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Guo S, Ge JX, Liu SN, Zhou JY, Li C, Chen HJ, Chen L, Shen YQ, Zhou QL. Development of a convenient and effective hypertension risk prediction model and exploration of the relationship between Serum Ferritin and Hypertension Risk: a study based on NHANES 2017-March 2020. Front Cardiovasc Med 2023; 10:1224795. [PMID: 37736023 PMCID: PMC10510409 DOI: 10.3389/fcvm.2023.1224795] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 07/28/2023] [Indexed: 09/23/2023] Open
Abstract
Background Hypertension is a major public health problem, and its resulting other cardiovascular diseases are the leading cause of death worldwide. In this study, we constructed a convenient and high-performance hypertension risk prediction model to assist in clinical diagnosis and explore other important influencing factors. Methods We included 8,073 people from NHANES (2017-March 2020), using their 120 features to form the original dataset. After data pre-processing, we removed several redundant features through LASSO regression and correlation analysis. Thirteen commonly used machine learning methods were used to construct prediction models, and then, the methods with better performance were coupled with recursive feature elimination to determine the optimal feature subset. After data balancing through SMOTE, we integrated these better-performing learners to construct a fusion model based for predicting hypertension risk on stacking strategy. In addition, to explore the relationship between serum ferritin and the risk of hypertension, we performed a univariate analysis and divided it into four level groups (Q1 to Q4) by quartiles, with the lowest level group (Q1) as the reference, and performed multiple logistic regression analysis and trend analysis. Results The optimal feature subsets were: age, BMI, waist, SBP, DBP, Cre, UACR, serum ferritin, HbA1C, and doctors recommend reducing salt intake. Compared to other machine learning models, the constructed fusion model showed better predictive performance with precision, accuracy, recall, F1 value and AUC of 0.871, 0.873, 0.871, 0.869 and 0.966, respectively. For the analysis of the relationship between serum ferritin and hypertension, after controlling for all co-variates, OR and 95% CI from Q2 to Q4, compared to Q1, were 1.396 (1.176-1.658), 1.499 (1.254-1.791), and 1.645 (1.360-1.989), respectively, with P < 0.01 and P for trend <0.001. Conclusion The hypertension risk prediction model developed in this study is efficient in predicting hypertension with only 10 low-cost and easily accessible features, which is cost-effective in assisting clinical diagnosis. We also found a trend correlation between serum ferritin levels and the risk of hypertension.
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Affiliation(s)
- Shuang Guo
- Information Center, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
| | - Jiu-Xin Ge
- Department of Cardiology, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
| | - Shan-Na Liu
- Information Center, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
| | - Jia-Yu Zhou
- Xinjiang Second Medical College, Karamay, China
| | - Chang Li
- Information Center, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
| | - Han-Jie Chen
- Information Center, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
| | - Li Chen
- Information Center, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
| | - Yu-Qiang Shen
- Information Center, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
| | - Qing-Li Zhou
- Information Center, The Fourth Affiliated Hospital, Zhejiang University School of Medicine, Yiwu, China
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Mirjalili SR, Soltani S, Heidari Meybodi Z, Marques-Vidal P, Kraemer A, Sarebanhassanabadi M. An innovative model for predicting coronary heart disease using triglyceride-glucose index: a machine learning-based cohort study. Cardiovasc Diabetol 2023; 22:200. [PMID: 37542255 PMCID: PMC10403891 DOI: 10.1186/s12933-023-01939-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 07/24/2023] [Indexed: 08/06/2023] Open
Abstract
