www.jogh.org year estimates a sensitivityanalysisofthevaluelife Economics in“GlobalHealth2035”: James KHammitt Resch [email protected] USA Boston MA 02115 677 Huntington Ave Harvard TH Chan School of Public Health Department of and Population Angela Y Chang Correspondence to: 4 3 2 1 Angela YChang     Toulouse Capitole,Toulouse,France Toulouse SchoolofEconomics,University School ofPublicHealth,Boston,MA,USA Center forRiskAnalysis,HarvardT.H.Chan MA, USA T.H. ChanSchoolofPublicHealth,Boston, Center forHealthDecisionScience,Harvard Boston, MA,USA Harvard T.H.ChanSchoolofPublicHealth, Department ofGlobalHealthandPopulation, 2 • doi:10.7189/jogh.07.010401 1 , LisaARobinson 2,3,4 , StephenC 2,3 , developed an innovative method for estimating the value of an increase in economistsing DeanJamison, ,Kenneth andArrow, To support this approach, prominent members of the Commission, includ ments at the population level. improvehealtheffectsgrosscapturedomestictheofproduct to (GDP) changesexpectancylifevalueofinchanges value ofthein addedare to health improvements into national accounts [ mended the use of a “full income” approach to incorporate the benefits of eration,” In its 2013 report, “Global health 2035: a world converging within a gen Methods expectancy they experienced from 2000 to 2011 are permanent. and middle–income countries (LMICs) assuming the changes in life value of a life year (VLY) averages 2.3 times GDP per capita for low- assumptions to bridge gaps in the empirical research. It finds that the Tovalue changes in life expectancy, the CIH relies on several strong grossdomestic product (GDP)whenassessing national well–being. adds the value of increased life expectancy to the value of growth in generation,” Background work is needed to investigate options for improving the approach. tivity of their conclusions to reasonable alternative assumptions.acteristicsofthe affected population.More Analysts should test the sensi tailortheestimates theimpactsto theintervention of andthechar tions,analystsinterested applyinginapproachthis elsewhere must Conclusion the sequencing of the calculations reduces the VLY. thereduction foryoung children increases theVLY, while reversing LMICs.capitaRemovingforpertimesGDP 2.1 to estimates 0.2 to effectstheincome,expectancylifeand ofage,reduce VLYmay the Findings and life expectancy, and the sequencing of the calculations. to the underlying assumptions, including the effects of income, age, dren ages 0 through 4. We investigate the sensitivity of this estimate lationexpectancylifepercent includes50and reductiona chil for The Lancet The 1 The CIH VLY estimate is based on a specific shift in popu We find that reasonable alternative assumptions regarding Because the VLY is sensitive to the underlying assump In “Global health 2035: a world converging within a convergingwithinworld a 2035: health“Global In The Lancet The Commission on Investing in Health (CIH) recom (CIH) Health in Investing on Commission Commission on Investing in Health (CIH) Health in Investing onCommission June 2017 •Vol. 7 No. 1• 010401 1 ]. Under this approach, the global journal of health ------

