Innovation in unruptured intracranial aneurysm coiling: At which price or efficacy are new technologies cost-effective?

Background Unruptured intracranial aneurysms (UIA) are increasingly being treated by endovascular coiling as opposed to open surgical clipping. Unfortunately, endovascular coiling imparts an approximate 25% recanalization rate, leading to additional procedures and increased rupture risk. While a new health technology innovation (HTI) that reduces this recanalization rate would benefit patients, few advancements have been made. We aim to determine whether cost-effectiveness has been a barrier to HTI. Methods A probabilistic Markov model was constructed from the healthcare payer perspective to compare standard endovascular treatment of UIA to standard treatment plus the addition of a HTI adjunct. Costs were measured in 2018 USD and health outcomes were measured in quality-adjusted life-years (QALY). In the base case, the HTI was a theoretical mesenchymal stem cell therapy which reduced the aneurysm recanalization rate by 50% and cost $10,000 per procedure. All other model inputs were derived from the published scientific literature. Results Based on the model results, we found that for a given HTI price (y) and relative risk reduction of aneurysm recanalization (x), the HTI was always cost-effective if the following equation was satisfied: y ≤ 20268 ∙ x, using a willingness-to-pay threshold of $50,000 per QALY. The uncertainty surrounding whether an aneurysm would recanalize was a significant driver within the model. When the uncertainty around the risk of aneurysm recanalization was eliminated, the 10-year projected additional benefit to the United States healthcare system was calculated to be $113,336,994. Conclusion Cost-effectiveness does not appear to be a barrier to innovation in reducing the recanalization rate of UIA treated by endovascular coil embolization. Our model can now be utilized by academia and industry to accentuate economically feasible HTI and by healthcare payers to calculate their maximum willingness-to-pay for a new technology. Our results also indicate that predicting a patient’s baseline risk of aneurysm recanalization is a critical area of future research.


Supplement 5
Model simulation methodology 23 Optimizing number of iterations per simulation 23 Fig S5. References 31 1

Introduction
Background and objectives 3 Provide an explicit statement of the broader context for the study.

3-4
Present the study question and its relevance for health policy or practice decisions. 4

Methods
Target population and subgroups 4 Describe characteristics of the base case population and subgroups analyzed, including why they were chosen.

4-5
Setting and location 5 State relevant aspects of the system(s) in which the decision(s) need(s) to be made.

4-5
Study perspective 6 Describe the perspective of the study and relate this to the costs being evaluated.

4-5
Comparators 7 Describe the interventions or strategies being compared and state why they were chosen.

4-5
Time horizon 8 State the time horizon(s) over which costs and consequences are being evaluated and say why appropriate.
4-5, Supp. 15 Discount rate 9 Report the choice of discount rate(s) used for costs and outcomes and say why appropriate. 4 Choice of health outcomes 10 Describe what outcomes were used as the measure(s) of benefit in the evaluation and their relevance for the type of analysis performed.

Measurement of effectiveness 11a
Single study-based estimates: Describe fully the design features of the single effectiveness study and why the single study was a sufficient source of clinical effectiveness data.

NA 11b
Synthesis-based estimates: Describe fully the methods used for identification of included studies and synthesis of clinical effectiveness data.

5, Supp. 9-14
Measurement and valuation of preference based outcomes 12 If applicable, describe the population and methods used to elicit preferences for outcomes.

5, Supp. 9-14
Estimating resources and costs 13a Single study-based economic evaluation: Describe approaches used to estimate resource use associated with the alternative interventions. Describe primary or secondary research methods for valuing each resource item in terms of its unit cost. Describe any adjustments made to approximate to opportunity costs. Incremental costs and outcomes 19 For each intervention, report mean values for the main categories of estimated costs and outcomes of interest, as well as mean differences between the comparator groups. If applicable, report incremental cost-effectiveness ratios.

25
Characterizing uncertainty 20a Single study-based economic evaluation: Describe the effects of sampling uncertainty for the estimated incremental cost and incremental effectiveness parameters, together with the impact of methodological assumptions (such as discount rate, study perspective).

NA 20b
Model-based economic evaluation: Describe the effects on the results of uncertainty for all input parameters, and uncertainty related to the structure of the model and assumptions.

8-10, 25
Characterizing heterogeneity 21 If applicable, report differences in costs, outcomes, or costeffectiveness that can be explained by variations between subgroups of patients with different baseline characteristics or other observed variability in effects that are not reducible by more information.

Discussion
Study findings, limitations, generalizability, and current knowledge 22 Summarize key study findings and describe how they support the conclusions reached. Discuss limitations and the generalizability of the findings and how the findings fit with current knowledge.

