Class Of Statistical Models Research Articles

Machine Learning-Based Prediction for Incident Hypertension Based on Regular Health Checkup Data: Derivation and Validation in 2 Independent Nationwide Cohorts in South Korea and Japan.

Worldwide, cardiovascular diseases are the primary cause of death, with hypertension as a key contributor. In 2019, cardiovascular diseases led to 17.9 million deaths, predicted to reach 23 million by 2030. This study presents a new method to predict hypertension using demographic data, using 6 machine learning models for enhanced reliability and applicability. The goal is to harness artificial intelligence for early and accurate hypertension diagnosis across diverse populations. Data from 2 national cohort studies, National Health Insurance Service-National Sample Cohort (South Korea, n=244,814), conducted between 2002 and 2013 were used to train and test machine learning models designed to anticipate incident hypertension within 5 years of a health checkup involving those aged ≥20 years, and Japanese Medical Data Center cohort (Japan, n=1,296,649) were used for extra validation. An ensemble from 6 diverse machine learning models was used to identify the 5 most salient features contributing to hypertension by presenting a feature importance analysis to confirm the contribution of each future. The Adaptive Boosting and logistic regression ensemble showed superior balanced accuracy (0.812, sensitivity 0.806, specificity 0.818, and area under the receiver operating characteristic curve 0.901). The 5 key hypertension indicators were age, diastolic blood pressure, BMI, systolic blood pressure, and fasting blood glucose. The Japanese Medical Data Center cohort dataset (extra validation set) corroborated these findings (balanced accuracy 0.741 and area under the receiver operating characteristic curve 0.824). The ensemble model was integrated into a public web portal for predicting hypertension onset based on health checkup data. Comparative evaluation of our machine learning models against classical statistical models across 2 distinct studies emphasized the former's enhanced stability, generalizability, and reproducibility in predicting hypertension onset.

Robust prediction of colorectal cancer via gut microbiome 16S rRNA sequencing data.

Introduction. The study addresses the challenge of utilizing human gut microbiome data for the early detection of colorectal cancer (CRC). The research emphasizes the potential of using machine learning techniques to analyze complex microbiome datasets, providing a non-invasive approach to identifying CRC-related microbial markers.Hypothesis/Gap Statement. The primary hypothesis is that a robust machine learning-based analysis of 16S rRNA microbiome data can identify specific microbial features that serve as effective biomarkers for CRC detection, overcoming the limitations of classical statistical models in high-dimensional settings.Aim. The primary objective of this study is to explore and validate the potential of the human microbiome, specifically in the colon, as a valuable source of biomarkers for colorectal cancer (CRC) detection and progression. The focus is on developing a classifier that effectively predicts the presence of CRC and normal samples based on the analysis of three previously published faecal 16S rRNA sequencing datasets.Methodology. To achieve the aim, various machine learning techniques are employed, including random forest (RF), recursive feature elimination (RFE) and a robust correlation-based technique known as the fuzzy forest (FF). The study utilizes these methods to analyse the three datasets, comparing their performance in predicting CRC and normal samples. The emphasis is on identifying the most relevant microbial features (taxa) associated with CRC development via partial dependence plots, i.e. a machine learning tool focused on explainability, visualizing how a feature influences the predicted outcome.Results. The analysis of the three faecal 16S rRNA sequencing datasets reveals the consistent and superior predictive performance of the FF compared to the RF and RFE. Notably, FF proves effective in addressing the correlation problem when assessing the importance of microbial taxa in explaining the development of CRC. The results highlight the potential of the human microbiome as a non-invasive means to detect CRC and underscore the significance of employing FF for improved predictive accuracy.Conclusion. In conclusion, this study underscores the limitations of classical statistical techniques in handling high-dimensional information such as human microbiome data. The research demonstrates the potential of the human microbiome, specifically in the colon, as a valuable source of biomarkers for CRC detection. Applying machine learning techniques, particularly the FF, is a promising approach for building a classifier to predict CRC and normal samples. The findings advocate for integrating FF to overcome the challenges associated with correlation when identifying crucial microbial features linked to CRC development.

