Proton radiotherapy outperforms medulloblastoma irradiation with photons in economic savings in Brazil (PROMISE)

Abstract

Objective

This study aimed to evaluate the cost-effectiveness of proton therapy compared to photon therapy for pediatric medulloblastoma treatment from the payer's perspective in Brazil, assessing its economic viability and potential to improve long-term outcomes by reducing late complications.

Materials and methods

A Markov chain model simulated outcomes for a cohort of 5-year-old children with medulloblastoma over a 30-year horizon. The base case involved craniospinal irradiation (36 Gy) with a 54 Gy posterior fossa boost, tracking 11 health states, including hearing loss, cognitive deficit, and coronary artery disease (CAD), with CAD and congestive heart failure (CHF) onset after 10 years. Annual transition probabilities were derived from systematic reviews. Costs (photons: US$3000; protons: US$50,000) reflected Brazilian and international data, with a willingness-to-pay (WTP) threshold of US$50,000/QALY. Incremental cost-effectiveness ratio (ICER), net monetary benefit (NMB), and probabilistic sensitivity analysis (PSA) via Monte Carlo simulations (1000 iterations, 25,000 patients) were calculated using Python 3.11.

Results

Proton therapy yielded 20.45 QALYs at US$102,933, versus 16.87 QALYs at US$141,971 for photons, with an ICER of -US$22,857/QALY, indicating dominance. PSA showed a mean NMB of US$70,290 (95 % CI: US$42,377–US$98,662), with protons cost-effective in >95 % of simulations. Survival at 30 years was 40.5 % (protons) versus 27.1 % (photons), driven by reduced late effects (e.g., 68 % vs. 45 % cumulative events).

Conclusion

Proton therapy is a cost-effective, dominant strategy for pediatric medulloblastoma in Brazil, offering superior outcomes and cost savings. These findings support its adoption through innovative funding models like public-private partnerships.

1. Introduction

Medulloblastoma is the most common malignant brain tumor in children, accounting for approximately 20 % of pediatric central nervous system (CNS) tumors [1]. The standard treatment involves maximal safe surgical resection, followed by craniospinal irradiation (CSI) with photons and adjuvant chemotherapy. While CSI with photons is effective in disease control, it is associated with high rates of late complications. Studies show that up to 70 % of survivors develop late side effects, such as cognitive deficits, endocrinopathies, hearing loss, and osteoporosis [2]. Additionally, the risk of second primary tumors is significant, with a cumulative incidence of up to 10 % at 10 years [3]. These adverse effects profoundly impact the quality of life of surviving patients, increasing long-term healthcare costs and imposing a considerable burden on both individuals and their families. Proton therapy emerges as a promising alternative to CSI with photons, distinguished by its technical and dosimetric advantages. Unlike photons, protons deposit most of their energy at the end of their path (Bragg peak), allowing for more precise dose delivery to the tumor and reducing exposure to adjacent healthy tissues [4]. This is particularly advantageous in treating medulloblastoma, given the need to irradiate critical areas such as the brain and spinal cord. Dosimetric studies indicate that proton therapy can reduce the dose to organs at risk, such as the heart, lungs, and endocrine glands, by up to 50–70 % compared to photons [5,6]. Such reduction may result in lower rates of late complications and second tumors, potentially improving long-term outcomes for patients.

Despite these advantages, the global distribution of proton therapy remains uneven. Currently, over 100 proton centers are operational in North America, Europe, and Asia, but their presence in low- and middle-income countries (LMICs) is scarce, with few centers in Asia and none in Latin America [7,8]. Brazil, as the largest economy in Latin America, faces significant challenges in establishing a proton center, including high capital costs (estimated $150 million), substantial operational and maintenance expenses, and the need for highly specialized personnel [9]. A previous cost-effectiveness analysis in Brazil, from the government's perspective and focused on case volume, concluded that proton therapy would not be cost-effective for the public healthcare system due to the limited number of eligible patients [10]. However, this analysis did not consider the payer's perspective, which is crucial for private sector companies and public-private partnerships (PPPs) to assess the true economic and social benefit of proton therapy. Such an analysis is fundamental to determine the economic viability and impact on patients' and society's quality of life, especially considering that reducing late complications can mitigate long-term care costs. Therefore, this study aims to fill this gap by evaluating the cost-effectiveness of proton versus photon therapy for pediatric medulloblastoma treatment from the payer's perspective, tailored to the Brazilian context. Moreover, the present study supports the WHO Sustainable Development Goal to ensure healthy lives and promote well-being at all ages and aligns with the WHO Global Cancer Plan to reduce premature mortality from non-communicable diseases, including pediatric cancers, by one-third by 2030.

