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Keramat A, Flores-Gerónimo J, Alastruey J, Zhang Y. Uncertainty quantification of the pressure waveform using a Windkessel model. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024:e3867. [PMID: 39239830 DOI: 10.1002/cnm.3867] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Revised: 08/09/2024] [Accepted: 08/23/2024] [Indexed: 09/07/2024]
Abstract
The Windkessel (WK) model is a simplified mathematical model used to represent the systemic arterial circulation. While the WK model is useful for studying blood flow dynamics, it suffers from inaccuracies or uncertainties that should be considered when using it to make physiological predictions. This paper aims to develop an efficient and easy-to-implement uncertainty quantification method based on a local gradient-based formulation to quantify the uncertainty of the pressure waveform resulting from aleatory uncertainties of the WK parameters and flow waveform. The proposed methodology, tested against Monte Carlo simulations, demonstrates good agreement in estimating blood pressure uncertainties due to uncertain Windkessel parameters, but less agreement considering uncertain blood-flow waveforms. To illustrate our methodology's applicability, we assessed the aortic pressure uncertainty generated by Windkessel parameters-sets from an available in silico database representing healthy adults. The results from the proposed formulation align qualitatively with those in the database and in vivo data. Furthermore, we investigated how changes in the uncertainty of the Windkessel parameters affect the uncertainty of systolic, diastolic, and pulse pressures. We found that peripheral resistance uncertainty produces the most significant change in the systolic and diastolic blood pressure uncertainties. On the other hand, compliance uncertainty considerably modifies the pulse pressure standard deviation. The presented expansion-based method is a tool for efficiently propagating the Windkessel parameters' uncertainty to the pressure waveform. The Windkessel model's clinical use depends on the reliability of the pressure in the presence of input uncertainties, which can be efficiently investigated with the proposed methodology. For instance, in wearable technology that uses sensor data and the Windkessel model to estimate systolic and diastolic blood pressures, it is important to check the confidence level in these calculations to ensure that the pressures accurately reflect the patient's cardiovascular condition.
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Affiliation(s)
- Alireza Keramat
- Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
| | - Joaquín Flores-Gerónimo
- Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
| | - Jordi Alastruey
- Department of Biomedical Engineering, School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Yuanting Zhang
- Department of Electronic Engineering, The Chinese University of Hong Kong, Sha Tin, Hong Kong
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Olender RT, Roy S, Nishtala PS. Application of machine learning approaches in predicting clinical outcomes in older adults - a systematic review and meta-analysis. BMC Geriatr 2023; 23:561. [PMID: 37710210 PMCID: PMC10503191 DOI: 10.1186/s12877-023-04246-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 08/19/2023] [Indexed: 09/16/2023] Open
Abstract
BACKGROUND Machine learning-based prediction models have the potential to have a considerable positive impact on geriatric care. DESIGN Systematic review and meta-analyses. PARTICIPANTS Older adults (≥ 65 years) in any setting. INTERVENTION Machine learning models for predicting clinical outcomes in older adults were evaluated. A random-effects meta-analysis was conducted in two grouped cohorts, where the predictive models were compared based on their performance in predicting mortality i) under and including 6 months ii) over 6 months. OUTCOME MEASURES Studies were grouped into two groups by the clinical outcome, and the models were compared based on the area under the receiver operating characteristic curve metric. RESULTS Thirty-seven studies that satisfied the systematic review criteria were appraised, and eight studies predicting a mortality outcome were included in the meta-analyses. We could only pool studies by mortality as there were inconsistent definitions and sparse data to pool studies for other clinical outcomes. The area under the receiver operating characteristic curve from the meta-analysis yielded a summary estimate of 0.80 (95% CI: 0.76 - 0.84) for mortality within 6 months and 0.81 (95% CI: 0.76 - 0.86) for mortality over 6 months, signifying good discriminatory power. CONCLUSION The meta-analysis indicates that machine learning models display good discriminatory power in predicting mortality. However, more large-scale validation studies are necessary. As electronic healthcare databases grow larger and more comprehensive, the available computational power increases and machine learning models become more sophisticated; there should be an effort to integrate these models into a larger research setting to predict various clinical outcomes.
