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We consider finite continued fractions whose elements are numbers 1 2 and 1 (the so-called A2-continued fractions): 1/a1+1/a2+...+1/an = [0; a1,a2,... ,an], ai ∈ A 2 = 1 2 , 1. We study the structure of the set F of values of all these fractions and the problem of the number of representations of numbers from the segment 1 2 ; 1 by fractions of this kind. It is proved that the set F ⊏ 1 3 ; 2 has a scaleinvariant structure and is dense in the segment 1 2 ; 1 ; the set of its elements that are greater than 1 is the set of terms of two decreasing sequences approaching 1, while the set of its elements that are smaller than 1 2 is the set of terms of two increasing sequences approaching 1 2 . The fundamental difference between the representations of numbers with the help of finite and infinite A2-fractions is emphasized. The following hypothesis is formulated: every rational number from the segment 1 2 ; 1 can be represented in the form of a finite A2-continued fraction. [ABSTRACT FROM AUTHOR]

Background: Health economic assessments are used to determine whether the resources needed to generate net benefit from an antenatal or newborn screening programme, driven by multiple benefits and harms, are justifiable. It is not known what benefits and harms have been adopted by economic evaluations assessing these programmes and whether they omit benefits and harms considered important to relevant stakeholders., Objectives: (1) To identify the benefits and harms adopted by health economic assessments in this area, and to assess how they have been measured and valued; (2) to identify attributes or relevance to stakeholders that ought to be considered in future economic assessments; and (3) to make recommendations about the benefits and harms that should be considered by these studies., Design: Mixed methods combining systematic review and qualitative work., Systematic Review Methods: We searched the published and grey literature from January 2000 to January 2021 using all major electronic databases. Economic evaluations of an antenatal or newborn screening programme in one or more Organisation for Economic Co-operation and Development countries were considered eligible. Reporting quality was assessed using the Consolidated Health Economic Evaluation Reporting Standards checklist. We identified benefits and harms using an integrative descriptive analysis and constructed a thematic framework., Qualitative Methods: We conducted a meta-ethnography of the existing literature on newborn screening experiences, a secondary analysis of existing individual interviews related to antenatal or newborn screening or living with screened-for conditions, and a thematic analysis of primary data collected with stakeholders about their experiences with screening., Results: The literature searches identified 52,244 articles and reports, and 336 unique studies were included. Thematic framework resulted in seven themes: (1) diagnosis of screened for condition, (2) life-years and health status adjustments, (3) treatment, (4) long-term costs, (5) overdiagnosis, (6) pregnancy loss and (7) spillover effects on family members. Diagnosis of screened-for condition (115, 47.5%), life-years and health status adjustments (90, 37.2%) and treatment (88, 36.4%) accounted for most of the benefits and harms evaluating antenatal screening. The same themes accounted for most of the benefits and harms included in studies assessing newborn screening. Long-term costs, overdiagnosis and spillover effects tended to be ignored. The wide-reaching family implications of screening were considered important to stakeholders. We observed good overlap between the thematic framework and the qualitative evidence., Limitations: Dual data extraction within the systematic literature review was not feasible due to the large number of studies included. It was difficult to recruit healthcare professionals in the stakeholder's interviews., Conclusions: There is no consistency in the selection of benefits and harms used in health economic assessments in this area, suggesting that additional methods guidance is needed. Our proposed thematic framework can be used to guide the development of future health economic assessments evaluating antenatal and newborn screening programmes., Study Registration: This study is registered as PROSPERO CRD42020165236., Funding: This award was funded by the National Institute for Health and Care Research (NIHR) Health Technology Assessment programme (NIHR award ref: NIHR127489) and is published in full in Health Technology Assessment ; Vol. 28, No. 25. See the NIHR Funding and Awards website for further award information.

