Classification using class-imbalanced data is biased in favor of the majority class. The bias is even larger for high-dimensional data, where the number of variables greatly exceeds the number of samples. The problem can be attenuated by undersampling or oversampling, which produce class-balanced data. Generally undersampling is helpful, while random oversampling is not. Synthetic Minority Oversampling TEchnique (SMOTE) is a very popular oversampling method that was proposed to improve random oversampling but its behavior on high-dimensional data has not been thoroughly investigated. In this paper we investigate the properties of SMOTE from a theoretical and empirical point of view, using simulated and real high-dimensional data.

The goal of class prediction studies is to develop rules to accurately predict the class membership of new samples. The rules are derived using the values of the variables available for each subject: the main characteristic of high-dimensional data is that the number of variables greatly exceeds the number of samples. Frequently the classifiers are developed using class-imbalanced data, i.e., data sets where the number of samples in each class is not equal. Standard classification methods used on class-imbalanced data often produce classifiers that do not accurately predict the minority class; the prediction is biased towards the majority class. In this paper we investigate if the high-dimensionality poses additional challenges when dealing with class-imbalanced prediction. We evaluate the performance of six types of classifiers on class-imbalanced data, using simulated data and a publicly available data set from a breast cancer gene-expression microarray study. We also investigate the effectiveness of some strategies that are available to overcome the effect of class imbalance.

Objectives (1) To develop reference values for health-related fitness in European children and adolescents aged 6–18 years that are the foundation for the web-based, open-access and multilanguage fitness platform (FitBack); (2) to provide comparisons across European countries. Methods This study builds on a previous large fitness reference study in European youth by (1) widening the age demographic, (2) identifying the most recent and representative country-level data and (3) including national data from existing fitness surveillance and monitoring systems. We used the Assessing Levels of PHysical Activity and fitness at population level (ALPHA) test battery as it comprises tests with the highest test–retest reliability, criterion/construct validity and health-related predictive validity: the 20 m shuttle run (cardiorespiratory fitness); handgrip strength and standing long jump (muscular strength); and body height, body mass, body mass index and waist circumference (anthropometry). Percentile values were obtained using the generalised additive models for location, scale and shape method. Results A total of 7 966 693 test results from 34 countries (106 datasets) were used to develop sex-specific and age-specific percentile values. In addition, country-level rankings based on mean percentiles are provided for each fitness test, as well as an overall fitness ranking. Finally, an interactive fitness platform, including individual and group reporting and European fitness maps, is provided and freely available online (www.fitbackeurope.eu). Conclusion This study discusses the major implications of fitness assessment in youth from health, educational and sport perspectives, and how the FitBack reference values and interactive web-based platform contribute to it. Fitness testing can be conducted in school and/or sport settings, and the interpreted results be integrated in the healthcare systems across Europe.

Prediction models are used in clinical research to develop rules that can be used to accurately predict the outcome of the patients based on some of their characteristics. They represent a valuable tool in the decision making process of clinicians and health policy makers, as they enable them to estimate the probability that patients have or will develop a disease, will respond to a treatment, or that their disease will recur. The interest devoted to prediction models in the biomedical community has been growing in the last few years. Often the data used to develop the prediction models are class-imbalanced as only few patients experience the event (and therefore belong to minority class).

Background: For finite samples with binary outcomes penalized logistic regression such as ridge logistic regression has the potential of achieving smaller mean squared errors (MSE) of coefficients and predictions than maximum likelihood estimation. There is evidence, however, that ridge logistic regression can result in highly variable calibration slopes in small or sparse data situations.Methods: In this paper, we elaborate this issue further by performing a comprehensive simulation study, investigating the performance of ridge logistic regression in terms of coefficients and predictions and comparing it to Firth’s correction that has been shown to perform well in low-dimensional settings. In addition to tuned ridge regression where the penalty strength is estimated from the data by minimizing some measure of the out-of-sample prediction error or information criterion, we also considered ridge regression with pre-specified degree of shrinkage. We included ‘oracle’ models in the simulation study in which the complexity parameter was chosen based on the true event probabilities (prediction oracle) or regression coefficients (explanation oracle) to demonstrate the capability of ridge regression if truth was known.Results: Performance of ridge regression strongly depends on the choice of complexity parameter. As shown in our simulation and illustrated by a data example, values optimized in small or sparse datasets are negatively correlated with optimal values and suffer from substantial variability which translates into large MSE of coefficients and large variability of calibration slopes. In contrast, in our simulations pre-specifying the degree of shrinkage prior to fitting led to accurate coefficients and predictions even in non-ideal settings such as encountered in the context of rare outcomes or sparse predictors.Conclusions: Applying tuned ridge regression in small or sparse datasets is problematic as it results in unstable coefficients and predictions. In contrast, determining the degree of shrinkage according to some meaningful prior assumptions about true effects has the potential to reduce bias and stabilize the estimates.