Cardiovascular diseases (CVDs) rank among the leading global causes of mortality, underscoring the necessity for early detection and effective management. This research presents a novel prediction model for CVDs utilizing a bagging algorithm that incorporates histogram gradient boosting as the estimator. This study leverages three preprocessed cardiovascular datasets, employing the Local Outlier Factor technique for outlier removal and the information gain method for feature selection. Through rigorous experimentation, the proposed model demonstrates superior performance compared to conventional machine learning approaches, such as Logistic Regression, Support Vector Classification, Gaussian Naïve Bayes, Multi-Layer Perceptron, k-nearest neighbors, Random Forest, AdaBoost, gradient boosting, and histogram gradient boosting. Evaluation metrics, including precision, recall, F1 score, accuracy, and AUC, yielded impressive results: 93.90%, 98.83%, 96.30%, 96.25%, and 0.9916 for dataset I; 94.17%, 99.05%, 96.54%, 96.48%, and 0.9931 for dataset II; and 89.81%, 82.40%, 85.91%, 86.66%, and 0.9274 for dataset III. The findings indicate that the proposed prediction model has the potential to facilitate early CVD detection, thereby enhancing preventive strategies and improving patient outcomes.

Logistic regression is one of statistical methods that used to analyze the correlation between categorical response variables and predictor variables which are categorical or continuous. Many studies on logistic regression have been carried out by assuming that the predictor variable and its logit link function have a linear relationship. However, in several cases it was found that the relationship was not always linear, but could be quadratic, cubic, or in the form of other curves, so that the assumption of linearity was incorrect. Therefore, this study will develop a bivariate polynomial ordinal logistic regression (BPOLR) model which is an extension of ordinal logistic regression, with two correlated response variables in which the relationship between the continuous predictor variable and its logit is modeled as a polynomial form. There are commonly two correlated response variables in scientific research. In this study, each response variable used consisted of three categories. This study aims to obtain parameter estimators of the BPOLR model using the maximum likelihood estimation (MLE) method, obtain test statistics of parameters using the maximum likelihood ratio test (MLRT) method, and obtain algorithms of estimating and hypothesis testing for parameters of the BPOLR model. The results of the first partial derivatives are not closed-form, thus, a numerical optimization such as the Berndt–Hall–Hall–Hausman (BHHH) method is needed to obtain the maximum likelihood estimator. The distribution statistically test is followed the Chi-square limit distribution, asymptotically.

Stunting is a chronic nutritional problem in toddlers characterized by a shorter height than other children of their age. Stunting is a major nutritional problem faced by Indonesia. This research aimed to develop a risk model for the incidence of stunting in toddlers. This research was conducted in the village of stunting locus in the Public Health Center area that was selected to be the sample in Probolinggo District. Data were collected in the villages of Alaspandan, Bucorwetan, Petunjungan, and Sukodadi. The samples taken were 202 toddlers. The results show that the prevalence of a stunted toddler was 26.7% consisting of 21.3% moderately stunting and 5.4% severely stunting, and birth length, maternal height, and health services were important determinants of stunting in toddlers. Also, the value of the classification accuracy of the obtained model using parametric ordinal logistic regression approach was 72.45% which is less than that using nonparametric ordinal logistic regression approach namely 73.98%. It means that the best model for modeling risk of toddlers stunting in Probolinggo District was obtained based on the nonparametric logistic regression approach.

In this study, we develop a regression analysis method, namely, the Semiparametric Binary Logistic Regression (SBLR), by extending the classical logistic regression that integrates both parametric and nonparametric components, which allows it to simultaneously model linear and non-linear relationships. Here, to obtain the estimation of a nonparametric component in the form of a non-linear curve (sigmoid curve), we use the penalized spline, which is a smoothing technique used in the nonparametric approach due to its ability to produce smooth and adaptive curves for fluctuating data. In this smoothing technique, selecting the optimal smoothing parameters plays an important role in fitting the model. Commonly, this selection is based on the minimum value of ordinary Cross-Validation (CV) or Generalized Cross-Validation (GCV). However, these CV and GCV criteria cannot be used when the CV and GCV curves continuously decline and never rise; the minimum CV and GCV values would not be achieved because they are not directly applicable due to the non-quadratic nature of the log-likelihood function. Therefore, a Generalized Approximate Cross-Validation (GACV) criterion is used to address such cases. This distinguishes it from previous studies that used the CV or GCV criterion. In the application to real data, we define an SBLR model of Coronary Heart Disease (CHD) risk factors that can be used for prediction and interpretation purposes. The results of the study successfully demonstrate the efficacy of the proposed method in identifying critical non-linear thresholds for CHD risk factors, and it is statistically valid and highly effective for CHD risk prediction. In the future, we can use the results of this research as a basis of an early warning system, specifically alerting individuals with moderate stress levels and dietary habits exceeding the identified thresholds to be aware of the heightened probability of developing CHD. In addition, this research aligns with point three of the Sustainable Development Goals (SDGs), namely, premature mortality reduction from non-communicable diseases by 2030.