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Marshall DA, Gerber B, Lorenzetti DL, MacDonald KV, Bohach RJ, Currie GR. Are We Capturing the Socioeconomic Burden of Rare Genetic Disease? A Scoping Review of Economic Evaluations and Cost-of-Illness Studies. PHARMACOECONOMICS 2023; 41:1563-1588. [PMID: 37594668 DOI: 10.1007/s40273-023-01308-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 07/23/2023] [Indexed: 08/19/2023]
Abstract
BACKGROUND AND OBJECTIVES Rare diseases have a significant impact on patients, families, the health system, and society. Measuring the socioeconomic burden is crucial to valuing interventions for rare diseases. Healthcare system costs are significant, but so are costs to other government sectors, patients, families, and society. To understand the breadth of costs captured in rare disease studies, we examined the cost categories and elements of socioeconomic burden captured in published studies. METHODS A scoping review was conducted using five electronic databases to identify English language economic evaluations and cost-of-illness studies of interventions for rare diseases (2011-21). We mapped costs using a previously developed evidence-informed framework of socioeconomic burden costs for rare disease. RESULTS Of 4890 studies identified, 48 economic evaluations and 22 cost-of-illness studies were included. While 18/22 cost-of-illness studies utilized a societal perspective, only 7/48 economic evaluations incorporated societal costs. Most reported cost categories related to medical costs, with medication and hospitalizations being the most common elements for both study designs. Costs borne by patients, families, and society were reported less among economic evaluations than cost-of-illness studies. These included: productivity (10% vs 77%), travel/accommodation (6% vs 68%), government benefits (4% vs 18%), and family impacts (0% vs 50%). CONCLUSIONS Contrary to cost-of-illness analyses, most of the included economic evaluations did not account for the hidden burden of rare diseases, that is, costs borne by patients, families, and societies. Including these types of costs in future studies would provide a more comprehensive picture of the burden of disease, providing empirical data to inform how we value and make decisions regarding rare disease interventions, health policy, and resource allocation.
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Affiliation(s)
- Deborah A Marshall
- Department of Community Health Sciences, University of Calgary, Calgary, AB, Canada
- McCaig Institute for Bone and Joint Health, University of Calgary, Calgary, AB, Canada
- O'Brien Institute for Public Health, University of Calgary, Calgary, AB, Canada
- Alberta Children's Hospital Research Institute, University of Calgary, Calgary, AB, Canada
| | - Brittany Gerber
- Department of Community Health Sciences, University of Calgary, Calgary, AB, Canada
| | - Diane L Lorenzetti
- Department of Community Health Sciences, University of Calgary, Calgary, AB, Canada
- O'Brien Institute for Public Health, University of Calgary, Calgary, AB, Canada
- Health Sciences Library, University of Calgary, Calgary, AB, Canada
| | - Karen V MacDonald
- Department of Community Health Sciences, University of Calgary, Calgary, AB, Canada
| | - Riley Jewel Bohach
- Department of Community Health Sciences, University of Calgary, Calgary, AB, Canada
| | - Gillian R Currie
- Department of Community Health Sciences, University of Calgary, Calgary, AB, Canada.
- Alberta Children's Hospital Research Institute, University of Calgary, Calgary, AB, Canada.
- Department of Pediatrics, University of Calgary, Room 3C56, Health Research Innovation Centre, 3280 Hospital Drive NW, Calgary, AB, T2N 4Z6, Canada.