Markov Model Structure
Following the index coiling procedure, patients enter the Coiled state where their aneurysm is assumed to be treated. During the coiling procedure, complications may not occur, leading to good post-operative function (defined as modified Rankin Score (mRS)=0), or complications may occur which lead to mild disability (defined as mRS=1-2), moderate to severe disability (defined as mRS=3-5), or death. Therefore, there is a separate Coiled state for each functional status (good, mild disability, and moderate to severe disability). While in Coiled, patients may remain in place or they may transition to one of three other states. Patients may develop a recanalization that is treated and transition to Recoiled, develop a recanalization that is not treated and transition to Recanalized, or develop a de novo aneurysm that is treated and transition to De Novo. These three states also depend on functional disability, where patients can only transition from Coiled to states with the same functional status. For example, a patient that is in CoiledMild would transition to RecoiledMild as opposed to RecoiledGood. Patients may only transition to Recoiled or Recanalized within 6 years (12 cycles) of a coiling procedure. After this time, the rate of aneurysm recanalization drops to 0%, however, patients may still develop a de novo aneurysm.
From the Recoiledi and De Novoi states, after having their aneurysm (re)coiled, patients transition to a new Coiled state with the subscript i+1. However, as in the index procedure, on account of procedural complications, patients may again develop deficits and enter a state with lower functional status. In this model, patients may maintain or decline in functional status but cannot improve.
While in Recanalized, patients may remain in place, or develop a de novo aneurysm and transition to De Novo. Alternatively, since these patients have a recanalized unprotected aneurysm, although rare, they may develop an aneurysmal subarachnoid hemorrhage (aSAH). Following an aSAH, patients may die immediately and transition directly to Dead. Alternatively, patients transition to the aSAH state, and from there may die in hospital and transition to Dead, or may survive and transition to Post SAH. As in the case of coiling procedures, aSAH can cause a permanent decrease in a patient's functional status. Therefore, there is a separate state of Post SAH for each functional status (good, mild disability, and moderate to severe disability). Once in Post SAH, patients remain in this state for the remainder of their lives.
After patients transition from their fourth coiling procedure to Coiled4, they are no longer offered aneurysmal treatment in this model (see Supplement 4, Assumption S4.05 for justification). Therefore, if they develop a de novo aneurysm or a recanalization, further treatment is not pursued. However, patients in both these states (Recanalized4 and De Novo4) will still be at risk of developing an aSAH, since they have an unprotected intracranial aneurysm. Patients in this model may die as a result of a complication from an endovascular coiling procedure, an aSAH, or from non-aneurysmal causes. Rates for non-aneurysmal causes of death are based on age-specific population statistics [3]. Patients may therefore transition from any state to Dead, however, these arrows have been removed by convention from Fig 1 and S2.01 for visual simplicity.

Supplement 3
To identify the relevant articles used to derive the model parameters, a MEDLINE search was performed using the following search terms: Preference was given to articles with a higher-level study design including meta-analyses and randomized controlled trials. More recently published articles were also preferred. Once parameters were derived, they were screened by two independent experts in neurosurgery and neurointerventional radiology (APM, ME) for face validity. The following are detailed derivations of the model parameters and their distributions.
Variable 1: Probability of developing mild disability (mRS=1-2) from a coiling procedure Variable 2: Probability of developing moderate to severe disability (mRS=3-5) from a coiling procedure These transitional probabilities were derived from the meta-analysis by Lanterna  After converting from percentages to probabilities, this resulted in standard errors of 0.005944 and 0.002730 for mild disability and moderate to severe disability respectively. Both variables were drawn from beta distributions, a common distribution used for probabilities in economic analyses, as it inherently bounds the probability between 0 and 1. Values for a and b for each beta distribution were calculated using the following formulas: .03: where µ represents the deterministic mean and s represents the SE for each variable.
Variable 3: Probability of death from a coiling procedure This transitional probability was derived from the meta-analysis by Naggara et al. [5]. This article found that 59 of 5044 (1.2%) patients died while undergoing an endovascular coiling procedure. With a random-effect weighted average, this rate was found to be 2.0% (99%CI: [1.5, 2.6]). Using the 99%CI, the SE was derived with the following formula: .04: *+ = -. − 0. 5.15 where -. and 0. represent the upper and lower bound of the 99%CI respectively.
After converting from a percent to a probability, this resulted in a SE of 0.00213592. This variable was drawn from a beta distribution, a common distribution used for probabilities in economic analyses, as it inherently bounds the probability between 0 and 1. The values for a and b for the beta distribution were calculated using Equations S3.02 and S3.03.

Variable 4:
Probability of developing a recanalization of a coiled aneurysm Variable 5: Probability of a coiled aneurysm requiring re-treatment These transitional probabilities were derived from the meta-analysis by Naggara et al. [5]. The SE for Variable 4 was therefore estimated to be 0.03592446. These variables were drawn from beta distributions, a common distribution type used for probabilities in economic analyses, as it inherently bounds the probability between 0 and 1. The values for a and b for each beta distribution were calculated using Equations S3.02 and S3.03. Naggara et al., however, did not provide clear time intervals for when these recanalizations or retreatments occurred. Therefore, the retrospective cohort study by Ries et al. which looked at the long-term outcomes of coiled UIA, was used to estimate this time interval [6]. Ries et al. found recanalizations occurred between 0 and 77 months from the index coiling procedure. Since our cycle length was 6 months and the majority of recanalizations occurred early in the follow-up period, this interval was approximated at 72 months (12 cycles). The temporal distribution of the recanalizations was not provided and therefore assumed to be uniform. After 12 cycles, the recanalization rate was assumed to be 0. Once these variables were calculated, they were converted to a per-cycle probability using the following formula: .06: where D is the transitional probability and > is the timeframe in number of cycles for the original transitional probability.