2. Material and methods

2.1. Study description and base case

This study aimed to evaluate the cost-effectiveness of proton therapy compared to photon therapy in the management of pediatric medulloblastoma from the payer's perspective. A Markov chain model was employed to simulate the clinical and economic outcomes of a hypothetical cohort of children diagnosed with medulloblastoma at age 5 years. The analysis adopted a 30-year time horizon, extending to age 35 years, to capture long-term consequences of treatment, reflecting the prolonged life expectancy of pediatric survivors and the latency of radiation-induced adverse events. A willingness-to-pay (WTP) threshold of US$50,000 per quality-adjusted life-year (QALY) was selected, aligning with international benchmarks and previous cost-effectiveness studies [2,11], including adjusted for the project's scope and context.

The base case assumed craniospinal irradiation (CSI) with a dose of 36 Gy to the cranium and spine, followed by a 54 Gy boost to the posterior fossa, consistent with standard treatment protocols for medulloblastoma [1]. The model tracked annual cycles, starting with 100 % of the cohort in the “Alive without complications” state, with transitions to adverse event states or death occurring annually based on specified probabilities. Adverse events were modeled to begin after the first year post-treatment, except for coronary artery disease (CAD) and congestive heart failure (CHF), which were assumed to manifest after 10 years (age 15 years), reflecting their typical latency as late radiation-induced toxicities [3].

2.2. Health states and transition probabilities

A systematic review identified high-quality studies on long-term outcomes in pediatric medulloblastoma survivors treated with CSI. The review prioritized publications providing reliable estimates of survival, late toxicity rates, and utility values (quality of life).The Markov model included 11 health states: “Alive without complications,” “Hearing loss,” “Hypothyroidism,” “Osteoporosis,” “Growth hormone deficiency (GHD),” “Non-fatal secondary malignancies,” “Cognitive deficit,” “Dysfunctionality,” “CAD,” “CHF,” and “Death” (subdivided into “Death due to cancer” and “Death due to complications”). Transition probabilities were derived from a comprehensive literature review [2,5,6,[11], [12], [13], [14], [15], [16], [17], [18], [19]]. Table 1 presents the annual transition probabilities for protons and photons, along with their respective references. Cognitive deficit was defined as impairments in memory, attention, and problem-solving abilities, commonly observed in medulloblastoma survivors due to craniospinal irradiation affecting developing brain tissue. This aligns with findings from Pulsifer et al. [5], where declines in IQ and neurocognitive function were noted post-radiotherapy. Dysfunctionality encompassed a broader range of functional limitations, including motor deficits, balance issues, and other neurological impairments impacting daily activities. This state, adapted from Michalski et al. [6], may include conditions such as ataxia or cranial nerve palsies, distinct from cognitive-specific deficits. (See Fig. 1.)

Table 1.

Annual Transition Probabilities for Health States in the Markov Model.

Transitions Health State	Photon Probability (%)	Proton Probability (%)	Reference
Hearing Loss	14.30	2.10	Paulino et al. (2018)
Hypothyroidism	15.40	3.70	Aldrich et al. (2021)
Osteoporosis	14	4	Lundkvist et al. (2005)
Growth Hormone Deficiency (GHD)	11.40	10.20	Aldrich et al. (2021)
Non-Fatal Secondary Malignancies	0.83	0.36	Yock et al. (2006)
Cognitive Deficit	2.50	1.00	Pulsifer et al. (2019)
Dysfunctionality	1.70	0.74	Michalski et al. (2015)
Coronary Artery Disease (CAD)*	1.36	0.75	Mailhot Vega et al. (2013)
Congestive Heart Failure (CHF)*	0.68	375	Mailhot Vega et al. (2013)
Death due to Cancer	2.00	2.00	Michalski et al. (2015)
Death due to Complications	16	96	Lundkvist et al. (2005)

Fig. 1.