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Özcan S, Erdoğan Uzunoğlu Ü, Levent S, Can NÖ. Liquid chromatographic determination of lumacaftor in the presence of ivacaftor and identification of five novel degradation products using high-performance liquid chromatography ion trap time-of-flight mass spectrometry. J Sep Sci 2023; 46:e2300228. [PMID: 37409384 DOI: 10.1002/jssc.202300228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Revised: 06/06/2023] [Accepted: 06/25/2023] [Indexed: 07/07/2023]
Abstract
Lumacaftor is a transmembrane conductance regulator potentiator drug, prescribed for the treatment of cystic fibrosis in patients who are homozygous for the F508del mutation. Quantitation of lumacaftor besides its degradation products and ivacaftor was achieved on a fused-core silica particle column packed with pentafluorophenylpropyl stationary phase (Ascentis Express F5, 2.7 μm particle size 100 mm × 4.6 mm; Supelco) using gradient elution (A: 0.1% [v/v] formic acid in water, B: 0.1% [v/v] formic acid in acetonitrile [the mobile phase pH 2.5]). A constant flow rate at 1 mL/min was applied, and the detection was realized using a photodiode array detector set at 216 nm. The pseudo tablet formulation of the lumacaftor/ivacaftor fixed-dose combination preparation, namely, Orkambi®, was prepared in vitro and used for the analytical performance validation and method application studies. In addition, five novel degradation products, four of which even have no Chemical Abstracts Services registry number, were identified using high-resolution mass spectrometry instrument, and their possible mechanisms of formation were proposed. According to current literature, this paper can be regarded as the most comprehensive liquid chromatographic study on lumacaftor determination, among its counterparts.
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Affiliation(s)
- Saniye Özcan
- Department of Analytical Chemistry, Faculty of Pharmacy, Anadolu University, Eskisehir, Türkiye
- Central Analysis Laboratory, Faculty of Pharmacy, Anadolu University, Eskişehir, Türkiye
| | - Ülfet Erdoğan Uzunoğlu
- Department of Analytical Chemistry, Faculty of Pharmacy, Yeditepe University, Istanbul, Türkiye
| | - Serkan Levent
- Central Analysis Laboratory, Faculty of Pharmacy, Anadolu University, Eskişehir, Türkiye
- Department of Pharmaceutical Chemistry, Faculty of Pharmacy, Anadolu University, Eskisehir, Türkiye
| | - Nafiz Öncü Can
- Department of Analytical Chemistry, Faculty of Pharmacy, Anadolu University, Eskisehir, Türkiye
- Central Analysis Laboratory, Faculty of Pharmacy, Anadolu University, Eskişehir, Türkiye
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3
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Pratz KW, Chai X, Xie J, Yin L, Nie X, Montez M, Iantuono E, Downs L, Ma E. Cost-Effectiveness Analysis of Venetoclax in Combination with Azacitidine Versus Azacitidine Monotherapy in Patients with Acute Myeloid Leukemia Who are Ineligible for Intensive Chemotherapy: From a US Third Party Payer Perspective. PHARMACOECONOMICS 2022; 40:777-790. [PMID: 35696071 PMCID: PMC9300490 DOI: 10.1007/s40273-022-01145-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Accepted: 04/07/2022] [Indexed: 06/15/2023]
Abstract
OBJECTIVES Using individual patient-level data from the phase 3 VIALE-A trial, this study assessed the cost-effectiveness of venetoclax in combination with azacitidine compared with azacitidine monotherapy for patients newly diagnosed with acute myeloid leukemia (AML) who are ineligible for intensive chemotherapy, from a United States (US) third-party payer perspective. METHODS A partitioned survival model with a 28-day cycle and three health states (event-free survival (EFS), progressive/relapsed disease, and death) was developed to estimate costs and effectiveness of venetoclax + azacitidine versus azacitidine over a lifetime (25-year) horizon. Efficacy inputs (overall survival (OS), EFS, and complete remission (CR)/CR with incomplete marrow recovery (CRi) rate) were estimated using VIALE-A data. Best-fit parametric models per Akaike Information Criterion were used to extrapolate OS until reaching EFS and extrapolate EFS until Year 5. Within EFS, the time spent in CR/CRi was estimated by applying the CR/CRi rate to the EFS curve. Past Year 5, patients still in EFS were considered cured and to have the same mortality as the US general population. Mean time on treatment (ToT) for both regimens was based on the time observed in VIALE-A. Costs of drug acquisition, drug administration (initial and subsequent treatments), subsequent stem cell transplant procedures, adverse events (AEs), and healthcare resource utilization (HRU) associated with health states were obtained from the literature/public data and inflated to 2021 US dollars. Health state utilities were estimated using EuroQol-5 dimension-5 level data from VIALE-A; AE disutilities were obtained from the literature. Incremental cost-effectiveness ratios (ICERs) per life-year (LY) and quality-adjusted life-year (QALY) gained were estimated. Deterministic sensitivity analyses (DSA), scenario analyses, and probabilistic sensitivity analyses (PSA) were also performed. RESULTS Over a lifetime horizon, venetoclax + azacitidine versus azacitidine led to gains of 1.89 LYs (2.99 vs. 1.10, respectively) and 1.45 QALYs (2.30 vs. 0.84, respectively). Patients receiving venetoclax + azacitidine incurred higher total lifetime costs ($250,486 vs. $110,034 (azacitidine)). The ICERs for venetoclax + azacitidine versus azacitidine were estimated at $74,141 per LY and $96,579 per QALY gained. Results from the DSA and scenario analyses supported the base-case findings, with ICERs ranging from $60,718 to $138,554 per QALY gained. The results were most sensitive to varying the parameters for the venetoclax + azacitidine base-case EFS parametric function (Gompertz), followed by alternative approaches for ToT estimation, treatment costs of venetoclax + azacitidine, standard mortality rate value and ToT estimation, alternative sources to inform HRU, different cure modeling assumptions, and the parameters for the venetoclax + azacitidine base-case OS parametric function (log-normal). Results from the PSA showed that, compared with azacitidine, venetoclax + azacitidine was cost-effective in 99.9% of cases at a willingness-to-pay threshold of $150,000 per QALY. CONCLUSIONS This analysis suggests that venetoclax + azacitidine offers a cost-effective strategy in the treatment of patients with newly diagnosed AML who are ineligible for intensive chemotherapy from a US third-party payer perspective. TRIAL REGISTRATION ClinicalTrials.gov, NCT02993523. Date of registration: 15 December 2016.
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Affiliation(s)
- Keith W Pratz
- Hospital of the University of Pennsylvania, 3400 Spruce St, Philadelphia, PA, 19104, USA.
| | | | - Jipan Xie
- Analysis Group, Inc., Los Angeles, CA, USA
| | - Lei Yin
- Analysis Group, Inc., Los Angeles, CA, USA
| | - Xiaoyu Nie
- Analysis Group, Inc., Los Angeles, CA, USA
| | | | | | - Lisa Downs
- Genentech, Inc., South San Francisco, CA, USA
| | - Esprit Ma
- Genentech, Inc., South San Francisco, CA, USA
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Liao W, Xu H, Hutton D, Wu Q, Zhou K, Luo H, Lei W, Feng M, Yang Y, Wen F, Li Q. Cost-Effectiveness Analysis of Fourth- or Further-Line Ripretinib in Advanced Gastrointestinal Stromal Tumors. Front Oncol 2021; 11:692005. [PMID: 34938653 PMCID: PMC8685288 DOI: 10.3389/fonc.2021.692005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 11/05/2021] [Indexed: 02/05/2023] Open
Abstract
Background The INVICTUS trial assessed the efficacy and safety of ripretinib compared with placebo in the management of advanced gastrointestinal stromal tumors. Method We used a Markov model with three health states: progression-free disease, progression disease and death. We parameterized the model from time-to-event data (progression-free survival, overall survival) of ripretinib and placebo arms in the INVICTUS trial and extrapolated to a patient’s lifetime horizon. Estimates of health state utilities and costs were based on clinical trial data and the published literature. The outcomes of this model were measured in quality-adjusted life-years (QALYs), costs, and incremental cost-effectiveness ratios (ICERs). Uncertainty was tested via univariate and probabilistic sensitivity analyses. Results The base-case model projected improved outcomes (by 0.29 QALYs) and additional costs (by $70,251) and yielded an ICER of $244,010/QALY gained for ripretinib versus placebo. The results were most sensitive to progression rates, the price of ripretinib, and health state utilities. The ICER was most sensitive to overall survival. When overall survival in the placebo group was lower, the ICER dropped to $127,399/QALY. The ICER dropped to $150,000/QALY when the monthly cost of ripretinib decreased to $14,057. Probabilistic sensitivity analyses revealed that ripretinib was the cost-effective therapy in 41.1% of simulations at the willingness-to-pay (WTP) threshold of $150,000. Conclusion As the fourth- or further-line therapy in advanced gastrointestinal stromal tumors, ripretinib is not cost-effective in the US. Ripretinib would achieve its cost-effectiveness with a price discount of 56% given the present effectiveness.