Variable 6: Probability of developing a de novo aneurysm
This transitional probability was derived from the meta-analysis by Giordan et al. [7]. This article found that 62 of 2219 (0.6%, 95%CI: [0.35, 0.88]) patients per year with a history of an UIA developed a de novo aneurysm. Using the 95%CI, the SE was derived using Equation S3.01. After converting from a percent to a probability, this resulted in a SE of 0.002995513. This variable was drawn from a beta distribution, a common distribution used for probabilities in economic analyses, as it inherently bounds the probability between 0 and 1. The values for a and b for the beta distribution were calculated using Equations S3.02 and S3.03. Once this variable was calculated, it was converted into a per-cycle probability using Equation S3.06, where > = 2.
Variable 7: Probability of having an aSAH with an untreated aneurysm This transitional probability was derived from the meta-analysis by Greving et al. [8]. This article found that 230 of 8382 patients suffered from a rupture of their known UIA, over 29,166 patient-years. This resulted in an annual rupture risk of 1.4% (95%CI: [1.1, 1.6]). Using the 95%CI, the SE was derived using Equation S3.01. After converting from a percent to a probability, this resulted in a SE of 0.001275. This variable was drawn from a beta distribution, a common distribution used for probabilities in economic analyses, as it inherently bounds the probability between 0 and 1. The values for a and b for the beta distribution were calculated using Equations S3.02 and S3.03. Once this variable was calculated, it was converted into a per-cycle probability using Equation S3.06, where > = 2.
Variable 8: Probability of death from an aSAH prior to reaching hospital This transitional probability was derived from the meta-analysis by Huang et al. [9]. This article found that 578 of 3832 (12.4%, 95%CI: [11,14]) patients died following an aSAH prior to reaching hospital. Using the 95%CI, the SE was derived using Equation S3.01. After converting from a percent to a probability, this resulted in a SE of 0.007653. This variable was drawn from a beta distribution, a common distribution used for probabilities in economic analyses, as it inherently bounds the probability between 0 and 1. The values for a and b for the beta distribution were calculated using Equations S3.02 and S3.03.
Variable 9: Probability of death from an aSAH after reaching hospital This transitional probability was derived from a National Inpatient Sample (NIS) Registry retrospective cohort study by Qureshi et al. [10]. This article found that 12,797 of 48,389 (26.5%) patients who reached hospital alive following an aSAH died during their hospital admission. The SE for this variable was not provided and therefore calculated to be 0.002001, using method of moments and the following formula: .07 where 2 = 12,797 and 7 = 35,592.
This variable was drawn from a beta distribution, a common distribution used for probabilities in economic analyses, as it inherently bounds the probability between 0 and 1.
Variable 10: Probability of developing mild disability (mRS=1-2) from an aSAH after reaching hospital Variable 11: Probability of developing moderate to severe disability (mRS=3-5) from an aSAH after reaching hospital These transitional probabilities were derived from a NIS Registry retrospective cohort study by Qureshi et al. [10] in conjunction with a systematic review by Hop et al. [11]. Qureshi [13]. Since the IQRs were provided in place of the SEs, we estimated the SE using the following formula: .08: *+ = K LMN 1.35 which assumes the distribution is normal.
Because we had to assume a normal distribution, we drew these variables from a truncated normal distribution, bounded by 0 and four times the SE. In order to ensure that Variable 12 remained the least expensive while Variable 14 remained the most expensive when converting to a probabilistic model, we follow a Dirichlet style approach. Variable  These healthcare costs were derived from a contemporary stroke cohort of 958 patients and calculated in the SWIFT-PRIME Trial costs analysis by Shireman et al. [14]. This article reported annual healthcare costs by patients' 90-day mRS in 2015 USD. Therefore, for each variable, the cost was calculated by taking a relative weighted average of costs for the relevant mRS using the following formula: . 10: where OPQR 0+ is the cost for Variable >, XN* 78 is the lowest mRS score possible as Variable > is defined, XN* 98 is the highest mRS score possible as Variable > is defined, OPQR 1 is the annual healthcare cost for a patient with mN* = Y, and U 1 is the number of patients with mN* = Y.  [15]. This article found that among 3,844 respondents, their average utility per year as measured by the EQ-5D by age in years was: 45-54: 0.87, 55-64: 0.85, 65-74: 0.86, 75: 0.84. All had a SE of 0.01. The appropriate utility was selected based on the age of patients at each cycle of the model. Variable 20 and 21 were derived from the systematic review by Post et al. [16]. This article found that based on the Time-Trade-Off method, the mean utility for patients with a stroke causing mild disability was 0.72 (Range: [0.71, 0.81]) and with a stroke causing moderate to severe disability was 0.41 (Range: [0.37, 0.71]). Since the ranges were provided in place of the SEs, we estimated the SE by assuming a normal distribution and using the following formula: SEs were therefore calculated to be 0.025 and 0.085 for variables 20 and 21 respectively. Variables 19 to 21 were drawn from truncated normal distributions bounded by 0 and 1. To preserve the relative order of utilities among Variables 19 to 21, the Dirichlet style methodology described for Variables 12 to 14 was followed.