VIEWPOINTSPAPERS PVIEWPOINTSapers June 2017 •Vol. 7 No. 1• 010401 Chang etal. exceedthe present value of future income or consumption because VSL reflects non–monetary benefits tial elasticities may affect the resulting VSL by orders of magnitude. Theoretical models suggest VSL will importance when extrapolating from very high to very low income countries because the rangeties asof highpoten as two or three while others report values less than one [ theory and empirical studies generally support elasticities greater than one, some studies report elastici change in VSL in response to a proportional change in income generallyVSL(ie,and confirms that increasesVSL its with income, anticipated. as income However, elasticity) proportionalthe is uncertain. While Most VSL studies address high analysis, the CIH focuses on the variation associated with income and age tion and the mortalitythetionand risks.effectsThe many characteristicsof wellarenot Monetaryvalues forimproved survival areexpected varywithtocharacteristics theaffectedof popula “VLY” to distinguish their population steps to calculate the VLY associated with a particular policy. We expectancy.follow the AnalystsinterestedarewhoapproachapplyingCIH sameCIHfollow inthethe to wouldneed practice and use the term indetail in the Methods section. The result is the average value of a specified population increase in life The CIH also derives a value per life year from a VSL estimate, but uses a different approach, as described ing life expectancy yields values that decrease with age. the average individual [ allyestimated constant,aas dividingby average VSLthebyremaining (discounted) lifeexpectancy for individuals place on an increase in life expectancy, but few empirical studies exist. Instead, VSLY is usu The associated value per statistical life year (VSLY) could be estimated directly by researching the values for a small change in one’s own risk by the risk change. nificant inconsistencies available the in gaps research and high for even riod [ age of individuals’ marginal rates of substitution between money and mortality risk in a defined timeThe pe CIH starts with an estimate of the value per statistical life (VSL), which represents a population aver differ in significant respects. tencies in the empirical research, these values must be extrapolated fromsuch analysesstudies would ofrely otheron estimates populations from the affectedthat population. However, due to gaps and inconsis pectancyincrease.acrosspreferencesindividualsBecausevarythesesocieties, andideallytolikely are the extent to which individuals are willing to trade consumption of other goods and services for aspecific life ex changes in their own life expectancies. In this context, money is not of interestConceptually, per se:theCIHapproach itintendedis measuresreflectto the value that members population a of place on General framework the 2001 Commission on Macroeconomics in Health (CMH), currently used as cost This VLY is within the range of the illustrative estimates of 1.0 to 3.0 times GDP per capita referenced by the interventions it recommends. try groups and time periods using the same approach, and applies the results to estimate the benefits of the reduction for young children. The CIH also reports the value of life expectancy gains for other coun tries (LMICs) from 2000 to 2011, assuming the gain is permanent, or 3.0 times GDP per capita without 2.3 times 2000 GDP per capita for life expectancy gains experienced by low 0 through 4 by 50 percent, then divide the total by the life expectancy gain to estimate VLY. This VLY is per capita and to remaining life expectancy. In their main result, they decreaseadjust a theUS estimatevalue of thefor valuechildren of mortality aged risk reduction, assuming this value is proportional to GDP population life expectancy and translating the results into an average value of a life year (VLY) [ ties in the results as well as the issues that arise in tailoring the approach for application elsewhere. is to investigate the effects of plausible alternative assumptions and to provideGDPper capita insightsestimate highlighted into in its themain report uncertainto changes in the parameter values [ TheCIH faced many challenges in developing its approach. We examine the sensitivity of the 2.3 times a specific historical gain. might place on an incremental change in life expectancy [ olds in the World Health Organization’s Choosing Interventions that are Cost where[ 5 ]. Conventionally, VSL is estimated by dividing empirical estimates of individual willingness to pay 2 , 3 ].TheCMH multipliers were intended asrough estimates ofthevalue anaverage individual

