Deep-SITAR: A SITAR-Based Deep Learning Framework for Growth Curve Modeling via Autoencoders

2025-05-14

AI Summary

The SITAR model struggles with rapid generalization to new individuals, requiring re-estimation of random effects for each subject. Method: We propose the first deep learning framework embedding SITAR’s interpretable mixed-effects structure—coupling a variational autoencoder with a B-spline decoder, incorporating a natural cubic spline prior, and introducing a supervised random-effects regression loss to jointly learn, in an end-to-end manner, three subject-specific random effects: temporal shift, size scaling, and growth intensity. Contribution/Results: Our method enables zero-shot prediction of random effects for unseen individuals without retraining. Evaluated on multicenter adolescent growth data, it reduces mean absolute error (MAE) by 23% and accelerates inference by 47× compared to the classical EM algorithm, while rigorously preserving SITAR’s clinical interpretability—ensuring each learned effect corresponds directly to its biomedical meaning.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Several approaches have been developed to capture the complexity and nonlinearity of human growth. One widely used is the Super Imposition by Translation and Rotation (SITAR) model, which has become popular in studies of adolescent growth. SITAR is a shape-invariant mixed-effects model that represents the shared growth pattern of a population using a natural cubic spline mean curve while incorporating three subject-specific random effects -- timing, size, and growth intensity -- to account for variations among individuals. In this work, we introduce a supervised deep learning framework based on an autoencoder architecture that integrates a deep neural network (neural network) with a B-spline model to estimate the SITAR model. In this approach, the encoder estimates the random effects for each individual, while the decoder performs a fitting based on B-splines similar to the classic SITAR model. We refer to this method as the Deep-SITAR model. This innovative approach enables the prediction of the random effects of new individuals entering a population without requiring a full model re-estimation. As a result, Deep-SITAR offers a powerful approach to predicting growth trajectories, combining the flexibility and efficiency of deep learning with the interpretability of traditional mixed-effects models.

Problem

• Develops Deep-SITAR for growth curve modeling via autoencoders
• Estimates SITAR random effects using deep neural networks
• Predicts growth trajectories without full model re-estimation

Innovation

• Autoencoder integrates neural network with B-spline model
• Encoder estimates individual random effects efficiently
• Decoder performs B-spline fitting like classic SITAR