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Affiliation(s)
- Weiting Liao
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
| | - Huiqiong Xu
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China
| | - David Hutton
- Department of Health Management and Policy, University of Michigan, Ann Arbor, MI, United States
| | - Qiuji Wu
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
| | - Kexun Zhou
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
| | - Hui Luo
- State Key Laboratory of Biotherapy and Cancer Center, West China Hospital, Sichuan University and Collaborative Innovation Center, Chengdu, China
| | - Wanting Lei
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
| | - Mingyang Feng
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
| | - Yang Yang
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
| | - Feng Wen
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
| | - Qiu Li
- Department of Medical Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, China.,West China Biomedical Big Data Center, Sichuan University, Chengdu, China
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Shrestha CL, Zhang S, Wisniewski B, Häfner S, Elie J, Meijer L, Kopp BT. (R)-Roscovitine and CFTR modulators enhance killing of multi-drug resistant Burkholderia cenocepacia by cystic fibrosis macrophages. Sci Rep 2020; 10:21700. [PMID: 33303916 PMCID: PMC7728753 DOI: 10.1038/s41598-020-78817-x] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 11/30/2020] [Indexed: 01/01/2023] Open
Abstract
Cystic fibrosis (CF) is characterized by chronic bacterial infections and heightened inflammation. Widespread ineffective antibiotic use has led to increased isolation of drug resistant bacterial strains from respiratory samples. (R)-roscovitine (Seliciclib) is a unique drug that has many benefits in CF studies. We sought to determine roscovitine’s impact on macrophage function and killing of multi-drug resistant bacteria. Human blood monocytes were isolated from CF (F508del/F508del) and non-CF persons and derived into macrophages (MDMs). MDMs were infected with CF clinical isolates of B. cenocepacia and P. aeruginosa. MDMs were treated with (R)-roscovitine or its main hepatic metabolite (M3). Macrophage responses to infection and subsequent treatment were determined. (R)-roscovitine and M3 significantly increased killing of B. cenocepacia and P. aeruginosa in CF MDMs in a dose-dependent manner. (R)-roscovitine-mediated effects were partially dependent on CFTR and the TRPC6 channel. (R)-roscovitine-mediated killing of B. cenocepacia was enhanced by combination with the CFTR modulator tezacaftor/ivacaftor and/or the alternative CFTR modulator cysteamine. (R)-roscovitine also increased MDM CFTR function compared to tezacaftor/ivacaftor treatment alone. (R)-roscovitine increases CF macrophage-mediated killing of antibiotic-resistant bacteria. (R)-roscovitine also enhances other macrophage functions including CFTR-mediated ion efflux. Effects of (R)-roscovitine are greatest when combined with CFTR modulators or cysteamine, justifying further clinical testing of (R)-roscovitine or optimized derivatives.