6 , 7 ]. Valuing current mortality risk as the product of a constant VSLY and remain – income countries [ – based quantity from the conventional VSLY. 2 10 – 12 ]. Research on the relationship between income 4 ]. In contrast, the CIH multiplier is based on 13 ]. Income elasticity is of particular www.jogh.org – – incomecountries[ specific life expectancy. – – – and middle Effective program and else understood;therearesig • doi:10.7189/jogh.07.010401 – effectiveness thresh – income coun 1 ].Our goal 8 , 9 1 ]. In its In ]. ]. They ------www.jogh.org • doi:10.7189/jogh.07.010401 more than to themselves [ researchthehigher–incomeof Much in countriessuggests adultsthatvaluereducing children risks to stant with age [ Other studies, which include adults older than working age, find that betweenvalues mayVSL decreaseand age or forremain working–age con adults, consistent with the expectancyprediction nor the applicationof oflife–cycle a constant VSLYmodels [ [ consistent,generallyandsupport notdoes hypothesisthe proportional is VSLthat (discounted)to life The theoretical and empirical evidence on the relationship between VSL and age or life expectancy is in justed VSL should not fall below the present value of income or consumption [ additionlivingmonetarytheconsumptioninofvaluetoof future andearnings. income–ad theThus mate by 10 by mate TheCIH approach to the first challenge is relatively straightforward. They begin by dividing a VSL esti life extension. available values are for a reduction in current mortality risk, while the CIH was interested in the value of high–incomeinterestedLMICs.Second,onfocusvaluesthetionswasfor countries, CIH in the while The CIH faced two major challenges. First, most empirical estimates of the value of mortality risk reduc METHODS value that an individual places on small changes in his or her own mortality risk, such as a 1–in–10 misunderstood [ ingness to pay for this risk change. They use this terminology in part because the VSL concept is widely “SMU” to refer to a 1 in 10 supporting such lower values is “limited.” ages less than reducing death rates among, say, 25 year olds.” [ mortality, “[i]t is plausible that many societies and individualslylow life expectancies, will where much valueof the life expectancy reducinggain results from deathdecreased infant ratesand child at very young presentvalue ofan infinite stream of annual values using percent3 a annual discount rate. Dividing by futuregenerations),calculatessustainedacrossthereductionall CIHmortalityis risk the (ie, manent in that age group in 2005 (midpoint of 2000 and 2011). Assuming the increase in life expectancy is per product of the age–specific VSMU, the age–specific risk change, and the fraction of the LMIC populationcalculatesCIH presentthe valuechangetheoflife expectancyin summing,by overgroups,ageall the maining life expectancy, estimated using the 1958 (midpoint of 1955 and 1961) life table for Japan. ues for other countries at age 35. This anchor VSMU is then adjusted for other ages in proportion to re individual aged 35, who has 45 years of remaining life expectancy, and anchor the income–adjusted val midpoint of each age group from the life tables. They assume that the US VSMU reflects the value for an are used for ages 0 through 9 and a single category is used for age 80 and higher), applyingInits calculations, values the CIH foruses age thegroups (generally 10–year increments, although 5–year increments ity rates to calculate changes in age–specific mortality risk for LMICs. reflect a similar life expectancy at birth. CIH then uses the corresponding Japanese age–specific mortal 2000 and 2011 was 65 and 68 years, respectively. They find that Japanese life tables for 1955 and 1961 historical“gooddata.”specifically,More expectancy estimate acrossin birth LMICs life they that all at providesJapanthatnotingconcern, ofperiod theover LMICs the infound as birth expectancylifeat ableformost LMICs. They instead rely onJapanese life tables which reflect similara change in average these VSMUs, the CIH requires data on population survival rates for each year of set ofage, age–specific which changesare in currentnot mortalityavail risk valued using a set of age–specific VSMUs. To derive used.To estimate thevaluechange aof populationin lifeexpectancy, theyassociate thatchange witha The CIH approach to the second challenge is more complex, and differs from the approaches commonly US$ 2718 and US$ 4201, respectively. in VSL and VSMU. For LMICs, the CIH uses the average of 2000 and 2011 GDP per capita, estimated as an income elasticity of 1.0: a one percent change in GDP per in capitathe year is 2000, associatedand that thiswith ratioa is oneconstant percent across changetime and populations. In other Thewords,CIH states that itthey is reasonable assumeto assume that the US VSMU was 1.8 percent of US GDP per capita reduction.

000 to yield the value of a standardized mortality unit (VSMU) in 2011 dollars. They use dollars.They2011 standardized in(VSMU) a mortalityunit of value the yield to 000 19,20 24 ]. It is not the value of saving a life with certainty; rather the VSL is derived from the ]. 21

000 risk reduction for the current year and “VSMU” to refer to individual will – 23 ]. The CIH posits, however, that particularly for countries with relative 3 14,15 ]. Some studies find an inverse–U relationship 1 ]. The CIH notes that empirical evidence June 2017 •Vol. 7 No. 1• 010401 Economics inGlobalHealth2035 13 ]. 16 –