Schametic of decision analitic/Markov model for Mdulloblastoma treated by protons vs. photons radiotherapy. After treatment, patients may remain free of adverse events or experience late effects begining after 1 year (hypothyroidism, hearing loss, osteoporosis, cognitive decline, growth hormone deficiency and functional impairament). After 10 years, late cardiac effects (coronary arterial disease and congestive heart failure) may occur. A longlife time risk for secondary malignancy is modeled with pathways to cure, or to death from complications. Arrowas indicate allowed transitions states in each cycle. The model runs on annual cycles over a long term horizon.

2.3. Costs and utilities

Costs were estimated from the payer's perspective, incorporating initial treatment costs and annual management costs for each adverse event state. Initial costs were US$ 3000 for photons (average of public and private sector costs in Brazil, reflecting local healthcare pricing in 2025) and US$ 50,000 for protons, based on international estimates adjusted for implantation, operational, maintenance, treatment planning systems, and human resources [2,11]. Table 2 summarizes the costs and utilities for each health state, with explanations of included components. Costs include consultations (e.g., endocrinologist, cardiologist), diagnostic exams (e.g., audiometry, TSH tests, ECG), and interventions (e.g., hearing aids, hormone replacement, pharmacological management). For protons, the higher initial cost reflects capital investments (e.g., US$ 140 million facility cost) [10] amortized over patient volume, operational expenses, and staffing, adjusted to 2025 values. WTP Justification: The US$ 50,000/QALY threshold was based on international standards and prior studies [2,5,11,12], balancing clinical benefits with infrastructure costs [10].

Table 2.

Costs and Utilities Associated with Health States.

Health State	Annual Cost (US$)	Cost Components	Utility	Reference
Hearing Loss	5500,00	Hearing aids (hearing implant devices), audiometric tests, speech therapy	0.82	Mailhot Vega et al. (2013)
Hypothyroidism	150	Levothyroxine, annual TSH/free T4 tests, physician visits	0.90 (1st year), 1.0 after	Lundkvist et al. (2005)
Osteoporosis	500	Calcium/vitamin D supplements, nutritional counseling, bone density tests	0.98	Lundkvist et al. (2005)
Growth Hormone Deficiency (GHD)	18,000 (≤19 yrs), 1800 (>19 yrs)	Growth hormone injections, IGF-1/glucose tests, endocrinologist visits, imagin exams	0.80	Lundkvist et al. (2005)
Non-Fatal Secondary Malignancies	30,000 (one-time)	Diagnostics (biopsies, imaging), surgery, chemotherapy/radiotherapy, image exams (CT/PET-CT and MRI)	0.60	Lundkvist et al. (2005)
Cognitive Deficit	9800,00	Neuropsychological evaluations, educational support, psychotherapy, social support	0.95	Pulsifer et al. (2019)
Dysfunctionality	10,000,00	Physical/occupational therapy, assistive devices, home support	0.85	Michalski et al. (2015)
Coronary Artery Disease (CAD)	3362 (3419 1st yr)	Ramipril, simvastatin, metoprolol, aspirin, stress ECG, lipid profile, catheterism, Angio MRI	0.63 (10 years after)	Mailhot Vega et al. (2013)
Congestive Heart Failure (CHF)	1362 (1394 1st yr)	Ramipril, chlorthalidone, ECG, echocardiogram, blood tests, Angio MRI	0.60 (10 years after)	Sullivan et al. (2006)

2.4. Analytical methods and calculations

The analysis calculated the incremental cost-effectiveness ratio (ICER) as the difference in total costs divided by the difference in QALYs between proton and photon therapies. Cost-effectiveness analysis (CEA) assessed whether protons met the WTP threshold, while net monetary benefit (NMB) was computed as (QALYs × WTP) - Costs to quantify absolute economic value. A discount was applied (3 % rate), per the base case specification. One-way analyses varied key parameters (e.g., transition probabilities, costs) to assess their impact on ICER, identifying the most influential factors (e.g., GHD, hearing loss, CAD). A Monte Carlo simulation with 1000 iterations and 25,000 patients per iteration tested joint uncertainty. Beta distributions were used for risks based on patient data (e.g., hearing loss), and uniform distributions for modeled estimates (e.g., costs, CAD/CHF risks), reflecting greater uncertainty in derived values. Monte Carlo methods estimated survival curves, tracking the proportion of patients alive over 30 years, accounting for transitions to death states. The model was implemented in Python (version 3.11), leveraging libraries such as NumPy for numerical computations, SciPy for statistical distributions, and Matplotlib for visualization of survival curves and PSA scatter plots.