BACKGROUND Various predictive models have been developed for predicting the incidence of coronary heart disease (CHD), but none of them has had optimal predictive value. Although these models consider diabetes as an important CHD risk factor, they do not consider insulin resistance or triglyceride (TG). The unsatisfactory performance of these prediction models may be attributed to the ignoring of these factors despite their proven effects on CHD. We decided to modify standard CHD predictive models through machine learning to determine whether the triglyceride-glucose index (TyG-index, a logarithmized combination of fasting blood sugar (FBS) and TG that demonstrates insulin resistance) functions better than diabetes as a CHD predictor. METHODS Two-thousand participants of a community-based Iranian population, aged 20-74 years, were investigated with a mean follow-up of 9.9 years (range: 7.6-12.2). The association between the TyG-index and CHD was investigated using multivariate Cox proportional hazard models. By selecting common components of previously validated CHD risk scores, we developed machine learning models for predicting CHD. The TyG-index was substituted for diabetes in CHD prediction models. All components of machine learning models were explained in terms of how they affect CHD prediction. CHD-predicting TyG-index cut-off points were calculated. RESULTS The incidence of CHD was 14.5%. Compared to the lowest quartile of the TyG-index, the fourth quartile had a fully adjusted hazard ratio of 2.32 (confidence interval [CI] 1.16-4.68, p-trend 0.04). A TyG-index > 8.42 had the highest negative predictive value for CHD. The TyG-index-based support vector machine (SVM) performed significantly better than diabetes-based SVM for predicting CHD. The TyG-index was not only more important than diabetes in predicting CHD; it was the most important factor after age in machine learning models. CONCLUSION We recommend using the TyG-index in clinical practice and predictive models to identify individuals at risk of developing CHD and to aid in its prevention.
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Affiliation(s)
- Seyed Reza Mirjalili
- Yazd Cardiovascular Research Center, Non-Communicable Diseases Research Institute, Shahid Sadoughi University of Medical Sciences, Yazd, Iran
| | - Sepideh Soltani
- Yazd Cardiovascular Research Center, Non-Communicable Diseases Research Institute, Shahid Sadoughi University of Medical Sciences, Yazd, Iran
| | - Zahra Heidari Meybodi
- Yazd Cardiovascular Research Center, Non-Communicable Diseases Research Institute, Shahid Sadoughi University of Medical Sciences, Yazd, Iran
| | - Pedro Marques-Vidal
- Department of Internal Medicine, BH10-642, Rue du Bugnon 46, CH-1011, Lausanne, Switzerland
| | - Alexander Kraemer
- Department of Health Sciences, Bielefeld University, Bielefeld, Germany
| | - Mohammadtaghi Sarebanhassanabadi
- Yazd Cardiovascular Research Center, Non-Communicable Diseases Research Institute, Shahid Sadoughi University of Medical Sciences, Yazd, Iran.
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Mehrabani-Zeinabad K, Feizi A, Sadeghi M, Roohafza H, Talaei M, Sarrafzadegan N. Cardiovascular disease incidence prediction by machine learning and statistical techniques: a 16-year cohort study from eastern Mediterranean region. BMC Med Inform Decis Mak 2023; 23:72. [PMID: 37076833 PMCID: PMC10116769 DOI: 10.1186/s12911-023-02169-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 04/04/2023] [Indexed: 04/21/2023] Open
Abstract
BACKGROUND Cardiovascular diseases (CVD) are the predominant cause of early death worldwide. Identification of people with a high risk of being affected by CVD is consequential in CVD prevention. This study adopts Machine Learning (ML) and statistical techniques to develop classification models for predicting the future occurrence of CVD events in a large sample of Iranians. METHODS We used multiple prediction models and ML techniques with different abilities to analyze the large dataset of 5432 healthy people at the beginning of entrance into the Isfahan Cohort Study (ICS) (1990-2017). Bayesian additive regression trees enhanced with "missingness incorporated in attributes" (BARTm) was run on the dataset with 515 variables (336 variables without and the remaining with up to 90% missing values). In the other used classification algorithms, variables with more than 10% missing values were excluded, and MissForest imputes the missing values of the remaining 49 variables. We used Recursive Feature Elimination (RFE) to select the most contributing variables. Random oversampling technique, recommended cut-point by precision-recall curve, and relevant evaluation metrics were used for handling unbalancing in the binary response variable. RESULTS This study revealed that age, systolic blood pressure, fasting blood sugar, two-hour postprandial glucose, diabetes mellitus, history of heart disease, history of high blood pressure, and