In binary regression, imbalanced data result from the presence of values equal to zero (or one) in a proportion that is significantly greater than the corresponding real values of one (or zero). In this work, we evaluate two methods developed to deal with imbalanced data and compare them to the use of asymmetric links. The results based on simulation study show, that correction methods do not adequately correct bias in the estimation of regression coefficients and that the models with power links and reverse power considered produce better results for certain types of imbalanced data. Additionally, we present an application for imbalanced data, identifying the best model among the various ones proposed. The parameters are estimated using a Bayesian approach, considering the Hamiltonian Monte-Carlo method, utilizing the No-U-Turn Sampler algorithm and the comparisons of models were developed using different criteria for model comparison, predictive evaluation and quantile residuals.

Motivated for a medical data about schizophrenia symptoms where an imbalanced binary response is observed, we introduce a broad class of link functions, called power and reverse power, as an alternative to analyse longitudinal binary data, particularly when it is imbalanced as is common in medical data. Bayesian estimation using an MCMC procedure through the No-U-Turn Sampler algorithm is proposed. Posterior predictive checks, Bayesian randomized quantile residuals, and a Bayesian influence measures are considered for model diagnostics. Different models are compared using selection model criteria. A simulation study is developed to analyse the prior sensitivity of the variance of the random effect and to assess the performance of the proposed model in the presence of imbalanced data. Finally, an application of the methodology studied in a set of medical data on the presence of schizophrenia symptom “thought disorder” is considered. In this data set, the presence of symptoms is much less than the absence, thus we show, in practice, the usefulness of using alternative link functions in imbalanced data.

Introduction. The global shortage of physicians represents a major public health challenge, with significant disparities in Peru. Objective. To determine the machine learning model that identifies the factors associated with physicians working in remote areas, defined as remote or border zones (ZAF) by the Peruvian government. Method. A quantitative, non-experimental, cross-sectional, and correlational study was conducted. A population of 10,228 primary care physicians was analyzed using the INFORHUS database of the Peruvian Ministry of Health as of July 2022. Four machine learning techniques were applied, and their performance was evaluated using the F1-Score, Matthews correlation coefficient (MCC), and geometric mean (GM) metrics to address data imbalances. Results. The Random Forest model proved to be the most effective. The most relevant variables, with the highest percentage of association with medical professionals working in remote areas, were remuneration (40.6%), age (25.6%), whether the contract type was SERUMS (14.2%), and sex (5.2%). Conclusions. The Random Forest model identified the factors associated with physicians working in remote areas (ZAF) in Peru, highlighting the predominance of economic and personal factors. This finding provides evidence to inform policies aimed at improving the distribution of physicians in Peru.