The cohort began in “Alive without complications,” with adverse events (except CAD/CHF) occurring after the first year and CAD/CHF after 10 years (figure-1). Annual transitions were simulated, accumulating costs and QALYs per cycle. Results were validated against epidemiological survival rates (e.g., 5-year survival ∼80 %) and compared with prior models for consistency [2]. This methodology, building on Lundkvist et al. [2] and Mailhot Vega et al. [11], ensures a robust evaluation of proton versus photon CSI, capturing both clinical and economic outcomes over a 30-year horizon from a payer's perspective.

3. Results

In the base-case scenario, proton therapy resulted in 20.45 QALYs (quality-adjusted life years) at a total cost of $102.933 (Fig. 2A,B). In contrast, photon therapy yielded 16.87 QALYs at a total cost of $141,971(figura-2a,b). This represents an incremental gain of 3.5 QALYs with proton therapy, accompanied by a reduction of $39.038 in total costs. The Incremental Cost-Effectiveness Ratio (ICER) was calculated as –$22,857 per QALY, a negative value indicating the dominance of proton therapy, providing greater health benefits at a lower cost. The opportunity cost of choosing photon therapy (instead of proton therapy) is a loss of an additional 3.58 QALYs that could have been gained, and an extra expenditure of US$39,038,00 that could have been allocated to another health intervention with beneficial outcomes.The cumulative late effect event over the time was significantly lower with protons versus photons at 5, 10, 15 and 30 years (12 % vs 7 %, 26 % vs 15 %, 40 % vs 25 %, 68 % vs 45 %) (Fig. 2C). The ICER over the period fall off below WTP =50.000,00 at 5 years and it is negative after 15 years (Fig. 2D).

Fig. 2.

Model compartive outcomes comparing protons vs. photons over 30 years (base case). A- Cumulative QALYS over time;B-Cumulative Late Effect; C- Cumulative cost; D- Cumulative ICER.

The probabilistic sensitivity analysis yielded a mean Net Monetary Benefit (NMB) of US$70,290 for proton therapy at a willingness-to-pay (WTP) threshold of US$50,000 per QALY. The 95 % confidence interval ranged from US$42,377 to US$98,662, indicating a high probability that proton therapy is cost-effective under the predefined threshold (Fig. 3A). The PSA scatter plot shows that all simulated iterations fall below the willingness-to-pay (WTP) threshold of $50,000 per QALY, with the majority located in the southeast quadrant. This indicates that proton therapy consistently provides higher effectiveness (incremental QALYs) at lower costs compared to photon therapy (Fig. 3B). The tornado plot showed that the ICER was most sensitive to variations in proton therapy cost, cognitive deficit, and cancer mortality (Fig. 3C). Smaller impacts were observed for functional impairment, GHD, and treatment-related deaths. Parameters such as hearing loss, hypothyroidism, secondary malignancy, and osteoporosis had minimal influence on results. Overall, the model was primarily driven by neurocognitive outcomes and proton treatment cost. The robustness of the results was assessed through a probabilistic sensitivity analysis involving 1000 Monte Carlo simulations. At a WTP threshold of $50,000 per QALY, proton therapy was found to be cost-effective in over 95 % of the simulations (Fig. 3D). These findings reinforce the consistent economic and clinical superiority of proton therapy, even under variations in model parameters. Over the 30-year time horizon, the model predicted superior overall survival for patients treated with proton therapy compared to those receiving photon therapy. At year 5, the proportion of survivors was 90.4 % for protons versus 86.3 % for photons. By year 10, survival decreased to 81.9 % for protons and 74.4 % for photons. At year 15, these rates were 74.2 % and 62.9 %, respectively. By the end of the 30-year horizon, cumulative survival was 40.5 % for the proton cohort and 27.1 % for the photon cohort (Fig. 3E).

Fig. 3.

Uncertainty analysis for the base case comparison of protons vs. photons radiotherapy. A- Histogram of net monetary benefit; B- Probabilistic Sensitivity Analysis (cost effectiveness plane); C- Deterministic one-way analysis (tornado plot); D- Cost Effectivess Acceptability Curve (CEAC); E- Probabilist Overall Survival Over The Time.