Variable 22: Utility lost from living with the knowledge of having an untreated aneurysm
This decrease in utility was derived from the prospective cohort study by van der Schaaf et al. [17]. The article found using the EQ-5D that patients who developed a recurrent or de novo aneurysm reported a utility which was on average 0.07 (95%CI: [-0.01, 0.15]) lower than matched patients who did not develop a recurrent or de novo aneurysm. The SE was calculated to be 0.04082 using Equation S3.01. Variable 22 was drawn from a beta distribution, a common distribution used for disutilities in economic analyses, as it is inherently bounded between 0 and 1. The values for a and b for this distribution were calculated using Equations S3.02 and S3.03. Patients in the model who had an untreated aneurysm including all Recanalized states as well as all De Novo4 states would experience this disutility. Additionally, all patients undergoing treatment of a de novo or recanalized aneurysm, including all Recoiled states and all remaining De Novo states, would also experience this disutility, however, once their aneurysm was treated the disutility would no longer apply.
Variable 23: Utility for a patient that has an aSAH The utility of patients actively having an aSAH was not found in the published scientific literature. Therefore, we approximated this to be equivalent to the utility associated with moderate to severe disability (Variable 21). In the probabilistic model, Variable 23 and 21 are always equal.

Baseline Mortality Rate:
The baseline rate of mortality was taken from the US National Centre for Health Statistics' CDC WONDER Online Database and compiled from the 57 vital statistics jurisdictions through the Vital Statistics Cooperative Program [3]. This data spanned years 1999 to 2019 and was stratified by age. Both mortality rates as well as SEs by age were extracted. Baseline age-specific mortality rates were drawn from beta distributions, a common distribution type used for probabilities in economic analyses, as it inherently bounds probabilities between 0 and 1. The values for a and b for each beta distribution were calculated using Equations S3.02 and S3.03. For patients in a state that contained an aneurysmal-related cause for mortality, for example dying from a coiling procedure in De Novo, the overall mortality rate for that state was always calculated by summing the baseline age-specific mortality rate with the aneurysmal-related mortality rate.

Other Parameters:
The following parameters were not taken from the published scientific literature, rather they were calculated as a function of other parameters in the model. This approach was taken to ensure that the sum of the transitional probabilities associated with each state always equalled 1.
Variable O1: Probability of maintaining pre-procedural functional status following a coiling procedure This transitional probability was derived using the following formula: If pre-procedure status is good (mRS=0) Table 1), and ZA<[ 8 is the age specific baseline mortality rate.  Table 1), and ZA<[ 8 is the age specific baseline mortality rate.  Table 1), and ZA<[ 8 is the age specific baseline mortality rate.
Variable O4: Probability of reaching hospital alive following an aSAH This transitional probability was derived using the following formula: .17: D B = 1 − ; C where D B is the transitional probability of reaching hospital alive following an aSAH and ; + is Variable > (see Table 1).
Variable O5: Probability of having good functional status (mRS=0) following an aSAH, given patient reached hospital alive This transitional probability was derived using the following formula: is the transitional probability of having good functional status (mRS=0) following an aSAH, given patient reached hospital alive, ; + is Variable > (see Table 1), and ZA<[ 8 is the age specific baseline mortality rate.

Supplement 4
The following is a list of what is felt to be the main assumptions of the model and their respective justifications.

Assumption S4.01
The model was run for 30 years. Justification: Instead of running the model for the lifetime of patients, we followed patients for 30 years and stopped the model when all patients were 75. It was felt that after 30 years, all the effects of the HTI would have been realized. As patients age, especially beyond 75, we expect that their other medical conditions would begin to play a larger role in their overall functional status and life expectancy. Moreover, as patients become more advanced in age, they may no longer be candidates or wish to pursue endovascular therapy. Accounting for all these factors would be extremely complex yet would act equally on both treatment arms, thus it would have minimal impact on the ICER or study conclusions. We therefore chose to focus the model on ages 45 to 75, when patients would most likely be offered endovascular treatment and their other medical comorbidities play less of a role in their overall functional status.

Assumption S4.02
In this model, all de novo aneurysms that are identified are treated. Justification: Because we were unable to estimate on an individual basis which aneurysms would be treated and which would not, and furthermore because we had no objective way to estimate the risk of rupture for aneurysms that were not offered treatment, we chose to have all de novo aneurysms treated. This helped simplify the model and keep the number of health states manageable. We felt justified in making this assumption since it affects each treatment arm equally and thus does not impact the ICER or conclusions of this analysis.