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Affiliation(s)
- Robert T Olender
- Department of Life Sciences, University of Bath, Bath, BA2 7AY, UK.
| | - Sandipan Roy
- Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK
| | - Prasad S Nishtala
- Department of Life Sciences & Centre for Therapeutic Innovation, University of Bath, Bath, BA2 7AY, UK
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Cavallazzi R, Bradley J, Chandler T, Furmanek S, Ramirez JA. Severity of Illness Scores and Biomarkers for Prognosis of Patients with Coronavirus Disease 2019. Semin Respir Crit Care Med 2023; 44:75-90. [PMID: 36646087 DOI: 10.1055/s-0042-1759567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
The spectrum of disease severity and the insidiousness of clinical presentation make it difficult to recognize patients with coronavirus disease 2019 (COVID-19) at higher risk of worse outcomes or death when they are seen in the early phases of the disease. There are now well-established risk factors for worse outcomes in patients with COVID-19. These should be factored in when assessing the prognosis of these patients. However, a more precise prognostic assessment in an individual patient may warrant the use of predictive tools. In this manuscript, we conduct a literature review on the severity of illness scores and biomarkers for the prognosis of patients with COVID-19. Several COVID-19-specific scores have been developed since the onset of the pandemic. Some of them are promising and can be integrated into the assessment of these patients. We also found that the well-known pneumonia severity index (PSI) and CURB-65 (confusion, uremia, respiratory rate, BP, age ≥ 65 years) are good predictors of mortality in hospitalized patients with COVID-19. While neither the PSI nor the CURB-65 should be used for the triage of outpatient versus inpatient treatment, they can be integrated by a clinician into the assessment of disease severity and can be used in epidemiological studies to determine the severity of illness in patient populations. Biomarkers also provide valuable prognostic information and, importantly, may depict the main physiological derangements in severe disease. We, however, do not advocate the isolated use of severity of illness scores or biomarkers for decision-making in an individual patient. Instead, we suggest the use of these tools on a case-by-case basis with the goal of enhancing clinician judgment.
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Affiliation(s)
- Rodrigo Cavallazzi
- Division of Pulmonary, Critical Care Medicine, and Sleep Disorders, University of Louisville, Norton Healthcare, Louisville, Kentucky
| | - James Bradley
- Division of Pulmonary, Critical Care Medicine, and Sleep Disorders, University of Louisville, Norton Healthcare, Louisville, Kentucky
| | - Thomas Chandler
- Norton Infectious Diseases Institute, Norton Healthcare, Louisville, Kentucky
| | - Stephen Furmanek
- Norton Infectious Diseases Institute, Norton Healthcare, Louisville, Kentucky
| | - Julio A Ramirez
- Norton Infectious Diseases Institute, Norton Healthcare, Louisville, Kentucky
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Lee AK, Diaz-Ramirez LG, John Boscardin W, Smith AK, Lee SJ. A comprehensive prognostic tool for older adults: Predicting death, ADL disability, and walking disability simultaneously. J Am Geriatr Soc 2022; 70:2884-2894. [PMID: 35792836 PMCID: PMC9588505 DOI: 10.1111/jgs.17932] [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: 02/24/2022] [Revised: 05/03/2022] [Accepted: 05/23/2022] [Indexed: 11/30/2022]
Abstract
BACKGROUND Many clinical and financial decisions for older adults depend on the future risk of disability and mortality. Prognostic tools for long-term disability risk in a general population are lacking. We aimed to create a comprehensive prognostic tool that predicts the risk of mortality, of activities of daily living (ADL) disability, and walking disability simultaneously using the same set of variables. METHODS We conducted a longitudinal analysis of the nationally-representative Health and Retirement Study (HRS). We included community-dwelling adults aged ≥70 years who completed a core interview in the 2000 wave of HRS, with follow-up through 2018. We evaluated 40 predictors encompassing demographics, diseases, physical functioning, and instrumental ADLs. We applied novel methods to optimize three models simultaneously while prioritizing variables that take less time to ascertain during backward stepwise elimination. The death prediction model used Cox regression and both the models for walking disability and for ADL disability used Fine and Gray competing-risk regression. We examined calibration plots and generated optimism-corrected statistics of discrimination using bootstrapping. To simulate unavailable patient data, we also evaluated models excluding one or two variables from the final model. RESULTS In 6646 HRS participants, 2662 developed walking disability, 3570 developed ADL disability, and 5689 died during a median follow-up of 9.5 years. The final prognostic tool had 16 variables. The optimism-corrected integrated area under the curve (iAUC) was 0.799 for mortality, 0.685 for walking disability, and 0.703 for ADL disability. At each percentile of predicted mortality risk, there was a substantial spread in the predicted risks of walking disability and ADL disability. Discrimination and calibration remained good even when missing one or two predictors from the model. This model is now available on ePrognosis (https://eprognosis.ucsf.edu/alexlee.php) CONCLUSIONS: Given the variability in disability risk for people with similar mortality risks, using individualized risks of disabilities may inform clinical and financial decisions for older adults.