18 000 ]. ------

VIEWPOINTSPAPERS PVIEWPOINTSapers June 2017 •Vol. 7 No. 1• 010401 Chang etal. from 2.3 to 2.1 GDP per capita. percent1.7capitaper GDP20132013dollars.USinof Thissmallreduction decreases LMICtheVLY from the CIH spreadsheets [ CIH – Commission on Investing in Health, VSMU – value of a standardized mortality unit, GDP – gross domestic product lion, expressed in 2013 dollars at 2013 income levels [ recentaIn criteria–driven literature review, theauthors report centrala VSLUSestimate milUS$of9 Assumption 1: VSMU this assumption is inconsistent with much of the VSL research summarized above. of altering the assumption that changes in value are proportional to changes in life expectancy, although re–ordering the steps, calculating the VLY for the US then adjusting for income. WeWe do changenot eachtest assumptionthe effectsindividually then examine their joint effect. In addition, we test the effect of SENSITIVITY ANALYSIS RESULTS but occasionally differ from the description in their report [ In our calculations, we rely on data from spreadsheets provided by CIH staff, which include more detail ment, of excluding children under 10, and of excluding adults older than 70. thosethatoccurolder at ages. Elsewhere itsanalysis,in CIHteststheeffects eliminatingof thisadjust reflect the hypothesis that the affected populations place a lower value on these risk reductions than on Prior to calculating the VLY, the CIH reduces the VSMUs for children aged 0 through 4 by 50 percent, to results from the change in mortality rates. the increase in life expectancy yields the VLY. The CIH does not account for the age distribution shift that basedonthe average of2000 and 2011 USGDP per capita (US$ 44 We apply income elasticities of 1.5 and 2.0 to illustrate the effects of larger elasticities using an equation Assumption 2: income elasticity cators report as the source of the country classification used to define LMICstheir andestimate the of 2000 GDP GDP estimatesper capita. [ CIH references the World Bank’s 2013 World Development capita,calculateIndiperandVLYGDP2011the and 2000 average estimates multiplier the of of based on per capita, discount future values at 3 percent per year, calculate the value of risk reductions using their this inconsistency has little effect the resulting VLY.) Like the CIH, we tractusehealth expenditures income from asthe GDP per capita a estimates, shorthandbutdoes notdosoconsistently. for GDP However, We explore the key assumptions listed in Table 1. in life expectancy by an amount that exceeds what they would earn over the same time period. 0.6 and 0.2 GDP per capita, respectively, violating the expectation that individuals will value an increase significantly affects the estimates. Increasing income elasticity to 1.5 and 2.0 decreases the LMIC VLY to Becausechanging theelasticity hasanexponential effect, therange ofelasticities found intheliterature can alter the results by orders of magnitude. havethelargest effect. Theappropriate elasticity ishighly uncertain, andsmall changes intheelasticity described in more detail below. Of these assumptions, we expect that the range of income elasticities will which is the age at which US life expectancy is 45 years. life expectancy at each age and at the anchor age of 35, 3(b). Adjust the VSMU for age by the ratio of the remaining age–specific mortality rates using Japanese life tables. 3(a). Convert increases in life expectancy to changes in 2. Assume an income elasticity of 1.0. 1. Assume VSMU is 1.8 percent of GDP per capita. CIH M ain C Assumptions explored in sensitivity analysis ase

VSMU LMICs

= 13

VSMU ]. US

×

(GDP per capita Table 1 4

, basing our sensitivity analysis on plausible alternatives

remaining Bulgarian life expectancy is 45 years (age 25). 3(b). Replace the anchor age of 35 with the age at which 3(a). Replace Japanese life tables with Bulgarian life tables. 2(a,b). Assume an income elasticity of 1.5 or 2.0. 1. Assume VSMU is 1.7 percent of GDP per capita. S ensitvty 8 LMICs ]. Dividing by 10 /GDP per capita A 2 nalysis ]. (It appears that the CIH intended to sub

781and US$ 48 www.jogh.org

000 yields a VSMU of US$ 900; US ) Income Elasticity • doi:10.7189/jogh.07.010401