Artificial intelligence in prostate cancer: The potential of machine learning models and neural networks to predict biochemical recurrence after robot-assisted radical prostatectomy

ABSTRACT Introduction: This study aimed to evaluate the usefulness of machine learning (ML) and neural network (NN) models versus traditional statistical methods for estimating biochemical recurrence (BCR) in men following robot-assisted radical prostatectomy (RARP). Methods: Patients who underwent RARP from November 2011 to July 2022 were taken in the study. Patients with BCR were assigned to Group 2, whereas those without BCR were placed in Group 1. Preoperative and postoperative parameters, together with demographic data, were recorded in the database. This study used one NN, the radial basis function NN (RBFNN), and two ML approaches, the K-nearest neighbor and XGboost ML models, to predict BCR. Results: Following the application of exclusion criteria, 516 patients were deemed eligible for the study. Of those, 234 (45.3%) developed BCR, and 282 (54.7%) did not. The results showed that the median follow-up period was 24 (15–42) months, and the median BCR diagnosis was 12.23 ± 15.58 months. The area under the curve (AUC) for the Cox proportional hazard analysis was 0.77. The receiver-operating characteristic curves (AUCs) for the XGBoost and K closest neighbor models were 0.82 and 0.69, respectively. The RBFNN’s AUC was 0.82. Conclusions: The classical statistical model was outperformed by XGBoost and RBFNN models in predicting BCR.

Development of Econometric Models for Financial Performance Forecasting in Companies

This study develops an econometric model to predict corporate financial performance. The goal is to improve the accuracy of predictions by analysing relevant economic and financial variables. The model combines statistical and econometric analysis to identify significant input variables such as asset turnover, firm size, capital structure, and liquidity. The study also highlights the importance of external factors, such as environmental policies and knowledge management, that affect corporate financial performance. Using ARIMA and VAR models, the study shows that selecting the correct parameters, such as the number of lags, is critical to improving prediction accuracy. The developed model is evaluated based on RMSE, MAD, and MAPE metrics, which show that the econometric model offers more accurate predictions than the classical statistical model. These results contribute significantly to understanding corporate financial performance dynamics and can be a reliable tool in strategic decision-making across various industry sectors.

Predicting Economic Trends and Stock Market Prices with Deep Learning and Advanced Machine Learning Techniques

The volatile and non-linear nature of stock market data, particularly in the post-pandemic era, poses significant challenges for accurate financial forecasting. To address these challenges, this research develops advanced deep learning and machine learning algorithms to predict financial trends, quantify risks, and forecast stock prices, focusing on the technology sector. Our study seeks to answer the following question: “Which deep learning and supervised machine learning algorithms are the most accurate and efficient in predicting economic trends and stock market prices, and under what conditions do they perform best?” We focus on two advanced recurrent neural network (RNN) models, long short-term memory (LSTM) and Gated Recurrent Unit (GRU), to evaluate their efficiency in predicting technology industry stock prices. Additionally, we integrate statistical methods such as autoregressive integrated moving average (ARIMA) and Facebook Prophet and machine learning algorithms like Extreme Gradient Boosting (XGBoost) to enhance the robustness of our predictions. Unlike classical statistical algorithms, LSTM and GRU models can identify and retain important data sequences, enabling more accurate predictions. Our experimental results show that the GRU model outperforms the LSTM model in terms of prediction accuracy and training time across multiple metrics such as RMSE and MAE. This study offers crucial insights into the predictive capabilities of deep learning models and advanced machine learning techniques for financial forecasting, highlighting the potential of GRU and XGBoost for more accurate and efficient stock price prediction in the technology sector.

A comparative analysis of classical and machine learning methods for forecasting TB/HIV co-infection

TB/HIV coinfection poses a complex public health challenge. Accurate forecasting of future trends is essential for efficient resource allocation and intervention strategy development. This study compares classical statistical and machine learning models to predict TB/HIV coinfection cases stratified by gender and the general populations. We analyzed time series data using exponential smoothing and ARIMA to establish the baseline trend and seasonality. Subsequently, machine learning models (SVR, XGBoost, LSTM, CNN, GRU, CNN-GRU, and CNN-LSTM) were employed to capture the complex dynamics and inherent non-linearities of TB/HIV coinfection data. Performance metrics (MSE, MAE, sMAPE) and the Diebold-Mariano test were used to evaluate the model performance. Results revealed that Deep Learning models, particularly Bidirectional LSTM and CNN-LSTM, significantly outperformed classical methods. This demonstrates the effectiveness of Deep Learning for modeling TB/HIV coinfection time series and generating more accurate forecasts.

