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Aggregating person-level data across multiple clinical study sites is often constrained by privacy regulations, necessitating the development of decentralized modeling approaches in biomedical research. To address this requirement, a federated nonlinear regression algorithm based on the Choquet integral has been introduced for outcome prediction. This approach avoids reliance on prior statistical assumptions about data distribution and captures feature interactions, reflecting the non-additive nature of biomedical data characteristics. This work represents the first theoretical application of Choquet integral regression to multisite longitudinal trial data within a federated learning framework. The Multiple Imputation Choquet Integral Regression with LASSO (MIChoquet-LASSO) algorithm is specifically designed to reduce overfitting and enable variable selection in federated learning settings. Its performance has been evaluated using synthetic datasets, publicly available biomedical datasets, and proprietary longitudinal randomized controlled trial data. Comparative evaluations were conducted against benchmark methods, including ordinary least squares (OLS) regression and Choquet-OLS regression, under various scenarios such as model misspecification and both linear and nonlinear data structures in non-federated and federated contexts. Mean squared error was used as the primary performance metric. Results indicate that MIChoquet-LASSO outperforms compared models in handling nonlinear longitudinal data with missing values, particularly in scenarios prone to overfitting. In federated settings, Choquet-OLS underperforms, whereas the federated variant of the model, FEDMIChoquet-LASSO, demonstrates consistently better performance. These findings suggest that FEDMIChoquet-LASSO offers a reliable solution for outcome prediction in multisite longitudinal trials, addressing challenges such as missing values, nonlinear relationships, and privacy constraints while maintaining strong performance within the federated learning framework.