history of diabetes are the most contributing factors for predicting CVD incidence in the future. The main differences between the results of classification algorithms are due to the trade-off between sensitivity and specificity. Quadratic Discriminant Analysis (QDA) algorithm presents the highest accuracy (75.50 ± 0.08) but the minimum sensitivity (49.84 ± 0.25); In contrast, decision trees provide the lowest accuracy (51.95 ± 0.69) but the top sensitivity (82.52 ± 1.22). BARTm.90% resulted in 69.48 ± 0.28 accuracy and 54.00 ± 1.66 sensitivity without any preprocessing step. CONCLUSIONS This study confirmed that building a prediction model for CVD in each region is valuable for screening and primary prevention strategies in that specific region. Also, results showed that using conventional statistical models alongside ML algorithms makes it possible to take advantage of both techniques. Generally, QDA can accurately predict the future occurrence of CVD events with a fast (inference speed) and stable (confidence values) procedure. The combined ML and statistical algorithm of BARTm provide a flexible approach without any need for technical knowledge about assumptions and preprocessing steps of the prediction procedure.
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Affiliation(s)
- Kamran Mehrabani-Zeinabad
- Cardiovascular Research Center, Cardiovascular Research Institute, Isfahan University of Medical Sciences, Isfahan, Iran
| | - Awat Feizi
- Biostatistics and Epidemiology Department, School of Health, Isfahan University of Medical Sciences, Isfahan, Iran.
- Cardiac Rehabilitation Research Center, Cardiovascular Research Institute, Isfahan University of Medical Sciences, Isfahan, Iran.
| | - Masoumeh Sadeghi
- Cardiac Rehabilitation Research Center, Cardiovascular Research Institute, Isfahan University of Medical Sciences, Isfahan, Iran
| | - Hamidreza Roohafza
- Cardiovascular Research Center, Cardiovascular Research Institute, Isfahan University of Medical Sciences, Isfahan, Iran
| | - Mohammad Talaei
- Wolfson Institute of Population Health, Barts and The London School of Medicine and Dentistry, Queen Mary University of London, London, UK
| | - Nizal Sarrafzadegan
- Cardiovascular Research Center, Cardiovascular Research Institute, Isfahan University of Medical Sciences, Isfahan, Iran
- School of Population and Public Health, Faculty of Medicine, University of British Columbia, Vancouver, Canada
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Sriprasart T, Siasoco MB, Aggarwal B, Levy G, Phansalkar A, Van GV, Cohen M, Seemungal T, Pizzichini MMM, Mokhtar M, Daley-Yates P. The role of modeling studies in asthma management and clinical decision-making: a Delphi survey of physician knowledge and perceptions. J Asthma 2023:1-15. [PMID: 36825839 DOI: 10.1080/02770903.2023.2180748] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Abstract
OBJECTIVE To investigate the knowledge and perceptions of physicians on the role of modeling studies in asthma, using a modified Delphi procedure. METHODS Group opinions among a panel of respiratory experts were obtained using two online questionnaires and a virtual scientific workshop. A consensus was pre-defined as agreement by >75% of participants. RESULTS From 26 experts who agreed to participate, 22 completed both surveys. At the end of the process, the panel rated their own understanding of modeling as good (77%) but that among physicians in general as poor (77%). Participants agreed that data from modeling studies should be used, at least sometimes, to inform treatment guidelines (91%) and could be useful for guiding clinical decisions (100%). Perceived barriers to using modeling studies were 'A lack of understanding' (81%) and 'A lack of standardized methodology' (82%). Based on data from two modeling studies, no consensus was reached on physicians recommending regular inhaled corticosteroids (ICS) versus as-needed therapy for patients with mild asthma, whereas 77% agreed that they would recommend regular ICS over maintenance and reliever therapy for ≥80% of their patients with moderate asthma. No consensus was reached on the value of modeling data in relation to empirical data. CONCLUSION There is overall support among respiratory experts for the usefulness of modeling data to guide asthma treatment guidelines and clinical decision making. More publications on modeling data using robust models and accessible terminology will aid the understanding of physicians in general and help clarify the evidence-based value of modeling studies.
