Logistic and polynomial regression in biomedical research: methodological roles, applications, and practical guidance

Biomedical research applies regression modeling to help with clinical risk analysis, epidemiological analyses and complex health data interpretations. Logistic regression models use categorical outcomes, whereas polynomial regression extends the linear model to include the nonlinear relationships often seen with biological processes and biomarker profiles. The objective of this study was to provide a structured methodological synthesis and practical guidance for selecting between logistic and polynomial regression approaches in biomedical research. The structured narrative review (The search primarily focused on studies published from 2013 onward; however, seminal methodological references published before 2013 were additionally included because of their foundational importance to regression modeling) utilized PubMed, Scopus, and Web of Science to investigate the application and methodological characteristics of logistic & polynomial regression. Included studies were identified by criteria according to pre-defined requirements, and incorporated into a synthesis of the review. An artificial data set was created to demonstrate two examples of logistic and polynomial regression. Logistic regression is the most common method of categorical data analysis due to the ability to provide probability estimates and ease of interpretation. Polynomial regression identifies non-linear relationships (e.g., curves), usually for the purpose of exploratory analysis. Combining the two methods may be beneficial, based on the pattern of the data. Logistic regression should be used for categorical outcomes (binary) while polynomial regression will provide a better fit for continuous, non-linear data. Choosing the best method will depend on the nature of the outcome variable, the physical pattern of the data and the necessary level of interpretability. The conclusions are based solely on synthesizing existing literature.