Background: Tongue-tie can be diagnosed in 3-11% of babies, with some studies reporting almost universal breastfeeding difficulties, and others reporting very few feeding difficulties that relate to the tongue-tie itself, instead noting that incorrect positioning and attachment are the primary reasons behind the observed breastfeeding difficulties and not the tongue-tie itself. The only existing trials of frenotomy are small and underpowered and/or include only very short-term or subjective outcomes., Objective: To investigate whether frenotomy is clinically and cost-effective to promote continuation of breastfeeding at 3 months in infants with breastfeeding difficulties diagnosed with tongue-tie., Design: A multicentre, unblinded, randomised, parallel group controlled trial., Setting: Twelve infant feeding services in the UK., Participants: Infants aged up to 10 weeks referred to an infant feeding service (by a parent, midwife or other breastfeeding support service) with breastfeeding difficulties and judged to have tongue-tie., Interventions: Infants were randomly allocated to frenotomy with standard breastfeeding support or standard breastfeeding support without frenotomy., Main Outcome Measures: Primary outcome was any breastmilk feeding at 3 months according to maternal self-report. Secondary outcomes included mother's pain, exclusive breastmilk feeding, exclusive direct breastfeeding, frenotomy, adverse events, maternal anxiety and depression, maternal and infant NHS health-care resource use, cost-effectiveness, and any breastmilk feeding at 6 months of age., Results: Between March 2019 and November 2020, 169 infants were randomised, 80 to the frenotomy with breastfeeding support arm and 89 to the breastfeeding support arm from a planned sample size of 870 infants. The trial was stopped in the context of the COVID-19 pandemic due to withdrawal of breastfeeding support services, slow recruitment and crossover between arms. In the frenotomy with breastfeeding support arm 74/80 infants (93%) received their allocated intervention, compared to 23/89 (26%) in the breastfeeding support arm. Primary outcome data were available for 163/169 infants (96%). There was no evidence of a difference between the arms in the rate of breastmilk feeding at 3 months, which was high in both groups (67/76, 88% vs. 75/87, 86%; adjusted risk ratio 1.02, 95% confidence interval 0.90 to 1.16). Adverse events were reported for three infants after surgery [bleeding ( n = 1), salivary duct damage ( n = 1), accidental cut to the tongue and salivary duct damage ( n = 1)]. Cost-effectiveness could not be determined with the information available., Limitations: The statistical power of the analysis was extremely limited due to not achieving the target sample size and the high proportion of infants in the breastfeeding support arm who underwent frenotomy., Conclusions: This trial does not provide sufficient information to assess whether frenotomy in addition to breastfeeding support improves breastfeeding rates in infants diagnosed with tongue-tie., Future Work: There is a clear lack of equipoise in the UK concerning the use of frenotomy, however, the effectiveness and cost-effectiveness of the procedure still need to be established. Other study designs will need to be considered to address this objective., Trial Registration: This trial is registered as ISRCTN 10268851., Funding: This project was funded by the National Institute for Health and Care Research (NIHR) Health Technology Assessment Programme (project number 16/143/01) and will be published in full in Health Technology Assessment ; Vol. 27, No. 11. See the NIHR Journals Library website for further project information. The funder had no role in study design or data collection, analysis and interpretation. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care.

