Journal of Data Science and Modeling

Lognormal structured additive regression model for spatio-temporal data and its application to breast cancer data in Iran

Articles in Press

Document Type : original

Authors

Soudabe Sajjadipanah 1
Hasti Hashemi 2
Seyyed mahmoud Mirjalili 3

1 staff of Boushehr Medical University

2 Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

3 Department of Statistics, Velayat University, Velayat, Iran

https://doi.org/10.22054/jdsm.2026.88625.1079
Abstract
Medical data are typically recorded across geographic regions and over successive time points, giving rise to spatio-temporal structures that present important statistical modelling challenges. In this study, we propose a spatio-temporal regression model based on the lognormal distribution within the structured additive regression framework. The lognormal assumption accommodates the positive skewness and heteroscedasticity of the incidence rate data. Bayesian inference for the model parameters was conducted using the integrated nested Laplace approximation (INLA), which delivers substantial computational gains over Markov chain Monte Carlo methods while maintaining comparable accuracy. We systematically compared four types of spatio-temporal interactions (Types I–IV) to identify the most parsimonious and best-fitting dependence structure. To evaluate performance, we applied the proposed model and several competitors to breast cancer incidence data from all provinces of Iran over the period 2010–2019. The results demonstrated the clear superiority of the lognormal structured additive regression (LNSTAR) model, with the Type II (temporal-only) interaction providing the best fit. Beyond its methodological contribution, this analysis provides actionable risk stratification to inform targeted screening policies in Iran.

Keywords

Bayesian inference‎
‎Breast cancer‎
‎Integrated nested Laplace approximation‎
‎Lognormal structured additive regression model‎
‎Spatio-temporal interaction‎
Subjects
Journal of Data Science and Modeling

Articles in Press, Accepted Manuscript
Available Online from 03 August 2026

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