decision-analytic model.

‘In the context of economic evaluation, a decision-analytic model uses mathematical relationships to define a series of possible consequences that would flow from a set of alternative options being evaluated’.38

A decision-analytic model allows for data from a variety of sources to be used in a single model to extrapolate beyond the limits of a clinical trial. Examples could include: extrapolation to a different healthcare setting; including additional relevant comparators; and increasing the time horizon of the analysis. An example of why a longer time horizon may be important was provided from an analysis of extracorporeal membrane oxygenation.39 This included both a 6-month within-trial analysis and a long-term model. The intervention had extremely high costs which were incurred at the time treatment was given. It was also found to be effective, with potential long-term consequences. Estimates of cost per QALY were £1,631,124 for the within-trial analysis and £19,252 for a lifetime model.

For the comparison of craniotomy compared to DC, there was a concern that the conclusion of the within-trial analysis could differ from a longer time horizon. This was because DC would require additional surgery and higher costs. Any potential benefits would likely accrue over a long time horizon, so there was the potential for the within-trial analysis to not capture all relevant costs and benefits. For this reason, an additional analysis looking at a long-run time horizon was planned. The aim of this component was to construct a health economic decision-analytic model to evaluate the long-term costs and effects of the interventions from the perspective of the UK NHS.

Methods

Model development

The model comprised two parts. Firstly, a decision tree was used to allocate individuals to different model states based on the results of the within-trial analysis. The model states correspond to the outcomes in the trial, with individuals being classified as favourable or unfavourable based on the GOSE at 12 months. Unfavourable includes the dead state. The structure of the decision tree model is given in Figure 5. The square node represents the choice between the two interventions. In either case, individuals can have a favourable or unfavourable outcome at 12 months. For those who have an unfavourable outcome, individuals can either be alive or dead. All individuals who have a favourable outcome at 12 months are assumed to be alive at 12 months. The decision tree model covers the 12-month period from randomisation to the end of follow-up. And all costs and effects in this time are taken from the within-trial analysis, Chapter 5.

FIGURE 5 Decision tree structure used in the long-run health economic model. (Figure not reproduced here; see the original article.)

The model also comprised a long-run Markov model. This is shown in Figure 6. At the end of year 1, individuals are classified as in Figure 5. All those with a favourable outcome at 12 months are alive. For those with an unfavourable outcome, individuals can either be unfavourable and alive, or they can be in dead. Therefore, the Markov model has three states: favourable outcome; unfavourable and alive; and dead. At the start of the Markov process (end of year 1), the individuals in the dead state would be those who were classified as having an unfavourable outcome and who were dead at the end of follow-up. In the long-run model, individuals can transition to the dead state from both ‘favourable outcome’ and the ‘unfavourable and alive’ states. Additionally, individuals in the favourable outcome state can either remain in that state or transition to the ‘unfavourable but alive’ state, that is, the model allows for health to deteriorate. Similarly, individuals in the ‘unfavourable and alive’ state can either remain in that state or transition to the ‘favourable outcome’ state, that is, individuals can improve. The dead state is what is termed an absorbing state – individuals in the model can enter the state, but they cannot leave it.

FIGURE 6 Structure of the long-run Markov model. (Figure not reproduced here; see the original article.)

The model was developed in collaboration with a clinical expert (Harry Mee), who advised on the structure and data within the model. It was also informed with reference to a published model in a similar area by Behranwala et al.40 These authors presented two decision tree model structures, a simple decision tree based on outcomes of unfavourable or favourable, and a more complex tree structure with outcomes based on the individual GOSE scores. However, these authors only presented analyses over a 1-year time frame. The decision tree model used in the current analysis follows a similar structure to the simpler decision tree presented in Behranwala et al.; however, the model presented here specifically splits the unfavourable state into alive and dead to correspond with health states in the Markov model.

