Gajendra Kumar Vishwakarma

Rapid urbanization in heritage-rich cities like Varanasi has led to significant land use changes, necessitating high-resolution monitoring of built-up dynamics. This study addresses the research gap in quantifying fine-scale spatiotemporal urban transformations by employing the Normalized Difference Built-up Index (NDBI) from Sentinel-2 imagery over the period of 2019–2025. Statistical analysis reveals the lowest mean NDBI in 2021 −0.0568), indicating a temporary reduction in built-up intensity, followed by a steady increase to −0.0223 in 2025. Spatial autocorrelation assessed via Local Moran’s I shows strong clustering in 2019 (mean I = 0.2755; skewness = 3.53) and persistent hotspots through 2025, reflecting structured urban growth. k -means clustering identified the top five high-density built-up zones per year, with mean intercluster distance peaking in 2021 (0.0867°) and decreasing convex hull area to 0.0020 deg ² in 2025, suggesting increased decentralization yet confined urban expansion. A novel quantile-mapped gradient analysis detected an average NDBI shift magnitude of 5.76°, highlighting both directional growth and localized development shocks. The correlation analysis shows that absolute NDBI shifts are strongly influenced by both X - and Y -directional movements, with high Pearson correlations ( r > 0.76). In contrast, the weaker correlation between X and Y shifts ( r = 0.27) suggests spatially varied directional growth patterns. These results fill a methodological void by integrating spatial autocorrelation, clustering, and gradient-based shift analysis. The spatial data can guide equitable infrastructure planning and heritage conservation amid urban growth. Future scope includes integrating socioeconomic and policy variables with remote sensing indicators to develop predictive urban growth models supporting sustainable urban planning initiatives.

Protein-based molecular biomarkers play an important role in prognostic modeling and risk stratification in precision medicine. However, longitudinal survival studies involving high-dimensional biomarker data are frequently challenged by pervasive missingness and limited sample sizes, which can compromise model stability and interpretability. In this study, we present and evaluate a reproducible analytical pipeline for survival risk prediction that integrates established methods for missing data handling, feature selection, and time-to-event modeling. Missing values are addressed using an unsupervised random forest-based imputation approach that leverages internal covariate structure without incorporating outcome information, thereby reducing the risk of information leakage. Feature dimensionality is subsequently reduced using penalized Cox regression with the least absolute shrinkage and selection operator, followed by refinement and stability assessment using random survival forests to capture nonlinear effects and interactions. The final set of selected biomarkers is examined using univariate and multivariable Cox proportional hazards models to support clinical interpretability and risk stratification. Using a publicly available proteomic dataset from cancer patients, we demonstrate how this sequential modeling strategy can identify stable prognostic biomarkers while highlighting the challenges of overfitting in small-sample, high-dimensional survival settings. The proposed workflow serves as a practical and transparent framework for biomarker-driven survival analysis rather than a new statistical methodology.

Censoring is a key issue in survival analysis, especially when participants are lost to follow-up, potentially biasing treatment effect estimates. Imputation methods can help update censored observations, reducing bias. Multistate Models (MSMs) offer a flexible framework for modeling transitions between states over time, capturing dependencies and improving time-to-event comparisons. Traditional Cox models struggle to handle both censoring and multistate dynamics, particularly in the presence of unobserved heterogeneity. By incorporating transition-specific frailty, MSMs better account for individual variability. In this study, we addressed censoring using survival proximity score matching within an MSM framework, incorporating frailty to improve accuracy. Results showed increasing frailty variance across transitions and significant variation in survival probabilities across frailty levels, highlighting the value of frailty-adjusted MSMs.

There are unique challenges when analyzing high-dimensional survival data. The Accelerated Failure Time (AFT) model serves as a viable alternative to the Cox Proportional Hazards (CPH) model in such settings. Although the AFT model holds significant role, there is a lack of effective tools for its application to high-dimensional survival data, particularly within a Bayesian framework. This work aims to bridge that gap by proposing a comprehensive and practical solution. We use afthd, an R package designed to fit parametric AFT models to high-dimensional survival data. The package supports both frequentist and Bayesian inference and accommodates univariate and multivariable analyses. The results of simulation studies demonstrate that the parameter estimates are robust and consistent in various model specifications. The effectiveness and clarity of the proposed method are further illustrated through its application to two real high-dimensional liver cancer datasets.