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science.

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback-Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback-Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

A censored quantile transformation model for Alzheimer’s Disease data with multiple functional covariates

Abstract Alzheimer’s disease (AD) is a progressive disease that starts from mild cognitive impairment and may eventually lead to irreversible memory loss. It is imperative to explore the risk factors associated with the conversion time to AD that is usually right-censored. Classical statistical models like mean regression and Cox models fail to quantify the impact of risk factors across different quantiles of a response distribution, and previous research has primarily focused on modelling a single functional covariate, possibly overlooking the interdependence among multiple functional covariates and other crucial features of the distribution. To address these issues, this paper proposes a multivariate functional censored quantile regression model based on dynamic power transformations, which relaxes the global linear assumption and provides more robustness and flexibility. Uniform consistency and weak convergence of the quantile process are established. Simulation studies suggest that the proposed method outperforms the existing approaches. Real data analysis shows the importance of both left and right hippocampal radial distance curves for predicting the conversion time to AD at different quantile levels.

Optimization of the Use of Cloud Computing Resources Using Exploratory Data Analysis and Machine Learning

Abstract Rapid growth in the popularity of cloud computing has been largely caused by increasing demand for scalable IT solutions, which could provide a cost-effective way to manage the software development process and meet business objectives. Optimization of cloud resource usage remains a key issue given its potential to significantly increase efficiency and flexibility, minimize costs, ensure security, and maintain high availability of services. This paper presents a novel concept of a Cloud Computing Resource Prediction and Optimization System, which is based on exploratory data analysis that acknowledges, among others, the information value of outliers and dynamic feature selection. The optimization of cloud resource usage relies on long-term forecasting, which is considered a dynamic and proactive optimization category. The analysis presented here focuses on the applicability of classical statistical models, XGBoost, neural networks and Transformer. Experimental results reveal that machine learning methods are highly effective in long-term forecasting. Particularly promising results – in the context of potential prediction-based dynamic resource reservations – have been yielded by prediction methods based on the BiGRU neural network and the Temporal Fusion Transformer.

Fusion surface models: 2+1d lattice models from fusion 2-categories

We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with, for example, anomalous or non-anomalous one-form symmetries, 2-group symmetries, or non-invertible one-form symmetries that capture non-abelian anyon statistics. The construction of these models generalizes the construction of the 1+1d anyon chains formalized by Aasen, Fendley, and Mong. Along with the fusion surface models, we also obtain the corresponding three-dimensional classical statistical models, which are 3d analogues of the 2d Aasen-Fendley-Mong height models. In the construction, the “symmetry TFTs” for fusion 2-category symmetries play an important role.

Simulation of functional additive and non-additive genetic effects using statistical estimates from quantitative genetic models

Stochastic simulation software is commonly used to aid breeders designing cost-effective breeding programs and to validate statistical models used in genetic evaluation. An essential feature of the software is the ability to simulate populations with desired genetic and non-genetic parameters. However, this feature often fails when non-additive effects due to dominance or epistasis are modeled, as the desired properties of simulated populations are estimated from classical quantitative genetic statistical models formulated at the population level. The software simulates underlying functional effects for genotypic values at the individual level, which are not necessarily the same as effects from statistical models in which dominance and epistasis are included. This paper provides the theoretical basis and mathematical formulas for the transformation between functional and statistical effects in such simulations. The transformation is demonstrated with two statistical models analyzing individual phenotypes in a single population (common in animal breeding) and plot phenotypes of three-way hybrids involving two inbred populations (observed in some crop breeding programs). We also describe different methods for the simulation of functional effects for additive genetics, dominance, and epistasis to achieve the desired levels of variance components in classical statistical models used in quantitative genetics.