Characteristics of the model

The decision tree model uses data wholly taken from the within-trial analysis presented in this report (Chapter 5). It is used to estimate the accrued costs and QALYs for the two interventions in year 1. It is also used to assign numbers of individuals to each of the Markov states at the start of the Markov model. The decision tree model covers a period of 1 year. The Markov model covers 39 years. This gives a total duration of the model of 40 years. The Markov model has a cycle length of 1 year. It is a cohort model with an assumed cohort size of 1000. All individuals are assumed to have a starting age equal to the mean age for the sample used in the economic evaluation; this was 52 years of age. A duration of 40 years was chosen as this was assumed to be sufficient time for the majority of the cohort to enter the dead state. As the model covers a time span of 40 years, it is important to allow for the differential timing of costs and benefits. Discounting is not used in the first year, which is the convention in economic analysis and was the approach taken in the within-trial analysis. In subsequent years, both costs and benefits (QALYs) are discounted at an annual rate of 3.5%, as recommended by NICE.18 The proportion who are male was also based on the UK sample and was 79% (see Table 24). In a Markov model, all events, such as a transition to another state, are assumed to occur either at the beginning or the end of a cycle. Transitions in the real world would occur throughout the cycle. Assuming events happen either at the beginning or end of a cycle, it can generate results that may differ from those that would have been if events can happen at any point in the cycle. A half-cycle correction assumes that transitions occur, on average, half-way through the cycle and therefore approximates the situation where transitions happen continuously.41 A half-cycle correction was used in the Markov model.

Both the decision tree model component and the Markov model component were modelled using a probabilistic sensitivity analysis (PSA) in Microsoft Excel^® (Microsoft Corporation, Redmond, WA, USA). In this process, rather than using a fixed value for a parameter, such as the cost of spending a year in the favourable outcome state, a random draw from a distribution with specified characteristics is used. This allows sampling uncertainty to be allowed for in the model and will give more realistic results. The model is then rerun for a large number of simulations. Model results, such as means and 95% percentiles, are then taken from these simulations.

Model parameters

The parameters used to build the decision tree and Markov models are given in Table 34. Parameters can be divided into several categories. These are probabilities, QALYs or utilities, and costs. Where possible, parameters were assigned a distribution. The appropriate distribution used in each case varies with the characteristics of each parameter. Also provided is the distribution used, characteristics of this distribution and notes detailing the source of the data.

For the decision tree model, probabilities were used to determine the numbers of individuals allocated to each branch of the model after each chance node (chance nodes are represented as round nodes on the decision tree presented). For the Markov model, transition probabilities were required. These are the probabilities that an individual transitions from one state to another and are represented by the arrows in Figure 6. The probabilities used in the model are given in Table 34.

The probability of a favourable outcome with DC was taken from the within-trial analysis (Table 31). All probabilities included in the model would be constrained to have values between zero and one; for this reason, directly estimated probabilities were modelled using beta distributions. To infer the probability of a favourable outcome with craniotomy, we used the probability for DC multiplied by the estimated relative risk for craniotomy as compared to DC. The relative risk was derived from the OR presented in Table 33. This relative risk was modelled using a log-normal distribution. The probability of death in the first year was taken from the within-trial analysis. The QALYs generated in the first year in the DC group were taken from Table 30. As the QALY is for 1 year, it would have a maximum value of 1 (utility score of 1 for 1 year). Negative values of the QALY would also have been possible. These properties do not match commonly used distributions. So, it is common with QALYs or utilities to model them using a transformed distribution D, where D = 1-QALY.38 This then has a minimum value of zero, with scores above 1 possible, and this was modelled using a gamma distribution. The costs in the first year for DC were taken from the within-trial analysis (see Table 29). To estimate the costs in the craniotomy arm, we adjusted the DC costs by the estimated cost difference for craniotomy (see Table 32). The cost difference was modelled using a normal distribution. Uncertainty in cost estimates are derived from differences in resource use between participants; we did not assume uncertainty in unit cost estimates.

For the Markov model, we were unable to find long-run data on the transition of individuals between the favourable and unfavourable states. Therefore, these transitions were modelled with a value of zero, that is, assuming that individuals remained in the state they were in at the 1-year follow-up. However, these parameters were included in the model to allow for future updating should data become available. These assumptions were also varied in a SA to show the effects of allowing state transitions between favourable and unfavourable states. The utility value assigned to being in each state for the two interventions was estimated from the 12-month utility values from the within-trial analysis (see Table 30). As cycle lengths are 1 year in the Markov model, the utility values correspond to the QALYs generated per year. The distribution for utilities was modelled in the same way as QALYs, that is, with a transformed variable being created, and this transformed variable was modelled using a gamma distribution. Again, we did not find credible long-run data for the future costs of individuals with ASDH treated with surgery. The 1-year costs for those alive at 1 year, excluding inpatient costs, were used as a proxy for these. These values are not reported in Chapter 5 and were obtained from the within-trial analysis (SP – personal communication). Again, these were modelled using gamma distributions, and uncertainty would have originated from differences in resource use.