Assumption S4.03
Aneurysms are not clipped in this model, only coiled. Justification: For the index procedure specifically, this assumption is clearly justified given our population of interest consists only of patients undergoing coil embolization of their UIA, as these are the only patients that can receive the HTI. If a coiled aneurysm recanalizes, both coiling and surgical clipping have been shown to be equally effective treatments [18]. To help simplify the model, we have chosen to use only coiling procedures effectively limiting the number of health states. If clipping were included in the model, these patients would have a lower recanalization rate, however, the fraction of aneurysm that would be clipped would be minimal and would therefore not affect the overall findings of the study. Conversely, a reasonable proportion of de novo aneurysms may receive surgical clipping. Including clipping of de novo aneurysms in the model, however, would affect each treatment arm equally and have no impact on the ICER or study conclusions. Clipping of de novo aneurysms was therefore left out to reduce the number of health states and avoid unnecessary model complexity.

Assumption S4.04
Coiling procedures do not fail in this model. Justification: 10.3% of coiling procedures do not result in complete aneurysm occlusion [5]. It is unclear, however, if the risk of rupture for these aneurysms is similar to completely occluded aneurysms that subsequently recanalized. Including partially treated coiled aneurysms would dramatically increase the number of health states and complexity in the model. Because we have no reason to suspect the HTI would affect the rate of partial occlusion when coiling UIA, including this in the model should affect both treatment arms equally and therefore have no impact on the ICER or study conclusions.

Assumption S4.05
Patients are only offered at most 4 endovascular coiling procedures in this model. Justification: Each additional endovascular procedure added 48 new health states to the model, therefore we limited the number of endovascular procedures to 4 to keep the number of health states manageable. While it is possible that a patient may undergo more than 4 endovascular coiling procedures, it is extremely uncommon. In looking at long-term follow-up data for patients with coiled UIA, Ries et al. found 0 patients that underwent retreatment 4 or more times and only 3 of 342 patients underwent retreatment 3 times [6].

Assumption S4.06
All de novo and recanalized aneurysms in this model are identified and either coiled or managed conservatively; none present as an aSAH. Only known unprotected aneurysms can rupture in this model. Justification: A small proportion of the recanalized or de novo aneurysms would likely have presented with aSAH prior to diagnosis in a real clinical setting. This proportion would depend on the frequency of patient follow-ups and neurovascular imaging, as well as the waiting time for elective endovascular coiling procedures. Practice patterns vary significantly for both these metrics. Given the average aneurysm rupture risk is 1.4% per year [8] and the amount of time a patient lives with an undiagnosed new or recanalized aneurysm is likely short, including this in the model would add significant complexity without having a large effect on the model results. Furthermore, removing this assumption would result in better outcomes for the HTI arm, as these patients develop fewer recanalizations and would therefore be less at risk of living with an undiagnosed unprotected aneurysm.

Assumption S4.07
Aneurysms in this model can only recanalize within 6 years of coiling and during this time, the recanalization rate is constant. After the 6 years, if they have not recanalized, aneurysms are considered permanently cured. Justification: In a long-term follow-up study of coiled UIA by Ries et al., recanalizations did not occur more than 77 months following the index coiling procedure, with angiographic follow-up for some patients as long as 132 months [6]. Recanalizations happened closer to the time of the index procedure, with an average of 17.9 months. Given most recanalizations occur prior to 72 months, we felt justified rounding the recanalization window down to 72 months as opposed to 78 (given our cycle length was 6 months). Moreover, because we did not have detailed data on how the recanalization rate changes over time, we assumed a uniform distribution over the 72 months. We know that most recanalizations occur earlier on in the follow-up period, however, given our discount factor is 1.5% the additional delay in costs and QALY this assumption introduces should cause only minimal effects on the ICER.

Assumption S4.08
When an aneurysm is recoiled in this model, the recanalization rate is the same as for the index coiling procedure. Justification: It is possible that the recanalization rate of aneurysms that are recoiled is different from UIA coiled for the first time. In the study by Ries et al., of the 342 patients with coiled UIA, 33 underwent re-treatment. Of these 33, 4 (12%) underwent retreatment twice, and 3 (9%) underwent retreatment three times [6]. Given how small the sample is here, and how similar the percentages are to the 9.1% retreatment rate we used in our model (Variable 5), we felt it was reasonable to assume recanalization rates are the same, regardless of number of coiling attempts.

Assumption S4.09
Aneurysms in this model that have recanalized are treated if a patient undergoes a coiling procedure for a de novo aneurysm. Justification: If patients in Recanalizedi develop a de novo aneurysm, they transition to De Novoi and are indistinguishable from patients in De Novoi that transitioned from Coiledi. Once coiled, these patients all transition to Coiledi+1. These patients, therefore, no longer have a recanalized aneurysm. We assumed that during the coiling procedure, after the de novo aneurysm was treated, the recanalized aneurysm was also coiled and no longer at risk of rupture. It is possible that some recanalized aneurysms may not have been retreated at this time, however, accounting for this would have drastically increased the number of health states and complexity of the model. We felt justified in this assumption because interventionalists would likely defer recoiling the recanalized aneurysm only if the expected risk of rupture was low.