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Affiliation(s)
- Thitiwat Sriprasart
- Faculty of Medicine, Chulalongkorn University and King Chulalongkorn Memorial Hospital, Thai Red Cross Society, Bangkok, Thailand
| | - Ma Bella Siasoco
- Pulmonary Division, Department of Medicine, University of the Philippines College of Medicine - Philippine General Hospital, Manila, Philippines
| | | | - Gur Levy
- Respiratory Medical Emerging Markets, GSK, Ciudad de Panamá, Panama
| | | | - Giap Vu Van
- Respiratory Center, Bach Mai Hospital, Hanoi, Vietnam.,Internal Medicine Department, Hanoi Medical University, Hanoi, Vietnam
| | - Mark Cohen
- Edificio Clinicas Centro Médico 2, Guatemala city, Guatemala
| | - Terence Seemungal
- Faculty of Medical Sciences, The University of The West Indies, St. Augustine, Trinidad & Tobago
| | - Marcia M M Pizzichini
- Internal Medicine Division, Federal University of Santa Catarina, Florianópolis, Brazil
| | - Mahmoud Mokhtar
- Respiratory Unit, Mubarak Al-Kabeer Hospital, Jabriya, Kuwait
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Han J, Guo X, Zhao L, Zhang H, Ma S, Li Y, Zhao D, Wang J, Xue F. Development and Validation of Esophageal Squamous Cell Carcinoma Risk Prediction Models Based on an Endoscopic Screening Program. JAMA Netw Open 2023; 6:e2253148. [PMID: 36701154 PMCID: PMC9880791 DOI: 10.1001/jamanetworkopen.2022.53148] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
IMPORTANCE Assessment tools are lacking for screening of esophageal squamous cell cancer (ESCC) in China, especially for the follow-up stage. Risk prediction to optimize the screening procedure is urgently needed. OBJECTIVE To develop and validate ESCC prediction models for identifying people at high risk for follow-up decision-making. DESIGN, SETTING, AND PARTICIPANTS This open, prospective multicenter diagnostic study has been performed since September 1, 2006, in Shandong Province, China. This study used baseline and follow-up data until December 31, 2021. The data were analyzed between April 6 and May 31, 2022. Eligibility criteria consisted of rural residents aged 40 to 69 years who had no contraindications for endoscopy. Among 161 212 eligible participants, those diagnosed with cancer or who had cancer at baseline, did not complete the questionnaire, were younger than 40 years or older than 69 years, or were detected with severe dysplasia or worse lesions were eliminated from the analysis. EXPOSURES Risk factors obtained by questionnaire and endoscopy. MAIN OUTCOMES AND MEASURES Pathological diagnosis of ESCC and confirmation by cancer registry data. RESULTS In this diagnostic study of 104 129 participants (56.39% women; mean [SD] age, 54.31 [7.64] years), 59 481 (mean [SD] age, 53.83 [7.64] years; 58.55% women) formed the derivation set while 44 648 (mean [SD] age, 54.95 [7.60] years; 53.51% women) formed the validation set. A total of 252 new cases of ESCC were diagnosed during 424 903.50 person-years of follow-up in the derivation cohort and 61 new cases from 177 094.10 person-years follow-up in the validation cohort. Model A included the covariates age, sex, and number of lesions; model B included age, sex, smoking status, alcohol use status, body mass index, annual household income, history of gastrointestinal tract diseases, consumption of pickled food, number of lesions, distinct lesions, and mild or moderate dysplasia. The Harrell C statistic of model A was 0.80 (95% CI, 0.77-0.83) in the derivation set and 0.90 (95% CI, 0.87-0.93) in the validation set; the Harrell C statistic of model B was 0.83 (95% CI, 0.81-0.86) and 0.91 (95% CI, 0.88-0.95), respectively. The models also had good calibration performance and clinical usefulness. CONCLUSIONS AND RELEVANCE The findings of this diagnostic study suggest that the models developed are suitable for selecting high-risk populations for follow-up decision-making and optimizing the cancer screening process.
