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In modern data analysis, classical statistical methods and machine learning tools are increasingly integrated to produce improved predictive models. This article provides an overview of linear mixed models (LMMs), including their notation, assumptions, and restricted maximum likelihood estimation. We further review advanced extensions—such as mixed-effects ridge regression and mixed-effects regression trees (MERT) for clustered data, emphasizing their notation and current applications. A real-data application assesses and compares the predictive capabilities of the methods under consideration.

Keywords. Machine Learning, Variance Components, Random Effects, Mean Squared Error
Mathematics Subject Classification: 62J07, 62J05.

Early and accurate diagnosis of cancers from histopathology images remains a challenge due to inter-observer variability and complex tissue structures. This work proposes a DenseNet121-based, attention-augmented deep learning framework for multi-cancer type classification and stage prediction. The motivation behind this work is the requirement for strong, interpretable, clinically deployable models that address overfitting, limited generalizability, and failures in standard CNNs to focus on diagnostically relevant regions. Four variants of architectures were evaluated, and the architecture coupled with attention mechanisms, dense layers, and dropout regularization achieved the highest validation accuracy (~0.978). This work further refines the feature learning and boosts the diagnostic reliability of this framework with great potential for its integration with computer-assisted pathology systems.

Keywords: Cancer Classification, Histopathology Images, Deep Learning, DenseNet121, Attention Mechanism, Stage Prediction
Subject Classification Code: MSC: 68T07 (Artificial Neural Networks), 92C55 (Biomedical Imaging and Signal Processing).

Teenage birth is a pertinent public health and socio-economic subject in many developing countries, including Ghana. This paper offers a comprehensive statistical modeling of teenage births within the Central Gonja District of the Savannah Region. Using the mixed-methods design, the research integrates Geographic Information Systems, multilevel logistic regression, and time series analysis to identify spatial hotspots, sociodemographic determinants, and temporal trends in births among teenagers. Primary data were collected from 331 teenage girls aged between 10 and 19 years through a statistical consideration of representativeness and logical feasibility, reinforced by secondary data collected from health facilities from 2014-2024. Results showed that hotspots for teenage births were highly concentrated in the southwest and north-central parts of the district. Sociocultural determinants such as low educational attainment, rural residence, and early marriage were strongly associated with high teenage birth rates. Multilevel analysis showed that individual-level determinants of teenage birth results such as education level and marital status, and community-level determinants like mean level of education, prevalence of contraceptives, unemployment were significant, accounting for 21.5% variation at the community level. Seasonal patterns of adolescent births were revealed by time series analysis of births among adolescents characterized by a decline at the beginning and end of the year. The predictive model founded on socio-demographic variables, predicted a relatively stable birth rate over time. These findings propose the need for combined interventions that takes into account both individual behavior and broader structural factors. The study provided policy-relevant information to policymakers, healthcare providers, and Non-Governmental Organizations (NGOs) with an objective in reducing adolescent births and enhancement in reproductive health outcomes in rural Ghana.

Keywords: Adolescent Birth, Multilevel Modeling, GIS, SARIMA, Ghana, Public Health.
MSC 2020 Classification: 62P25, 62J12, 62M10, 62M30, 91D20.
 

Recalibration of binary probabilistic classiers to a target prior probability is an important task in areas like credit risk management. However, recalibration of a classifier learned on a training dataset to a target on a test dataset in general is not a well-dened problem because there might be more than one way to transform the original posterior probabilities such that the target is matched. In this paper, methods for recalibration are analysed from a distribution shift perspective. Distribution shift assumptions linked to the area under the curve (AUC) of a probabilistic classifier are found to be useful for the design of meaningful recalibration methods. Two new methods called parametric covariate shift with posterior drift (CSPD) and ROCbased quasi moment matching (QMM) are proposed and tested together with some other methods in an example setting. The outcomes of the test suggest that the QMM methods discussed in the paper can provide appropriately conservative results in evaluations with concave functions like for instance risk weights functions for credit risk.
Keywords: Probabilistic classifier, calibration, distribution shift, dataset shift, credit risk.

MSC classes: 68T09, 91G40.

This article addresses the analytical challenges posed by interval-censored (IC) survival data when intercurrent events (ICEs), such as study discontinuation due to lack of efficacy or Adverse Events (AE), introduce informative censoring. We assess the performance of the Rayleigh regression model with fixed co-variates within the Estimand framework to handle this issue. A simulation study was conducted to compare parameter estimates under three scenarios: a baseline analysis without imputation, a composite strategy using non-responder imputation (NRI), and a hypothetical strategy using logistic regression multiple imputation (LRMI). Performance was evaluated using Bias, Root Mean Square Error (RMSE), and coverage probability across various sample sizes and censoring proportions. Results show that while RMSE improves with larger sample sizes across all methods, the hypothetical strategy with LRMI is demonstrably superior. It yields less biased estimates and maintains a higher, more consistent coverage probability compared to the conservative NRI approach, which systematically underestimates treatment effects. We conclude that properly handling ICEs through a principled imputation method like LRMI is crucial for obtaining accurate and reliable results when modeling interval-censored data with the Rayleigh distribution.

Key Words: Rayleigh, Interval-censoring, Maximum likelihood estimation, Estimand, Hypothetical strategy, Composite strategy, Survival analysis, R.
MSC Classification: 62N01, 62N02, 62P10.