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Affiliation(s)
- Alexandra K. Lee
- Division of Geriatrics, Department of Medicine, UCSF, San Francisco, CA
- San Francisco Veterans Affairs Healthcare System, San Francisco, CA
| | | | - W. John Boscardin
- Division of Geriatrics, Department of Medicine, UCSF, San Francisco, CA
- San Francisco Veterans Affairs Healthcare System, San Francisco, CA
- Division of Biostatistics, Department of Epidemiology and Biostatistics, UCSF, San Francisco, CA
| | - Alexander K. Smith
- Division of Geriatrics, Department of Medicine, UCSF, San Francisco, CA
- San Francisco Veterans Affairs Healthcare System, San Francisco, CA
| | - Sei J. Lee
- Division of Geriatrics, Department of Medicine, UCSF, San Francisco, CA
- San Francisco Veterans Affairs Healthcare System, San Francisco, CA
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Diaz-Ramirez LG, Lee SJ, Smith AK, Gan S, Boscardin WJ. A Novel Method for Identifying a Parsimonious and Accurate Predictive Model for Multiple Clinical Outcomes. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2021; 204:106073. [PMID: 33831724 PMCID: PMC8098121 DOI: 10.1016/j.cmpb.2021.106073] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 03/22/2021] [Indexed: 06/12/2023]
Abstract
BACKGROUND AND OBJECTIVE Most methods for developing clinical prognostic models focus on identifying parsimonious and accurate models to predict a single outcome; however, patients and providers often want to predict multiple outcomes simultaneously. As an example, for older adults one is often interested in predicting nursing home admission as well as mortality. We propose and evaluate a novel predictor-selection computing method for multiple outcomes and provide the code for its implementation. METHODS Our proposed algorithm selected the best subset of common predictors based on the minimum average normalized Bayesian Information Criterion (BIC) across outcomes: the Best Average BIC (baBIC) method. We compared the predictive accuracy (Harrell's C-statistic) and parsimony (number of predictors) of the model obtained using the baBIC method with: 1) a subset of common predictors obtained from the union of optimal models for each outcome (Union method), 2) a subset obtained from the intersection of optimal models for each outcome (Intersection method), and 3) a model with no variable selection (Full method). We used a case-study data from the Health and Retirement Study (HRS) to demonstrate our method and conducted a simulation study to investigate performance. RESULTS In the case-study data and simulations, the average Harrell's C-statistics across outcomes of the models obtained with the baBIC and Union methods were comparable. Despite the similar discrimination, the baBIC method produced more parsimonious models than the Union method. In contrast, the models selected with the Intersection method were the most parsimonious, but with worst predictive accuracy, and the opposite was true in the Full method. In the simulations, the baBIC method performed well by identifying many of the predictors selected in the baBIC model of the case-study data most of the time and excluding those not selected in the majority of the simulations. CONCLUSIONS Our method identified a common subset of variables to predict multiple clinical outcomes with superior balance between parsimony and predictive accuracy to current methods.
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Affiliation(s)
- L Grisell Diaz-Ramirez
- Division of Geriatrics, University of California, San Francisco, 490 Illinois Street, Floor 08, Box 1265, San Francisco, CA 94143, United States; San Francisco Veterans Affairs (VA) Medical Center, 4150 Clement Street, 181G, San Francisco, CA 94121, United States.
| | - Sei J Lee
- Division of Geriatrics, University of California, San Francisco, 490 Illinois Street, Floor 08, Box 1265, San Francisco, CA 94143, United States; San Francisco Veterans Affairs (VA) Medical Center, 4150 Clement Street, 181G, San Francisco, CA 94121, United States.
| | - Alexander K Smith
- Division of Geriatrics, University of California, San Francisco, 490 Illinois Street, Floor 08, Box 1265, San Francisco, CA 94143, United States; San Francisco Veterans Affairs (VA) Medical Center, 4150 Clement Street, 181G, San Francisco, CA 94121, United States.
| | - Siqi Gan
- Division of Geriatrics, University of California, San Francisco, 490 Illinois Street, Floor 08, Box 1265, San Francisco, CA 94143, United States; San Francisco Veterans Affairs (VA) Medical Center, 4150 Clement Street, 181G, San Francisco, CA 94121, United States.
| | - W John Boscardin
- Division of Geriatrics, University of California, San Francisco, 490 Illinois Street, Floor 08, Box 1265, San Francisco, CA 94143, United States; San Francisco Veterans Affairs (VA) Medical Center, 4150 Clement Street, 181G, San Francisco, CA 94121, United States.
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