112,respectively) 25 ]. - - - - www.jogh.org • doi:10.7189/jogh.07.010401 countries (LMICs) in 2005. 1961) and Bulgaria (between 1955 and 1958), weighted by the population density of low– and middle–income in Japan. We illustrate the distribution in in Bulgarian survival rates between 1955 and 1958 were more concentrated in younger age groups than This analysis suggests that the VLY is sensitive to the age distribution of the survival gains. Improvements Moving the anchor to age 25 leads to a further decline to 1.4. Changing the life tables while keeping the anchor age at 35 reduces the GDP per capita multipliersumed to by the1.7. CIH for the US). For Bulgaria, this is age 25 using the midpoint (1956 or 1957) life table. changingthe anchor age from 35 years to the age at which remaining life expectancy is 45 years (as as erage of 2000 and 2011 GDP per capita as the base would decrease the multiplier. per capita. We find the multiplier becomes 1.3 to 2.0, depending on the income elasticity. Using the av bound at the average of 2000 and 2011 GDP per capita, and express the VLY fectas of a usingmultiplier GDP per ofcapita 2000as a GDPlower bound. To be consistent with the CIH approach, comewe elasticitiesset the lower of 1.5 and 2.0 are applied, contrary to theoretical expectations. Thus we explore the ef As in some of our earlier calculations, the resulting VLY is less than GDP per capita for LMICs when in ing on the income elasticity ( ues for young children, we find that the VLYs for LMICs range from 0.1 to 2.0 GDP per capita, depend adjusting for income based on the average of the LMIC 2000 and 2011 values. Without reducing the val (Ukraine)LMIC[ other one only sourcefortables thisincludeslife and 1958 as an illustrative example because they are from the same data sourcetancy as butthe withJapanese a lifedifferent tables; pattern of age–specific mortality.We Wereplace selectedthe Japanese thelife tables Bulgarian with life lifetables from tables a LMIC fromthat yields 1955 a similar change in life expec Assumption 3: life tables and anchor age Figure 1. the US (using US life tables from the same data source [ The CIH adjusts the VSMU for income then calculates the VLY. We reverse the order, calculating VLY for Alternative sequencing creases the estimates in each case, as expected. Repeating each analysis without the reduction for ages 0 through 4 used in the original CIH estimates in bles anchored at 25 years of age, and find the VLY decreases to 0.4 times GDP per capita. We combine a VSMU of 1.7 percent of GDP per capita, an income elasticity of 1.5, and Bulgarian life ta Combined effect ing each set of life tables and weights the results by the LMIC population within each age group. Distribution of the changes in the standard mortality unit by age group in Japan (between 1955 and Table 3 ). Figure 1 5 Table 2 , which calculates the change in age–specific SMUs us summarizes these results. 26 ]) for the same period (2000 and 2011), then 26 ]. Weeffect].considerof the also June 2017 •Vol. 7 No. 1• 010401 Economics inGlobalHealth2035 ------

VIEWPOINTSPAPERS PVIEWPOINTSapers June 2017 •Vol. 7 No. 1• 010401 Chang etal. domestic product LMIC – low– and middle–income country, VLY – value of a life year, VSMU – value of a standardized mortality unit, GDP – gross countries and regions, or across interventions. The resulting VLY estimate is an analytic The CIH approach is designed to compare the value of the historical life expectancy gains over in thetime, research across literature and the many ways in which they can be addressed. limitationsand illustrate the enormous challenges that analysts face, given the inconsistencies and gaps empiricalresearch it is difficult to determine which approach is most appropriate. Both have significant annually. Thus the choice of approach may significantly affect the analytic conclusions, but without more Table 2. is highly sensitive to the income elasticity used. However, our reviews of the literature suggest that more More specifically, as illustrated in our sensitivity analysis, the value of changes in life expectancy in LMICs making. alystsshouldexplicitly addressuncertainties discusstheseimplicationsvaluesandthein decision- for annual income. Thus GDP per capita should be used as a lower bound. Our results also suggest that an capita (for the same year) seem implausible, given that we expect the VLY (as well as the VSLY)sumptionsand adapt tothem to exceedtheir setting. Note, however, that multipliers less than 1.0 times GDP per tions,capita.rangingpertimesGDP3.0analystsThusfrom to 0.2 should examine inputs astheand calculations. We find that the CIH estimate of the average VLY is very sensitiveInstead,analysts interested to theapplyingin the CIHapproachunderlying would needfollowto assumpthesame steps theirin period. Thus the 2.3 times GDP per capita value should not be directly applied in other settings. derlying the average VLY vary by country and age group, and reflect survival gains over a particularvalueintended time tobeused asan VSLYa 170US$of 2000 and 2011 US GDP per capita). Dividing by an average remaining life expectancy of 45 years yields muchlarger value.assumptionsCIHThemillion7.5 US$ of VSL(180 times average UStheyield aof 2011roughlyis US$68 methodology,CIHexample,theForusing expectancylifetofromUS 2000VLY changeinthe the for population life expectancy gain (assuming it is permanent) to calculate the average VLY. age–specificpopulation distribution,the of value risks, weightsage changesby the in divides then by ing a VSLY from a VSL estimate then applying it to predicted life expectancy gains, Thethe CIHCIH methodologyestimates theis fundamentally different from the traditional VSLY approach. Rather than deriv DISCUSSION Table 3. a standardized mortality unit, GDP – gross domestic product LMIC – low– and middle–income country, VLY – value of a life year, CIH – Commission on Investing in Health, VSMU – value of (c) Income elasticity (b) Income elasticity (a) Income elasticity (1) VSMU Original CIH estimate Combination:VSMU (3b) Bulgarian life table, anchoring at age 25 (3a) Bulgarian life table, anchoring at age 35 (2b) Income elasticity (2a) Income elasticity Bulgarian life table anchoring at age 25 S ensitvty Results with alternative assumptions Results with alternative sequencing