For the first 2 years of the Markov model – that is, years 2 and 3 after suffering the ASDH – an annual probability of mortality was used based on data suggesting that for a population of blunt trauma survivors, the death rate was 0.089 in the 2-year period, covering the second and third years after injury.42 This was transformed into an annual probability of 0.0455 for the unfavourable group only, using a formula to convert rates to probabilities from a published source.38 For the favourable group and for all other cycles of the model for the unfavourable group, mortality was estimated based on age- and sex-adjusted population estimates for England and Wales for 2020.43

Analysis

The model was constructed in Microsoft Excel. The PSA was repeated for 5000 samples. Mean costs and QALYs were calculated for the simulated cohort. To evaluate the effects of uncertainty, a CEAC was created. This shows the probability that any intervention would be cost-effective at varying valuations of a unit of outcome – in this case, cost per QALY.

Sensitivity analysis

To show the effects of varying model parameters on results, we conducted a series of deterministic one-way SAs. In these analyses, parameters were varied in isolation between defined limits, and the effects on the model ICERs were noted. The following parameters were varied: OR of favourable outcomes with craniotomy compared to DC; QALY difference in year 1; cost difference in year 1; probability of transition from favourable to unfavourable (for both interventions); probability of transition from unfavourable to favourable (for both interventions); utility values for favourable and unfavourable for both interventions; yearly state costs for favourable and unfavourable for both interventions. For transitions between favourable and unfavourable states, an arbitrary range of 0–0.05 was used. For all other variables, we either used 95% CIs or 95% percentiles from the distributions.

Results

The results of the probabilistic SA are given in Table 35. These are estimates of QALYs accrued over a 40-year period, so estimated QALYs are much higher than for the within-trial analysis. The craniotomy arm generates an estimate of 3.2 additional QALYs, with an additional cost of £10,715. This gives an ICER of £3352.

A scatter plot of the 5000 separate simulations is given in Figure 7. Each point represents the individual results of each of the 5000 simulations. From Figure 7, it can be seen that craniotomy generated additional QALYs in almost all cases. This was because more individuals were in the favourable health state for this intervention, and the favourable health state had a higher utility value and hence generated more QALY for each individual spending a year in that state. It can also be seen that there are more points above the X-axis than below it. Generally, simulations, therefore, suggested a higher cost for craniotomy as compared to DC. This was because there was a higher cost associated with each year in the favourable and unfavourable health states than for DC. This difference was sufficient to offset the higher year 1 costs for the DC intervention, as shown in the within-trial analysis.

FIGURE 7 Incremental cost-effectiveness plane for craniotomy compared to DC. (Figure not reproduced here; see the original article.)

The CEAC for craniotomy compared to DC is shown in Figure 8. This shows the probability that craniotomy is cost-effective compared to DC at different values of a QALY. At a value of a QALY of £20,000, there is a 94% probability that craniotomy is cost-effective compared to DC. This is similar to the ‘within-trial’ results, where craniotomy is also given a high probability of being cost-effective at £20,000 per QALY (87%).

FIGURE 8 Cost-effectiveness acceptability curve for craniotomy compared to DC. (Figure not reproduced here; see the original article.)

Sensitivity analyses

The results of the various deterministic one-way SAs performed are given in Table 36. The model results were particularly sensitive to values used for some of the state transitions between favourable and unfavourable. Also important to the model results were long-term costs associated with being in the favourable and unfavourable states.

Discussion

Main findings

The results of the health economic model are similar to those of the ‘within-trial’ analysis and would lead to the same conclusions. Compared to DC, craniotomy generates increased numbers of QALY, with an additional 3.2 QALYs per person generated over the 40-year time horizon of the model. The ICER was £3352 per QALY; this is clearly below the NICE threshold of £20,000–30,000 per QALY as the point at which interventions can be considered cost-effective. Uncertainty analysis suggests a 94% probability of the intervention being cost-effective at £20,000 per QALY.