An Enhanced Long-Term Wind Speed Prediction Using Dynamic Unified Ensemble Learning and Data Assimilation Techniques: A Case Study in Tamil Nadu, India

Reliable wind speed prediction is essential for effective grid management since wind energy is a key component of renewable energy generation. However, controlling wind speed just right is no easy feat since the wind flow changes constantly. This paper presents an innovative method for predicting wind speeds in the future. It uses state-of-the-art data assimilation methods and a dynamic unified ensemble learning model. For efficient wind energy planning and monitoring, WSP accuracy is crucial. Data from a single site limited the accuracy of WSPs in previous research. An improved accuracy of long-term wind speed predictions is achieved by the proposed model via the integration of data assimilation and ensemble learning. To increase forecast accuracy, the model uses sophisticated data assimilation methods like the Kalman filter to combine data from many sources. Specifically, the model employs the Stacked CNN + BiLSTM with Data Assimilator (SCBLSTM+DA) technique, which integrates Wind Speed (WS) data from adjacent areas with the CNN + BiLSTM-based Ensemble Learning Model (ELM) and the Four-Dimensional Variational and Ensemble Kalman Filter (4DVar/EnKF) Data Assimilation method. Using real-world wind speed data from nine meteorological stations in Tamil Nadu, India, we find that current prediction models, including both classical statistical and cutting-edge machine learning models, perform better. Further, unlike standalone models, the suggested model shows less susceptibility to changes in prediction time scales. Promising a solution to improve long-term wind speed predictions accuracy, this study has significant consequences for wind energy management and production.

Decomposition and Holt-Winters Enhanced by the Whale Optimization Algorithm for Forecasting the Amount of Water Inflow into the Large Dam Reservoirs in Southern Thailand

This study introduces hybrid forecasting models integrating the Whale Optimization Algorithm (WOA) with Holt-Winters (HW) and decomposition methods, applied in both additive and multiplicative models, for time series forecasting. Focusing on monthly water inflow into four dam reservoirs in Southern Thailand, the study compares these hybrid models against classical statistical models, Grid Search for Holt-Winters (Grid-HW) and Classical Decomposition (Classic-D). The analysis comprises two phases: the training dataset phase and the testing dataset phase. In the training phase, WOA demonstrates superior parameter optimization, enhancing both HW and decomposition methods, resulting in lower Mean Absolute Error (MAE) values compared to classical models. In the testing phase, performance metrics such as Root Mean Square Error (RMSE), MAE, and Symmetric Mean Absolute Percentage Error (sMAPE) are employed. The findings reveal that the Whale Optimization Algorithm with Holt-Winters (WOA-HW) and Decomposition (WOA-D) models surpass classical approaches in long-term forecasting accuracy for three dam reservoirs. Over 24 data points, the WOA with Multiplicative Holt-Winters (WOA-HWx) is optimal for Pran Buri dam, the WOA with Additive Decomposition (WOA-D+) for Bang Lang dam, and the WOA with Multiplicative Decomposition (WOA-Dx) for Kaeng Krachan dam. The Box-Jenkins approach, further refined through a Box-Cox transformation employing a natural logarithm, emerged as the superior forecasting model for Rajjaprabha dam. This model satisfied all critical statistical criteria, including normality of residuals (Anderson-Darling: 0.359, p-value: 0.433), homoscedasticity (Levene's test: 1.24, p-value: 0.274), independence (Ljung-Box test: 14.10, p-value: 0.169), and zero mean (t-test: -0.39, p-value: 0.702), establishing its robustness and reliability for forecast analysis.

Identification of causal influences in quantum processes

Recent years have seen great interest in extending causal inference concepts developed in the context of classical statistical models to quantum theory. So far, this program has only barely addressed causal identification, a type of causal inference problem concerned with recovering from observational data and qualitative assumptions the causal relationships generating the data, and hence the effects of hypothetical interventions. A major obstacle to a theory of causal identification in the quantum setting is the question of what should play the role of “observational data,” as any means of extracting data at a locus will almost certainly disturb the system. One might think that quantum measurements are already too much like interventions, so that the problem of causal identification is trivialized. This is not the case: when we fix a limited class of quantum measurement instruments (namely, the class of all projective measurements) to play the role of “observations,” there exist scenarios for which causal identification is impossible. In this paper, we present a framework, based on process theories (also known as strict symmetric monoidal categories), for studying quantum causal identification scenarios on the same footing as their classical counterparts. Within this framework, we present sufficient conditions for quantum causal identification in networks with unobserved confounding systems, including quantum analogs of the well-known “back-door” and “front-door” criteria. These results arise from a type of causal model designed to facilitate the transfer of inference techniques from the classical to the quantum setting. Published by the American Physical Society 2024

Code-Free Machine Learning Approach for EVO-ICL Vault Prediction: A Retrospective Two-Center Study.