=

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1.7%GDP per capita, income elasticity

1.5 2.0 000, or US$ 300US$000,or S

with ensitvty

000.Usingtheconventional approach calculateto VSLYa fromVSLyields a a

a USVLY

analysis input

000 if futureif000 years arediscounted percentusing3rateCIH theof tovalue life expectancy gains inother settings. Theestimates un 6 LMIC VLY Without income floor as

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- - - - - www.jogh.org REFERENCES • doi:10.7189/jogh.07.010401 5 6 1 2

4 3

Hammitt doi:10.1093/heapol/czw096 Robinson 2013 cost-effectivenessthresholds within a generation. Lancet. 2013;382:1898-955. Jamison DT, Summers LH, Alleyne G, Arrow KJ, Berkley S, Binagwaho A, et al. Global health 2035: a world converging Commission on Macroeconomics and Health Robinson Health Organization. WorldHealthOrganization ment. Prepared for the World Health Organization. work is needed to determine the appropriate elasticity [ age, life expectancy, and income. studies are needed to estimate key inputs such as the appropriate VSL and the relationship betweentent VSL,empirical research means that there are numerous ways in with these values can be estimated. Moresumptions, nor do we intend to endorse or propose any particular approach. The limited and inconsis sensitivityOurcomprehensive aanalysisintended notbeis to assessment effectsastheCIH theof of discuss the implications of related uncertainties. boththerationale fortheir approach andtheextent whichtosupported is it availableby research, and normativeconcerns thatunderlie theseadjustments.age interim,theIn analysts shouldclearbe about approach lead to total values that decrease with age. More work is needed to examine the empirical and results, the CIH down–weights the values for young children, but otherwise both the VLY and the VSLY Boththe CIH VLY approach and the standard VSLY approach simplify this age relationship. Inits main patterns are likely to hold in LMICs, given cultural and other differences. thevalues held byolder adults mayremain constant ordecrease with age. Itisunclear whether similar values for their own risk reductions over their working years may follow an inverse–U pattern, and that inhigh–income countries may place higher values on risk reductions that accrue to children, that adult those affected). As discussed earlier, the available VSL research is not conclusive, but suggests thatvaries adultsage)byand normative issues (howsociety should value riskreductions depending theonageof solve, raising both empirical issues (whether individuals’ willingness to pay for their own risk Thereductionsrelationship ofthe VLY orVSLY toage orlife expectancy ismore complex and more difficult to re other stakeholders in understanding the degree to which they should have confidence in the results. cases, the conclusions may be more uncertain. Highlighting such findings will aid decision–makers and anintervention iscost–beneficial, or is not cost–beneficial, regardless of the elasticity estimate; in other sitivity of their conclusions to a reasonable range of elasticities. In some cases, they are likely to find that ; 4 Authorship contribution: Funding: feedback. shop at , the 2016 Society for Benefit–Cost Analysis conference,We andalso numerous thank seminarsparticipants for in the 2015 “Economic Evaluation in Health:hiscomments onCost–Effectivenesspreviousa draft, and Ole Norheim who provided anddetailed commentsBeyond” onan earlier version.work andforsharing theoriginal spreadsheets, Dean Jamison formany discussions ofthese calculations aswell as Acknowledgments: Jamison, co–chair of AYCreceivedhas research supportrelatedfor fromwork Disease theControl Priorities Project,Dean by led Competing interests: for all aspects of the work. mented on the revisions. All authors reviewed and approved the final manuscript, and agreeLAR, to and JKHbe checked accountable the analytic results and substantively revised the manuscript; SCR reviewed and com tent, and implementation. AYC conducted the analysis and developed the initial draft of the manuscript. AYC, peting Interest form at thor), and declare no conflict of interest. : 107

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