Comparison with the within-trial analysis

The original rational for including a modelling component in addition to the within-trial analysis (see Chapter 5) was to allow for longer-term considerations should these be relevant. As mentioned in the introduction to this chapter, there may be cases where an intervention has a much larger ‘upfront’ cost than a comparator but may generate advantages such as reduced mortality and/or increased quality of life that may persist over the long term. In these cases, a within-trial analysis may not give a true picture of the economic efficiency of that intervention. In this situation, a long-run decision-analytic model would be required.

However, the within-trial analysis shows that this was not the case in this trial. Craniotomy had a lower cost and generated more QALYs, and hence dominated DC. For this reason, the long-term model does not alter the conclusions drawn from the within-trial analysis. The main conclusion from the longer-term model is the same, being strongly suggestive of economic advantages for craniotomy. In terms of uncertainty, the CEACs suggest less uncertainty compared to the within-trial analysis, with a probability of being cost-effective of 94% at a value of £20,000. This suggests the long-run model is consistent with the conclusions of the within-trial analysis. However, unlike the within-trial analysis, it was not cost saving, with an expected additional discounted cost of £10,715 per person over the 40-year run of the model.

Study limitations

The long-run economic model draws heavily from the within-trial analysis, so the study limitations outlined in Chapter 5 also apply to this work. The main additional limitation relating to the model concern the paucity of reliable long-term follow-up data from patients who have received either craniotomy or DC for ASDH. Firstly, we did not have credible data on long-term transition between the favourable and unfavourable but alive health states. If these are similar for the two interventions, then conclusions would not be altered. In the case where transitions between these states were very different in the long term for the two interventions, then it would be possible that conclusions would be altered. SA performed on these variables suggests that long-term transition probabilities are likely to be important to model results. In terms of utilities, we estimated these based on the values of the EQ-5D-5L at 12 months from this trial. And these were assumed to remain constant over time. In reality, these would likely change, particularly if there were gradual health improvements over time. Similarly, mortality was assumed to be the same as the population of England and Wales, except for the first year, where mortality was high, and years 2 and 3, where a small increase in mortality was assumed. This may understate long-term mortality, particularly in the unfavourable but alive health state, and hence the estimates of total QALYs generated may be overstated. Finally, to estimate long-term costs, we used the within-trial estimate of non-inpatient stay costs in the 1-year follow-up as an estimate of long-run costs in the Markov model. These were higher in the craniotomy intervention than for DC, meaning that long-term costs were higher for craniotomy. However, these results were based on very small numbers, with 24 participants having data in each intervention group for the unfavourable but alive health state. For the favourable health state, there were 48 and 34 participants who had these data in the craniotomy and DC interventions, respectively. This means these estimates are likely to be subject to high levels of uncertainty. Again, one-way SA (see Table 36) suggests values for long-term costs are likely to be important for model conclusions. Also, there is no clear reason to conclude these costs would be constant over time. Additionally, there were numbers of individuals in the DC arm who had not had their reconstructive surgery by the 12-month follow-up. If these individuals went on to have this surgery in subsequent years, it would affect the cost results obtained in the model and may well lead to different estimates of cost.

Implications for future work

In this trial, the within-trial health economic analysis was sufficient for informing the efficient use of healthcare resources. However, in the treatment of ASDH, it is likely that evaluations of future interventions may cover situations where one intervention is associated with increased short-term costs and be more effective than a comparator. For good decision-making in these cases, it would be important to have reliable and credible long-term data to inform long-term modelling. This model may be able to be incorporated into the cranial reconstruction registry, a prospective registry following patients’ trajectory of recovery after decompression and how the cranioplasty influences such recovery. Being able to closely monitor healthcare resources will be an invaluable addition to this resource.

Conclusion

The results from a long-run economic model are consistent with the results of the ‘within-trial’ economic evaluation. To develop a reliable model on the longer-term costs and benefits of treatments for ASDH, improved data on long-term costs and effectiveness are needed.