Assumption S4.10
The HTI in this model does not cause any significant complications. Justification: In our base case, we explore the use of MSC therapy. MSC therapy has been shown to be very safe in clinical studies, with minimal side-effects and complications, as described in the review by Uccelli et al. on MSC use in neurologic diseases [19]. Complications were uncommon and mainly included fever and infection associated with IV insertion, treated effectively with antibiotics. There were no reported serious adverse events. It was felt that the small cost and brief decrease in QALY associated with these rare complications would not significantly affect the ICER, especially compared to the complications associated with the endovascular procedure itself, and were therefore not included in the model. If an HTI is developed that does impart complications with a reasonable likelihood of significant impact on the costs and QALY, this should be included in the model.

Assumption S4.11
The HTI in this model is only administered at the index procedure and imparts benefit only on the recanalization rate for the first coiling procedure. Justification: It may be possible for a HTI to be developed that has longstanding benefits, even following a retreatment procedure, in which case this assumption can be removed from the model. We chose to limit the benefits of the HTI to the first coiling procedure only, in order to be more conservative and avoid providing the HTI any undue advantage over standard treatment. We exclusively tested the strategy where the HTI would be administered only at the index procedure. This allowed our results to reflect a direct comparison between standard treatment and HTI use for a single coiling procedure. In future, should there be a need, we can use our model to test an alternative strategy where all coiling procedures utilize the HTI, permitting we have the necessary efficacy data.

Assumption S4.12
The aneurysm recanalization RRR imparted by the HTI in this model acts equally on both aneurysms that would be recoiled as well as aneurysms that would be managed conservatively. Therefore, the proportion of recanalized aneurysms that are treated remains the same with and without the use of the HTI. Justification: In the absence of clinical data, we assumed the HTI would affect all aneurysms equally. If an HTI is developed and the clinical data shows the HTI prevents recanalization of aneurysms that would have been managed conservatively more than it prevents recanalization of aneurysms that would have been treated (or vice-versa), this will have to be accounted for in the model and new results will be generated.

Assumption S4.13
The aneurysm recanalization RRR imparted by the HTI was drawn from a uniform distribution between 0% and 100% in the model's base case. Justification: Since no clinical efficacy data is available for the theoretical HTI (including for MSC therapy), this distribution was chosen by the authors. We did not think it would be reasonable to include negative values for the RRR since only HTI with positive RRR would translate to clinical practice. While this assumption is not founded on clinical evidence, it is only used in the base case, and the main results of the study use all values of RRR, thus removing this assumption from the model.

Assumption S4.14
In the EVPPI calculation, the aneurysm recanalization RRR imparted by the HTI was drawn from a normal distribution bounded by 0 and 1 with a mean of 50% and SD of 15%. Justification: Since no clinical efficacy data is available for the theoretical HTI (including for MSC therapy), this distribution was chosen by the authors. We were unable to perform this calculation without specifying at least some expected value and distribution for the RRR. The values presented in the paper for EVPPI are therefore conditional on the RRR distribution, and the calculation must be repeated if a HTI RRR expected value and distribution are not similar to the one used here.

Assumption S4.15
Following an aSAH, patients in this model can no longer develop recanalized or de novo aneurysms. Justification: To allow for patients with aSAH to develop recanalized or de novo aneurysms, while still allowing a maximum of four endovascular coiling procedures would have dramatically increased the number of health states and complexity of the model. While we acknowledge that some aSAH survivors do undergo repeat procedures, since the total number of patients in our model that develop aSAH is very low (only 1.4% of unprotected aneurysms develop aSAH per year and ~40% die either immediately or in hospital), making this assumption allowed the model to be much simpler while having minimal effect on the ICER and overall study results.
The following is a detailed description of how the simulations in this study were performed.
To determine the total costs and total QALY in a Markov model, all costs and QALY for each state are calculated and summed across all the states in a given cycle. The costs and QALY for each cycle are then discounted appropriately and added together to obtain the total costs and QALY for the model. Totals are then compared between the standard treatment arm and the HTI arm to determine whether the use of the HTI is cost-effective.

Iteration Simulation
In the first iteration, all variables were drawn from their respective distributions and used in the Markov model to calculate the total discounted costs and QALY for both the arm that received the HTI as well as the arm that received standard treatment. These values were recorded. Another iteration was completed where new values of each variable were again drawn from their respective distributions and used in the Markov model to generate total discounted costs and QALY. This process was completed a number of times. Once all a iterations were complete, all iterations were averaged together to generate the average total discounted costs and average total discounted QALY for both treatment arms. These averages were used to calculate the ICER using the following formula: where LO+N is the incremental cost-effectiveness ratio, OPQR HIJ is the average total discounted costs for the arm that received the HTI, OPQR 5<K. is the average total discounted costs for the arm that received standard care, M_0b HIJ is the average total discounted QALY for the arm that received the HTI, and M_0b 5<K. is the average total discounted QALY for the arm that received standard care.
We varied a from 10 to 500 in increments of 10, from 500 to 1,000 in increments of 100, from 1,000 to 10,000 in increments of 1,000, and finally 20,000. All values of a were run 10 times each, except for a = 10,000 and a = 20,000, which were repeated 20 times each. The SD of the ICER for each value of a was then calculated. Looking at the SD plotted over the values of a, the SD appears to stabilize at ~ 7,000 iteration (Fig S5.01). Therefore, for all subsequent simulations, 7,000 iterations were used for each run of the model.