4. Discussion

Our study, conducted from the payer's perspective within the Brazilian healthcare system, demonstrates that proton therapy is a cost-effective and dominant strategy compared to photon therapy for the treatment of pediatric medulloblastoma. Using a Markov model over a 30-year time horizon, we found that proton therapy yields 20.45 quality-adjusted life years (QALYs) at a cost of US$102,933, in contrast to 16.87 QALYs at US$141,971 for photon therapy. This results in an ICER of –US$22,857 per QALY, indicating that proton therapy is both more effective and less costly. Based on national cancer registry data, Brazil reports ≈450 new pediatric medulloblastoma cases annually. Extrapolating our model suggests proton therapy could prevent hundreds of long-term sequelae each year and generate significant cumulative societal savings. Probabilistic sensitivity analysis (PSA) reinforces this conclusion, showing that proton therapy is cost-effective in over 95 % of simulations at a WTP threshold of US$50,000 per QALY. These findings highlight proton therapy's potential to improve long-term outcomes while reducing costs associated with late toxicities in pediatric patients.

The distribution of NMB was approximately normal, with a mean of US$70,290 for proton therapy and a 95 % confidence interval ranging from US$42,377 to US$98,662. This wide interval suggests notable variability, potentially driven by fluctuations in proton therapy costs and the incidence rates of late complications. The tornado plot identified proton therapy cost as the most influential parameter on the ICER, followed by cognitive deficit and cancer mortality rates. Variations in proton therapy cost, which include capital investment, operational expenses, and maintenance, could reflect differences in facility scale, patient throughput, or amortization periods [9]. For instance, higher upfront costs in smaller centers with lower patient volumes could narrow the cost differential with photons, reducing NMB. Conversely, optimized centers with higher throughput might amplify cost savings, widening the NMB range. The sensitivity of the model to neurocognitive outcomes further underscores the economic impact of reducing cognitive deficits, a major driver of long-term healthcare and societal costs [5].

The estimated survival rates over the 30-year horizon—90.4 % vs. 86.3 % at 5 years, 81.9 % vs. 74.4 % at 10 years, 74.2 % vs. 62.9 % at 15 years, and 40.5 % vs. 27.1 % at 30 years for protons and photons, respectively—demonstrate a clear advantage for proton therapy [6]. These estimates incorporate a background mortality rate derived from standard Brazilian life tables (IBGE, 2025), adjusted for age-specific risks, alongside disease-specific mortality from cancer recurrence (2 % annually) and treatment-related complications (0.016 % for photons, 0.0096 % for protons) [7]. The model assumes competing risks, where transitions to death states (cancer or complications) are mutually exclusive within each cycle, potentially underestimating overall mortality if unmodeled comorbidities or interactions amplify risk. However, the superior survival with protons aligns with their dosimetric advantage in sparing healthy tissues, reducing the cumulative burden of late effects that contribute to mortality, such as cardiovascular events (CAD and CHF) modeled after 10 years [3].

This finding contrasts with Fernandes et al. [10], who concluded that proton therapy was not cost-effective in Brazil from the government's perspective, citing insufficient case volumes of medulloblastoma (∼110 cases annually) to justify infrastructure costs. Their analysis used a lifetime (~73-year) horizon with annual cycles, and late adverse effects can accumulate over time (at most one new event per cycle). Differences between our results likely reflect perspective (government vs payer), parameter choices, and other modeling assumptions such as endocrinopathies, neurocognitive decline, and secondary malignancies, which our 30-year horizon captures comprehensively [10]. Furthermore, Fernandes et al. [10] focused solely on public sector costs within the SUS, neglecting the payer's perspective relevant to private insurers and public-private partnerships (PPPs). Besides, our study, from a payer's perspective, accounts for multiple concurrent toxicities and long-term outcomes and is not limited to the relationship with potential patient volume. This approach aligns more closely with real-world outcomes observed in long-term survivors. [2,11] These methodological differences explain the divergent conclusions, emphasizing the importance of perspective and time horizon in cost-effectiveness assessments.

