Mathematical Characterisation of Cancer Burden in Egypt: Rank-based Relationships among Cumulative Risk, Incidence, and Mortality
Senyefia Bosson-Amedenu
*
Department of Mathematics, Statistics and Actuarial Science, Takoradi Technical University, Takoradi, Ghana.
Reem Ezzat
Internal Medicine Department, Faculty of Medicine, Assiut University, Assiut, Egypt.
Eric Justice Eduboah
Department of Economics Education, University of Education, Winneba, Ghana.
Mohamed El-Kassas
Endemic Medicine Department, Faculty of Medicine, Helwan University, Cairo, Egypt.
Hend Shousha
Endemic Medicine Department, Faculty of Medicine, Cairo University, Cairo, Egypt.
Noureddine Ouerfelli
Institut Supérieur des Technologies Médicales de Tunis, LR13SE07, Laboratoire de Biophysique et Technologies Médicales, Université de Tunis El Manar, Tunis, Tunisia.
*Author to whom correspondence should be addressed.
Abstract
This study examined rank-based mathematical relationships among cumulative cancer risk, age-standardised incidence rates, and age-standardised mortality rates in Egypt, using GLOBOCAN 2020 population-level estimates. The analysis included 35 cancer sites, excluding non-melanoma skin cancer, and compared Egypt-specific patterns with corresponding global cancer-burden indicators. Linear, logarithmic, polynomial, reciprocal-rank, and exponential saturation models were evaluated to describe associations between cancer rank, cumulative risk, incidence, and mortality. In 2020, Egypt recorded 134,632 new cancer cases and 89,042 cancer deaths. The cumulative risk of developing cancer before the age of 75 years was 16.27%, whereas the cumulative risk of death from cancer was 10.94%. Cumulative risk declined non-linearly with cancer rank. Third-degree polynomial models fitted incidence and mortality cumulative-risk distributions better than simple log-linear models, with R² values of 0.946 and 0.956, respectively. The estimated centres of symmetry occurred near rank 17.98 for incidence and rank 20.19 for mortality. Age-standardised incidence and mortality rates also showed structured empirical relationships. The fitted exponential saturation model for the incidence-mortality association had an R² of 0.758. The male-female age-standardised incidence correlation was moderate (R² = 0.462), indicating sex-specific differences in cancer distribution. The findings indicate that Egypt’s cancer burden in 2020 was unevenly distributed across cancer types, with liver, breast, and bladder cancers occupying prominent positions. Rank-based empirical modelling may provide a descriptive framework for comparing cancer-burden patterns across populations and for monitoring changes in future datasets. The models should be interpreted as population-level summaries rather than as individual risk-prediction tools, and their stability should be reassessed using updated registry and GLOBOCAN data.
Keywords: Cumulative risk, age-standardised incidence, age-standardised mortality, cancer rank, rank-based modelling, incidence-mortality relationship, GLOBOCAN 2020, Egypt, polynomial model, exponential saturation model, population-level estimates