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Affiliation(s)
- Junming Han
- Department of Biostatistics, School of Public Health, Cheeloo College of Medicine, Shandong University, Jinan, China
- Healthcare Big Data Research Institute, School of Public Health, Cheeloo College of Medicine, Shandong University, Jinan, China
| | - Xiaolei Guo
- The Department for Chronic and Noncommunicable Disease Control and Prevention, Shandong Center for Disease Control and Prevention and Academy of Preventive Medicine, Shandong University, Jinan, China
| | - Li Zhao
- Department of Scientific Research and Teaching, Feicheng Hospital Affiliated to Shandong First Medical University, Feicheng, China
| | - Huan Zhang
- School of Public Health, Shandong First Medical University and Shandong Academy of Medical Sciences, Jinan, China
| | - Siqi Ma
- School of Public Health, Shandong First Medical University and Shandong Academy of Medical Sciences, Jinan, China
| | - Yan Li
- Cancer Prevention and Treatment Center, Feicheng People’s Hospital, Feicheng, China
| | - Deli Zhao
- Cancer Prevention and Treatment Center, Feicheng People’s Hospital, Feicheng, China
| | - Jialin Wang
- School of Public Health, Shandong First Medical University and Shandong Academy of Medical Sciences, Jinan, China
- Department of Human Resource, Shandong Cancer Hospital and Institute, Shandong First Medical University and Shandong Academy of Medical Sciences, Jinan, China
| | - Fuzhong Xue
- Department of Biostatistics, School of Public Health, Cheeloo College of Medicine, Shandong University, Jinan, China
- Healthcare Big Data Research Institute, School of Public Health, Cheeloo College of Medicine, Shandong University, Jinan, China
- Qilu Hospital, Cheeloo College of Medicine, Shandong University, Jinan, China
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Subramani S, Varshney N, Anand MV, Soudagar MEM, Al-keridis LA, Upadhyay TK, Alshammari N, Saeed M, Subramanian K, Anbarasu K, Rohini K. Cardiovascular diseases prediction by machine learning incorporation with deep learning. Front Med (Lausanne) 2023; 10:1150933. [PMID: 37138750 PMCID: PMC10150633 DOI: 10.3389/fmed.2023.1150933] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Accepted: 03/09/2023] [Indexed: 05/05/2023] Open
Abstract
It is yet unknown what causes cardiovascular disease (CVD), but we do know that it is associated with a high risk of death, as well as severe morbidity and disability. There is an urgent need for AI-based technologies that are able to promptly and reliably predict the future outcomes of individuals who have cardiovascular disease. The Internet of Things (IoT) is serving as a driving force behind the development of CVD prediction. In order to analyse and make predictions based on the data that IoT devices receive, machine learning (ML) is used. Traditional machine learning algorithms are unable to take differences in the data into account and have a low level of accuracy in their model predictions. This research presents a collection of machine learning models that can be used to address this problem. These models take into account the data observation mechanisms and training procedures of a number of different algorithms. In order to verify the efficacy of our strategy, we combined the Heart Dataset with other classification models. The proposed method provides nearly 96 percent of accuracy result than other existing methods and the complete analysis over several metrics has been analysed and provided. Research in the field of deep learning will benefit from additional data from a large number of medical institutions, which may be used for the development of artificial neural network structures.