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Affiliation(s)
- Chandra L Shrestha
- Division of Pulmonary Medicine, Center for Microbial Pathogenesis, The Abigail Wexner Research Institute At Nationwide Children's Hospital, 700 Children's Drive, Columbus, OH, 43205, USA
| | - Shuzhong Zhang
- Division of Pulmonary Medicine, Center for Microbial Pathogenesis, The Abigail Wexner Research Institute At Nationwide Children's Hospital, 700 Children's Drive, Columbus, OH, 43205, USA
| | - Benjamin Wisniewski
- Division of Pulmonary Medicine, Center for Microbial Pathogenesis, The Abigail Wexner Research Institute At Nationwide Children's Hospital, 700 Children's Drive, Columbus, OH, 43205, USA
| | - Stephanie Häfner
- Rudolf-Boehm-Institut F. Pharmakologie U. Toxikologie Medizinische Fakultät, Universität Leipzig, Leipzig, Germany
| | - Jonathan Elie
- ManRos Therapeutics, Perharidy Peninsula, Roscoff, France
| | - Laurent Meijer
- ManRos Therapeutics, Perharidy Peninsula, Roscoff, France
| | - Benjamin T Kopp
- Division of Pulmonary Medicine, Center for Microbial Pathogenesis, The Abigail Wexner Research Institute At Nationwide Children's Hospital, 700 Children's Drive, Columbus, OH, 43205, USA.
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McGlynn JA, Langfelder-Schwind E. Bridging the Gap between Scientific Advancement and Real-World Application: Pediatric Genetic Counseling for Common Syndromes and Single-Gene Disorders. Cold Spring Harb Perspect Med 2020; 10:cshperspect.a036640. [PMID: 31570386 DOI: 10.1101/cshperspect.a036640] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Screening and diagnostic testing for single-gene disorders and common syndromes in the pediatric setting frequently generate data that are challenging to interpret, and the ability to diagnose genetic conditions has outpaced the development of successful treatments or cures. Genetic testing is now integrated purposefully into a variety of primary and specialty care clinics, creating an increased requirement for genetic literacy among providers and patients, as well as a growing need to incorporate genetic counseling services into mainstream clinical practice. The practice of pediatric genetic counseling encompasses a unique combination of skills and training designed to address the evolving psychological, social, educational, medical, and reproductive concerns of patients and their families, which complements the multidisciplinary services of physicians, nurses, and other allied health professionals caring for patients with pediatric-onset genetic conditions. The potential range of genetic counseling needs in the pediatric setting transcends the diagnostic period. The sustained nature of pediatric care presents opportunities for development of trusting and longstanding professional relationships that permit the evolving genetic counseling needs of patients and families to be met. A discussion of cystic fibrosis, a common autosomal recessive single-gene disorder with an increasingly broad clinical spectrum and genotype-phenotype variability, serves as a useful case study to illustrate the current and emerging genetic counseling practices, goals, and challenges impacting patients and their families.
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Affiliation(s)
- Julie A McGlynn
- Department of Obstetrics, Gynecology, and Reproductive Sciences, Yale School of Medicine, New Haven, Connecticut 06510, USA
| | - Elinor Langfelder-Schwind
- The Cystic Fibrosis Center, Mount Sinai Beth Israel, Icahn School of Medicine at Mount Sinai, New York, New York 10003, USA
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Lopes-Pacheco M. CFTR Modulators: The Changing Face of Cystic Fibrosis in the Era of Precision Medicine. Front Pharmacol 2020; 10:1662. [PMID: 32153386 PMCID: PMC7046560 DOI: 10.3389/fphar.2019.01662] [Citation(s) in RCA: 242] [Impact Index Per Article: 60.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Accepted: 12/19/2019] [Indexed: 12/22/2022] Open
Abstract