Base Case
To perform the base case probabilistic analysis, a Monte Carlo simulation using 7,000 iterations was completed. The average total discounted costs and average total discounted QALY for both treatment arms, as well as the ICER calculated using Equation S5.01 were all recorded. The probability that using the HTI would be cost-effective as well as the EVPI was calculated and recorded at multiple threshold levels varying from $0 per QALY to $150,000 per QALY (see CEAC and EVPI below). This simulation was repeated 100 times. Using the results from all 100 runs, the average values, SE, and 95% credible intervals (CrI) for the ICER, the probability of cost-effectiveness (over multiple thresholds), and the EVPI (over multiple thresholds) were calculated and recorded. SE and 95% CrI for the total discounted costs and the total discounted QALY of each treatment arm were calculated using the 7,000 iterations from the final (100 th ) run.

CEAC
Once the Monte Carlo simulation with 7,000 iterations was completed (see Base Case above), the NMB in each iteration for the HTI arm and the standard treatment arm were calculated using the following formula: .02: Uc. + = M_0b + × d − OPQR + where d is the threshold value (in 2018 USD per QALY) and > is the treatment arm (treatment with the HTI or standard treatment). Standard Deviation ($ per QALY)

Number of Iterations per Monte Carlo Simulation
Once the NMB for each treatment arm was calculated, the probability that HTI use was costeffective was calculated using the following formula: .03: D HIJ = U HIJ U IL<=* where D HIJ is the probability that HTI use is cost-effective, U HIJ is the number of iterations the NMB when using the HTI was greater than the NMB for standard treatment, and U IL<=* is the total number of iterations (7,000 in this case).
This process of calculating Uc. + and D HIJ using Equations S5.02 and S5.03 was repeated several times, with threshold levels varying from 0 to 1,000 in increments of 100, from 1,000 to 30,000 in increments of 1,000, and from 30,000 to 150,000 in increments of 5,000, where all threshold values are in 2018 USD per QALY. Fig S5.02 illustrates the CEAC at all threshold levels tested.

EVPI
Once the Monte Carlo simulation with 7,000 iterations was completed (see Base Case above) and the Uc. + was calculated for each iteration (see CEAC above), the treatment arm with the highest probability of cost-effectiveness was identified. This was carried out using a specific threshold level. If D HIJ > 0.5 the HTI arm was chosen to more likely be cost-effective and if D HIJ ≤ 0.5 the standard treatment arm was chosen. The arm which was chosen to more likely be cost-effective was termed the "expected best option". For each iteration Y, the Uc. + with the higher value (the NMB for either the HTI arm or the standard treatment arm) was also identified and termed the "true best option". The EVPI for each iteration was then calculated using the following formula: .04: +;DL 1 = Uc. I − Uc. D where +;DL 1 is the expected net benefit gained by resolving the uncertainty associated with all parameters used in the model for iteration Y, Uc. I is the NMB of the true best option for iteration Y, and Uc. D is the NMB in iteration Y for the expected best option. Note, the expected best option will be the same for all iterations (for a given threshold), while the true best option may change between iterations.
EVPI per procedure was then calculated by averaging the +;DL 1 across all 7,000 iterations. The SD and 95%CrI were also calculated. Assuming the HTI would be used in 15,925 procedures per year [20] for a total of 10 years, with a discount rate of 1.5%, the total EVPI was calculated using the following formula:  (15,925), = is the discount rate (1.5%), and > is the time in years the HTI is assumed to be used (10 years).
We then calculated the 95%CrI for +;DL I using the per procedure EVPI 95%CrI. This process was repeated for all values of threshold described in the CEAC simulation (see CEAC above). Fig S5.03 illustrates how the EVPI varies with changes in the threshold.

Sensitivity Analysis
To perform the one-way sensitivity analysis, we set each model parameter in turn to two standard errors below the mean, followed by two standard errors above the mean. Exceptions to this approach included the HTI efficacy (Variable 24) and cost (Variable 25), which were not tested in the sensitivity analysis, and the discount rate for cost and QALY which was tested at 0%, 3%, and 5% as per national guidelines [2,21]. For some parameters, however, two standard errors were not used for the following reasons: Healthcare cost of a coiling procedure without complications (Variable 12): Lower Value: This cost was not allowed to be negative and was therefore bounded by 0. Upper Value: This cost was not allowed to be greater than the healthcare cost of a coiling procedure with complications leading to functional disability (Variable 13) and was therefore bounded by the probabilistic value of Variable 13.
Healthcare cost of a coiling procedure with complications leading to functional disability (Variable 13): Lower Value: This cost was not allowed to be lower than the healthcare cost of a coiling procedure without complications (Variable 12) and therefore bounded by the probabilistic value of Variable 12. Upper Value: This cost was not allowed to be greater than the healthcare cost of a coiling procedure with complications leading to patient death (Variable 14) and was therefore bounded by the probabilistic value of Variable 14.  Similar bounds which maintained parameter face validity and the integrity of the Dirichlet-style distributions were also imposed on all other relevant parameter values, however, only the bounds mentioned above needed to be invoked.
For each value tested, a Monte Carlo simulation with 7,000 iterations was completed and average total discounted costs and average total discounted QALY for both treatment arms were recorded. The ICER for each Monte Carlo simulation was then calculated using Equation S5.01. For each model parameter, the absolute difference between the ICER in the base case and the ICER for the lower and upper values were calculated and added together to find the "total change in ICER". Model parameters were then arranged in order from largest to least total change in ICER. All parameters with total change in ICER less than or equal to the range of the base case ICER 95%CrI ($1,801.81 per QALY) were removed. The remaining parameter results were plotted in a Tornado diagram (Fig 3).