Brazil's radiotherapy infrastructure presents significant challenges to optimizing pediatric outcomes. With only 252 linear accelerators (linacs) in the SUS, of which just 20 % support advanced techniques like IMRT/VMAT with IGRT (RT2030, 2020) [16], access to precise photon-based treatments is limited [11]. This increases radiation exposure to healthy tissues, elevating risks of neurocognitive deficits, endocrine dysfunction, and secondary malignancies in medulloblastoma patients requiring craniospinal irradiation [5]. Proton therapy offers a solution by delivering targeted doses, minimizing these risks [6]. Currently, Brazil faces a shortage of linacs, and even with the governmental plan to procure 120 additional units, the deficit will persist [16]. Introducing proton therapy would demand roughly double the investment allocated to expanding linac capacity, suggesting that its implementation in Brazil would likely hinge on private sector involvement, possibly through PPPs [9]. The potential implementation of proton therapy in Brazil could benefit from a PPP model, optimizing resource allocation and enabling the initial capital investment required for infrastructure.

Historically, private entities in Brazil have explored proton therapy adoption but hesitated, partly due to the absence of cost-effectiveness analyses addressing payer benefits and willingness to pay [10]. Our study fills this gap, offering robust evidence that could catalyze such initiatives. For PPPs to be viable, a minimum patient volume of approximately 200–300 pediatric cases annually—encompassing medulloblastoma and other indications like sarcomas and CNS tumors—would be required to amortize capital costs (estimated at US$150 million) over a 30-year facility lifespan [9]. Incentives such as tax breaks for equipment importation, subsidies for operational costs, or reimbursement agreements with SUS and private insurers could lower the financial threshold [13]. Logistically, a proton center in a metropolitan hub like São Paulo or Rio de Janeiro, integrated with existing oncology networks, could optimize patient access and staff training, leveraging Brazil's established medical expertise.

Notably, proton therapy is already implemented in countries with lower per capita GDP than Brazil, such as Poland and South Africa, indicating that economic development alone does not preclude its adoption [7]. In these countries, where proton facilities operate despite lower GDP per capita, strategic partnerships and phased implementation (e.g., starting with a single gantry) could mitigate initial costs while scaling capacity over time [9].

Brazil has a bifurcated healthcare landscape, with the public sector serving approximately 70 % of the population and the private sector catering to about 30 % [12]. Our analysis evaluates proton therapy's cost-effectiveness across various WTP thresholds—US$50,000 per QALY—demonstrating its viability even under conservative scenarios [13]. This flexibility strengthens the case for its integration into both public and private healthcare systems, enabling payers to negotiate sustainable adoption. Such an approach is particularly compelling given that the high upfront costs of proton therapy can be offset by reduced long-term expenditures on late complications, delivering benefits to both patients and the broader healthcare ecosystem [2].

Although in this cost-effectiveness analysis the outcomes were favorable to protons, it is crucial to keep in mind that our analysis is based on immediate and modeled outcomes rather than prospective, real-world follow-up assessing retention and application of clinical benefits over decades. Future prospective studies should validate our model assumptions, capture long-term neurocognitive, endocrine, hearing, and quality-of-life outcomes, and incorporate patient-reported measures. Additionally, regional variations in healthcare infrastructure, access inequalities, and operational costs warrant granular investigation. Sensitivity to key toxicity and cost inputs highlights the need for Brazil-specific registry data and real-world experience as proton centers emerge. Finally, exploring ethical, psychological, and societal dimensions of access to advanced radiotherapy in mixed-method research will enrich policy-making. However, even with these caveats, our data may generalize to other LMICs with similar constraints, pending adaptation to local treatment volumes, infrastructure, and socioeconomic contexts. Future studies should evaluate implementation in underserved and remote regions to ensure equitable access.

5. Conclusion

Proton therapy emerges as a cost-effective and dominant option for pediatric medulloblastoma in Brazil from the payer's perspective, challenging prior assessments and highlighting the value of multi-perspective analyses. Its integration could address current radiotherapy constraints, improving outcomes. These findings urge stakeholders to explore innovative funding models, such as PPPs, to facilitate adoption, optimizing care for pediatric patients.

Data availability statement for this work

“Research data are stored and will be shared upon request to the corresponding author.”

CRediT authorship contribution statement

Gustavo A. Viani: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Carlos E. Cardoso: Writing – review & editing, Writing – original draft, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization. Ana Carolina Hamamura: Writing – review & editing, Writing – original draft, Methodology, Data curation. Helio A. Salmon: Writing – original draft, Supervision, Funding acquisition, Conceptualization. Gustavo O. Amaral: Writing – review & editing, Writing – original draft, Supervision, Funding acquisition, Conceptualization.

Funding

None.

Declaration of competing interest

All other authors have no competing interests.