Establishing a development environment for machine learning is difficult for medical researchers because learning to code is a major barrier. This study aimed to improve the accuracy of a postoperative vault value prediction model for implantable collamer lens (ICL) sizing using machine learning without coding experience. We used Orange data mining, a recently developed open-source, code-free machine learning tool. This study included eye-pair data from 294 patients from the B&VIIT Eye Center and 26 patients from Kim's Eye Hospital. The model was developed using OCULUS Pentacam data from the B&VIIT Eye Center and was internally evaluated through 10-fold cross-validation. External validation was performed using data from Kim's Eye Hospital. The machine learning model was successfully trained using the data collected without coding. The random forest showed mean absolute errors of 124.8 µm and 152.4 µm for the internal 10-fold cross-validation and the external validation, respectively. For high vault prediction (>750 µm), the random forest showed areas under the curve of 0.725 and 0.760 for the internal and external validation datasets, respectively. The developed model performed better than the classic statistical regression models and the Google no-code platform. Applying a no-code machine learning tool to our ICL implantation datasets showed a more accurate prediction of the postoperative vault than the classic regression and Google no-code models. Because of significant bias in measurements and surgery between clinics, the no-code development of a customized machine learning nomogram will improve the accuracy of ICL implantation.

Geospatial assessment of landslide-prone areas in the southern part of Anambra State, Nigeria using classical statistical models

Geospatial assessment of landslide-prone areas in the southern part of Anambra State, Nigeria using classical statistical models

Predicting dental anxiety in young adults: classical statistical modelling approach versus machine learning approach

ObjectivesTo predict and identify the key demographic and clinical exposure factors associated with dental anxiety among young adults, and to compare if the traditional statistical modelling approach provides similar results to the machine learning (ML) approach in predicting factors for dental anxiety.MethodsA cross-sectional study of Western Illinois University students. Three survey instruments (sociodemographic questionnaire, modified dental anxiety scale (MDAS), and dental concerns assessment tool (DCA)) were distributed via email to the students using survey monkey. The dependent variable was the mean MDAS scores, while the independent variables were the sociodemographic and dental concern assessment variables. Multivariable analysis was done by comparing the classical statistical model and the machine learning model. The classical statistical modelling technique was conducted using the multiple linear regression analysis and the final model was selected based on Akaike information Criteria (AIC) using the backward stepwise technique while the machine learining modelling was performed by comparing two ML models: LASSO regression and extreme gradient boosting machine (XGBOOST) under 5-fold cross-validation using the resampling technique. All statistical analyses were performed using R version 4.1.3.ResultsThe mean MDAS was 13.73 ± 5.51. After careful consideration of all possible fitted models and their interaction terms the classical statistical approach yielded a parsimonious model with 13 predictor variables with Akaike Information Criteria (AIC) of 2376.4. For the ML approach, the Lasso regression model was the best-performing model with a mean RMSE of 0.617, R2 of 0.615, and MAE of 0.483. Comparing the variable selection of ML versus the classical statistical model, both model types identified 12 similar variables (out of 13) as the most important predictors of dental anxiety in this study population.ConclusionThere is a high burden of dental anxiety within this study population. This study contributes to reducing the knowledge gap about the impact of clinical exposure variables on dental anxiety and the role of machine learningin the prediction of dental anxiety. The predictor variables identified can be used to inform public health interventions that are geared towards eliminating the individual clinical exposure triggers of dental anxiety are recommended.