Cystic fibrosis (CF) is a lethal inherited disease caused by mutations in the CF transmembrane conductance regulator (CFTR) gene, which result in impairment of CFTR mRNA and protein expression, function, stability or a combination of these. Although CF leads to multifaceted clinical manifestations, the respiratory disorder represents the major cause of morbidity and mortality of these patients. The life expectancy of CF patients has substantially lengthened due to early diagnosis and improvements in symptomatic therapeutic regimens. Quality of life remains nevertheless limited, as these individuals are subjected to considerable clinical, psychosocial and economic burdens. Since the discovery of the CFTR gene in 1989, tremendous efforts have been made to develop therapies acting more upstream on the pathogenesis cascade, thereby overcoming the underlying dysfunctions caused by CFTR mutations. In this line, the advances in cell-based high-throughput screenings have been facilitating the fast-tracking of CFTR modulators. These modulator drugs have the ability to enhance or even restore the functional expression of specific CF-causing mutations, and they have been classified into five main groups depending on their effects on CFTR mutations: potentiators, correctors, stabilizers, read-through agents, and amplifiers. To date, four CFTR modulators have reached the market, and these pharmaceutical therapies are transforming patients' lives with short- and long-term improvements in clinical outcomes. Such breakthroughs have paved the way for the development of novel CFTR modulators, which are currently under experimental and clinical investigations. Furthermore, recent insights into the CFTR structure will be useful for the rational design of next-generation modulator drugs. This review aims to provide a summary of recent developments in CFTR-directed therapeutics. Barriers and future directions are also discussed in order to optimize treatment adherence, identify feasible and sustainable solutions for equitable access to these therapies, and continue to expand the pipeline of novel modulators that may result in effective precision medicine for all individuals with CF.
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Affiliation(s)
- Miquéias Lopes-Pacheco
- Biosystems & Integrative Sciences Institute, Faculty of Sciences, University of Lisbon, Lisbon, Portugal
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Health Disparities. Respir Med 2020. [DOI: 10.1007/978-3-030-42382-7_3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Abstract
Maternal mortality rate (MMR) in China has reduced during a decade but still higher than many countries around the world. Rural China is the key region which affects over all maternal death. This study aims to develop a suitable model in forecasting rural MMR and offer some suggestions for rural MMR intervention. Data in this study were collected through the Health Statistical Yearbook (2017) which included the overall MMR in China and urban and rural mortality rate. A basic grey model (GM(1,1)), 3 metabolic grey models (MGM), and a hybrid GM(1,1)-Markov model were presented to estimate rural MMR tendency. Average relative error (ARE), the post-test ratio (C), and small error probability (P) were adopted to evaluate models' fitting performance while forecasting effectiveness was compared by relative error.The MMR in rural China reduced obviously from 63.0 per 100,000 live births in 2005 to 21.1 per 100,000 live births in 2017. One basic GM(1,1) model was built to fit the rural MMR and the expression was X^((1)) (k + 1) = 553.80e^0.0947k - 550.00 (C = 0.0456, P > .99). Three MGM models expressions were X^((1)) (k + 1) = 548.67e^0.0923k - 503.17 (C = 0.0540, P > .99), X^((1)) (k + 1) = 449.39e^0.0887k - 408.09 (C = 0.0560, P > .99), X^((1)) (k + 1) = 461.33e^0.0893k - 425.23(C = 0.0660, P > .99). Hybrid GM(1,1)-Markov model showed the best fitting performance (C = 0.0804, P > .99). The relative errors of basic GM(1,1) model and hybrid model in fitting part were 2.42% and 2.03%, respectively, while 5.35% and 2.08%, respectively, in forecasting part. The average relative errors of MGM were 2.07% in fitting part and 17.37% in forecasting part.Data update was crucial in maintain model's effectiveness. The hybrid GM(1,1)-Markov model was better than basic GM(1,1) model in rural MMR prediction. It could be considered as a decision-making tool in rural MMR intervention.
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Affiliation(s)
- Michael J Joyner
- Department of Anesthesiology and Perioperative Medicine, Mayo Clinic, Rochester, Minnesota, USA
| | - Nigel Paneth
- Departments of Epidemiology and Biostatistics and Pediatrics and Human Development, Michigan State University, College of Human Medicine, East Lansing, Michigan, USA
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