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Affiliation(s)
- Sivakannan Subramani
- Department of Advanced Computing, St. Joseph's University, Bengaluru, Karnataka, India
| | - Neeraj Varshney
- Department of Computer Engineering and Applications, GLA University, Mathura, Uttar Pradesh, India
| | - M. Vijay Anand
- Department of Mechanical Engineering, Kongu Engineering College, Perundurai, Erode, Tamil Nadu, India
| | | | | | - Tarun Kumar Upadhyay
- Department of Biotechnology, Parul Institute of Applied Sciences and Centre of Research for Development, Parul University, Vadodara, India
| | - Nawaf Alshammari
- Department of Biology, College of Science, University of Hail, Hail, Saudi Arabia
| | - Mohd Saeed
- Department of Biology, College of Science, University of Hail, Hail, Saudi Arabia
| | - Kumaran Subramanian
- Centre for Drug Discovery and Development, Sathyabama Institute of Science and Technology, Chennai, Tamil Nadu, India
| | - Krishnan Anbarasu
- Department of Bioinformatics, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India
| | - Karunakaran Rohini
- Unit of Biochemistry, Centre of Excellence for Biomaterials Engeneering, Faculty of Medicine, AIMST University, Semeleing, Bedong, Malaysia
- Centre for Excellence for Biomaterials Science AIMST University, Semeling, Bedong, Malaysia
- Department of Computational Biology, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India
- *Correspondence: Rohini Karunakaran,
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Smith H, Sweeting M, Morris T, Crowther MJ. A scoping methodological review of simulation studies comparing statistical and machine learning approaches to risk prediction for time-to-event data. Diagn Progn Res 2022; 6:10. [PMID: 35650647 PMCID: PMC9161606 DOI: 10.1186/s41512-022-00124-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 03/01/2022] [Indexed: 12/24/2022] Open
Abstract
BACKGROUND There is substantial interest in the adaptation and application of so-called machine learning approaches to prognostic modelling of censored time-to-event data. These methods must be compared and evaluated against existing methods in a variety of scenarios to determine their predictive performance. A scoping review of how machine learning methods have been compared to traditional survival models is important to identify the comparisons that have been made and issues where they are lacking, biased towards one approach or misleading. METHODS We conducted a scoping review of research articles published between 1 January 2000 and 2 December 2020 using PubMed. Eligible articles were those that used simulation studies to compare statistical and machine learning methods for risk prediction with a time-to-event outcome in a medical/healthcare setting. We focus on data-generating mechanisms (DGMs), the methods that have been compared, the estimands of the simulation studies, and the performance measures used to evaluate them. RESULTS A total of ten articles were identified as eligible for the review. Six of the articles evaluated a method that was developed by the authors, four of which were machine learning methods, and the results almost always stated that this developed method's performance was equivalent to or better than the other methods compared. Comparisons were often biased towards the novel approach, with the majority only comparing against a basic Cox proportional hazards model, and in scenarios where it is clear it would not perform well. In many of the articles reviewed, key information was unclear, such as the number of simulation repetitions and how performance measures were calculated. CONCLUSION It is vital that method comparisons are unbiased and comprehensive, and this should be the goal even if realising it is difficult. Fully assessing how newly developed methods perform and how they compare to a variety of traditional statistical methods for prognostic modelling is imperative as these methods are already being applied in clinical contexts. Evaluations of the performance and usefulness of recently developed methods for risk prediction should be continued and reporting standards improved as these methods become increasingly popular.
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Affiliation(s)
- Hayley Smith
- grid.9918.90000 0004 1936 8411Department of Health Sciences, University of Leicester, Leicester, LE1 7RH UK
| | - Michael Sweeting
- grid.9918.90000 0004 1936 8411Department of Health Sciences, University of Leicester, Leicester, LE1 7RH UK
- grid.417815.e0000 0004 5929 4381Statistical Innovation, Oncology Biometrics, Oncology R&D, AstraZeneca, Cambridge, UK
| | - Tim Morris
- grid.415052.70000 0004 0606 323XMRC Clinical Trials Unit at UCL, 90 High Holborn, London, WC1V 6LJ UK
| | - Michael J. Crowther
- grid.4714.60000 0004 1937 0626Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden
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