Identifying predictors of the tooth loss phenotype in a large periodontitis patient cohort using a machine learning approach

ObjectivesThis study aimed to identify predictors associated with the tooth loss phenotype in a large periodontitis patient cohort in the university setting. MethodsInformation on periodontitis patients and nineteen factors identified at the initial visit was extracted from electronic health records. The primary outcome is tooth loss phenotype (presence or absence of tooth loss). Prediction models were built on significant factors (single or combinatory) selected by the RuleFit algorithm, and these factors were further adopted by regression models. Model performance was evaluated by Area Under the Receiver Operating Characteristic Curve (AUROC) and Area Under the Precision-Recall Curve (AUPRC). Associations between predictors and the tooth loss phenotype were also evaluated by classical statistical approaches to validate the performance of machine learning models. ResultsIn total, 7840 patients were included. The machine learning model predicting the tooth loss phenotype achieved AUROC of 0.71 and AUPRC of 0.66. Age, periodontal diagnosis, number of missing teeth at baseline, furcation involvement, and tooth mobility were associated with the tooth loss phenotype in both machine learning and classical statistical models. ConclusionsThe rule-based machine learning approach improves model explainability compared to classical statistical methods. However, the model's generalizability needs to be further validated by external datasets. Clinical SignificancePredictors identified by the current machine learning approach using the RuleFit algorithm had clinically relevant thresholds in predicting the tooth loss phenotype in a large and diverse periodontitis patient cohort. The results of this study will assist clinicians in performing risk assessment for periodontitis at the initial visit.

Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage

Demonstrating quantum advantage requires experimental implementation of a computational task that is hard to achieve using state-of-the-art classical systems. One approach is to perform sampling from a probability distribution associated with a certain class of highly entangled many-body wave functions. It has been suggested that such a quantum advantage can be certified with the (XEB). We critically examine this notion. First, we consider a “benign” setting, where an honest implementation of a noisy quantum circuit is assumed, and characterize the conditions under which the XEB approximates the of quantum dynamics. Second, we assume an “adversarial” setting, where all possible classical algorithms are considered for comparisons, and show that achieving relatively high XEB values does not imply faithful simulation of quantum dynamics. Specifically, we present an efficient classical algorithm that achieves high XEB values, namely 5–12% of those obtained in the state-of-the-art experiments, within just a few seconds using a single GPU machine. This is made possible by identifying and exploiting several vulnerabilities of the XEB, which allows us to achieve high XEB values without simulating a full quantum circuit. Remarkably, our algorithm features with the system size than a noisy quantum device for commonly studied random circuit ensembles in various architecture. We quantitatively explain the success of our algorithm and the limitations of the XEB by using a theoretical framework, in which the dynamics of the average XEB and fidelity are mapped to classical statistical mechanics models. Using this framework, we illustrate the relation between the XEB and the fidelity for quantum circuits in various architectures, with different choices of gate sets, and in the presence of noise. Taken together, our results demonstrate that XEB’s utility as a proxy for fidelity hinges on several conditions, which should be independently checked in the benign setting, but cannot be assumed in the general adversarial setting. Therefore, the XEB on its own has a limited utility as a benchmark for quantum advantage. We briefly discuss potential ways to overcome these limitations. Published by the American Physical Society 2024

Sequential estimation for mixture of regression models for heterogeneous population

Heterogeneity among patients commonly exists in clinical studies and leads to challenges in medical research. It is widely accepted that there exist various sub-types in the population and they are distinct from each other. The approach of identifying the sub-types and thus tailoring disease prevention and treatment is known as precision medicine. The mixture model is a classical statistical model to cluster the heterogeneous population into homogeneous sub-populations. However, for the highly heterogeneous population with multiple components, its parameter estimation and clustering results may be ambiguous due to the dependence of the EM algorithm on the initial values. For sub-typing purposes, the finite mixture of regression models with concomitant variables is considered and a novel statistical method is proposed to identify the main components with large proportions in the mixture sequentially. Compared to existing typical statistical inferences, the new method not only requires no pre-specification on the number of components for model fitting, but also provides more reliable parameter estimation and clustering results. Simulation studies demonstrated the superiority of the proposed method. Real data analysis on the drug response prediction illustrated its reliability in the parameter estimation and capability to identify the important subgroup.