A STOCHASTIC MODELLING APPROACH TO THE ANALYSIS OF CANCER CELL GROWTH AND SURVIVAL IN THE INDIAN CLINICAL CONTEXT

Abstract

This study develops a dynamic stochastic exponential modelling framework for analysing cancer cell growth and survival outcomes using anonymized retrospective clinical observations from RST Regional Cancer Hospital, Nagpur, Maharashtra, India. The classical exponential model assumes a constant proportional growth rate and therefore produces a fixed deterministic trajectory. Clinical cancer progression, however, is patient-specific, time-dependent and uncertain because of treatment response, immune activity, necrosis, measurement error and biological heterogeneity. The proposed model represents the tumour volume of the ith patient by N_i (t), governed by a time-varying growth rate r_i (t) and a stochastic variability parameter  σ_i (t). The model is expressed as a stochastic differential equation in which the deterministic component describes dynamic exponential growth and the random component describes biological fluctuation through a Wiener process. Survival outcomes are analysed using Kaplan-Meier estimation, log-rank comparison and Cox proportional hazards regression. The RST Cancer Hospital data are used to demonstrate patient-level growth calculation, predicted tumour volume, group classification, sensitivity analysis and survival interpretation. The results show that higher initial growth rate and higher stochastic variability are associated with greater predicted tumour volume and poorer survival patterns, whereas growth reduction reduces predicted tumour burden. The paper also presents an Indian Knowledge Systems perspective by linking systematic observation, inferential reasoning and public-health decision-making within a contemporary statistical framework.