Background: Health economic assessments are used to determine whether the resources needed to generate net benefit from a screening programme, driven by multiple complex benefits and harms, are justifiable. We systematically identified the benefits and harms incorporated within economic assessments evaluating antenatal and newborn screening programmes., Methods: For this systematic review and thematic analysis, we searched the published and grey literature from January 2000 to January 2021. Studies that included an economic evaluation of an antenatal or newborn screening programme in an OECD country were eligible. We identified benefits and harms using an integrative descriptive analysis, and illustrated a thematic framework. (Systematic review registration PROSPERO, CRD42020165236)., Findings: The searches identified 52,244 articles and reports and 336 (242 antenatal and 95 newborn) were included. Eighty-six subthemes grouped into seven themes were identified: 1) diagnosis of screened for condition, 2) life years and health status adjustments, 3) treatment, 4) long-term costs, 5) overdiagnosis, 6) pregnancy loss, and 7) spillover effects on family members. Diagnosis of screened for condition (115 studies, 47.5%), life-years and health status adjustments (90 studies, 37.2%) and treatment (88 studies, 36.4%) accounted for most of the benefits and harms evaluating antenatal screening. The same themes accounted for most of the benefits and harms included in studies assessing newborn screening. Overdiagnosis and spillover effects tended to be ignored., Interpretation: Our proposed framework can be used to guide the development of future health economic assessments evaluating antenatal and newborn screening programmes, to prevent exclusion of important potential benefits and harms., Competing Interests: Declaration of competing interest OR-A, JF, BT and FB are members of the Foetal, Maternal and Child Health (FMCH) reference group of the UK National Screening Committee (UK NSC). ST-P is a member of the UK NSC Adult Reference Group. JF and AMS are members of the UK NSC. The remaining authors declare that they have no competing financial interests or personal relationshipts that could have appeared to influence the work reported in this paper., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Purpose: The most widely used generic questionnaire to estimate the quality of life for yielding quality-adjusted life years in economic evaluations is EQ-5D. Country-specific population value sets are required to use EQ-5D in economic evaluations. The aim of this study was to establish an EQ-5D-3L value set for Russia., Methods: A representative sample aged 18+ years was recruited from the Russia`s general population. Computer-assisted face-to-face interviews were conducted based on the standardized valuation protocol using EQ-Portable Valuation Technology. Population preferences were elicited utilizing both composite time trade-off (cTTO) and discrete choice experiment (DCE) techniques. To estimate the value set, a hybrid regression model combining cTTO and DCE data was used., Results: A total of 300 respondents who successfully completed the interview were included in the primary analysis. 120 (40.0%) respondents reported no health problems of any dimension, and 56 (18.7%) reported moderate health problems in one dimension of the EQ-5D-3L. Median self-rated health using EQ-VAS was 80 with IQR 70-90. Comparing cTTO and DCE-predicted values for 243 health states resulted in a similar pattern. This supports the use of hybrid models. The predicted value based on the preferred model for the worst health state "33333" was -0.503. Mobility dimension had the most significant impact on the utility decrement, and anxiety/depression had the lowest decrement., Conclusion: Determining a Russian national value set may be considered the first step towards promoting cost-utility analysis use to increase comparability among studies and improve the transferability of healthcare decision-making in Russia.

Introduction: Studies reporting on the cost-effectiveness of cancer screening usually account for quality of life losses and healthcare costs owing to cancer but do not account for future costs and quality of life losses related to competing risks. This study aims to demonstrate the impact of medical costs and quality of life losses of other diseases in the life years gained on the cost-effectiveness of U.S. cancer screening., Methods: Cost-effectiveness studies of breast, cervical, and colorectal cancer screening in the U.S. were identified using a systematic literature review. Incremental cost-effectiveness ratios of the eligible articles were updated by adding lifetime expenditures and health losses per quality-adjusted life year gained because of competing risks. This was accomplished using data on medical spending and quality of life by age and disease from the Medical Expenditure Panel Survey (2011-2015) combined with cause-deleted life tables. The study was conducted in 2018., Results: The impact of quality of life losses and healthcare expenditures of competing risks in life years gained incurred owing to screening were the highest for breast cancer and the lowest for cervical cancer. The updates suggest that incremental cost-effectiveness ratios are underestimated by $10,300-$13,700 per quality-adjusted life year gained if quality of life losses and healthcare expenditures of competing risks are omitted in economic evaluations. Furthermore, cancer screening programs that were considered cost saving, were found not to be so following the inclusion of medical expenditures of competing risks., Conclusions: Practical difficulties in quantifying quality of life losses and healthcare expenditures owing to competing risks in life years gained can be overcome. Their inclusion can have a substantial impact on the cost-effectiveness of cancer screening programs., (Copyright © 2019 American Journal of Preventive Medicine. Published by Elsevier Inc. All rights reserved.)