HTI Cost-Elasticity
To perform the HTI cost-elasticity probabilistic analysis, we began with a Monte Carlo simulation with 700,000 iterations. In this simulation, as in the base case, the aneurysm recanalization RRR imparted by the HTI (Variable 24) was drawn from a uniform distribution bounded by 0% and 100%. However, we set the HTI cost (Variable 25) to $0, such that all total costs derived from the model would not include the HTI cost. For each iteration, we recorded total discounted costs and total discounted QALY for both treatment arms, as well as the RRR drawn. Each RRR was then rounded to the nearest 1%.
Uc. + for each treatment arm for all iterations was then calculated using Equation S5.02 at a specific threshold level. A rounded RRR value was then selected, and for only the iterations which used this RRR, D HIJ was calculated using Equation S5.03. Because we set the HTI cost to $0 and because all HTI costs were incurred at a single point in time at the beginning of the model, we were able to see how D HIJ (for a specific RRR value) changed with changes in the HTI cost by simply subtracting HTI cost from Uc. HIJ . The HTI cost which resulted in a D HIJ = 0.5 was identified computationally using the "Goal Seek" function in Microsoft Excel® (Version 16.20) and recorded. This HTI costs was termed the "maximum willingness-to-pay" for the HTI at the given RRR (and threshold). The process was repeated for all values of RRR. Once the maximum willingness to pay for all levels of RRR was identified, the process was repeated using a different threshold level. Thresholds of $50,000, $100,000, and $150,000 per QALY were tested.

Scenario Analyses
To perform the scenario analyses, the methodology used in the base case was followed (see Base Case above). However, instead of drawing the HTI efficacy (Variable 24) from a uniform distribution between 0% and 100%, normal distributions bounded by 0% and 100%, with means (SD) of 10% (2%), 30% (5%), and 50% (15%) were used.

EVPPI
To estimate the expected benefit associated with resolving the uncertainty around the baseline rate of aneurysm recanalization, we first performed a Monte Carlo simulation with 7,000 iterations. For this simulation, the HTI efficacy (Variable 24) was drawn from a normal distribution bounded by 0% and 100%, with a mean (SD) of 50% (15%). In terms of the baseline rate of aneurysm recanalization (Variable 4), we drew a single value from Variable 4's base case distribution and used this same value for Variable 4 in all 7,000 iterations. Once the Monte Carlo simulation was completed, we recorded the value of Variable 4 used, as well as the average total discounted costs and average total discounted QALY for each treatment arm. We then calculated the Uc. + for each treatment arm using Equations S5.01 and S5.02 at threshold levels of $50,000, $100,000, and $150,000 per QALY. The average Uc. + for both treatment arms across all 7,000 iterations was calculated and recorded. D HIJ was also calculated for each threshold level using Equation S5.03 and recorded.
This entire process was repeated 1,000 times. The D HIJ was then averaged across all 1,000 runs at each threshold level. Similar to the process followed in the EVPI calculation (see EVPI above), if the average D HIJ > 0.5, the HTI arm was chosen to more likely be cost-effective (for a given threshold) and if D HIJ ≤ 0.5 the standard treatment arm was chosen. The arm which was chosen to more likely be cost-effective was termed the "expected best option". For each of the 1,000 runs, the treatment arm with the higher NMB was identified and termed the "true best option". The EVPPI for each run was then calculated using the following formula: .06: +;DDL 2 = Uc. I − Uc. D where +;DDL 2 is the expected net benefit gained by resolving the uncertainty associated with the baseline aneurysm recanalization rate for run h, Uc. I is the NMB of the true best option for run h, and Uc. D is the NMB of the expected best option for run h. Note, the expected best option will be the same for all runs (for a given threshold), while the true best option may change between runs.
EVPPI per procedure was then calculated by averaging +;DDL 2 across all 1,000 runs. The SD and 95%CrI were also calculated. Assuming the HTI would be used in 15,925 procedures per year [20] for a total of 10 years, with a discount rate of 1.5%, the total EVPPI was calculated using the following formula: .07: +;DDL I = +;DDL M • U M • 1 − (1 + =) /+ = where +;DDL I is the total EVPPI, +;DDL M is the per procedure EVPPI, U M is the number of procedures performed per year (15,925), = is the discount rate (1.5%), and > is the time in years the HTI is assumed to be used (10 years).
We then calculated the 95%CrI for +;DDL I using the per procedure EVPPI 95%CrI. This process was repeated for each threshold level.