Association between accelerometer-measured physical activity volume and sleep duration in older adults: a cross-sectional interpretable machine learning analysis

Objective This study aimed to examine the relationship between physical activity volume and sleep duration in older adults, using objective monitoring data to investigate their non-linear association and threshold effects, thereby providing references for developing exercise programs to improve sleep duration. Methods The study used two consecutive waves of NHANES cross-sectional data (2011–2014) as the derivation cohort and NHANES 2005–2006 data as the validation cohort. Analysis of the derivation cohort included weighted univariate analysis, weighted multivariate logistic regression, and interpretable machine learning analysis. The machine learning interpretability process involved dividing a 20% internal validation test set, using the grid search method and five-fold cross-validation to construct RF, GBDT, XGBoost, and LightGBM models, as well as a two-layer stacked ensemble model for model comparison, with external validation of the optimal model’s performance. The final model was used for SHAP interpretability analysis. Results Logistic regression results showed a positive correlation between physical activity volume and the probability of good sleep duration. Among the constructed models, GBDT performed best, with internal validation AUC = 0.859 (0.821–0.897, p 0.001) and external validation AUC = 0.707 (0.690–0.730, p 0.001). SHAP analysis results indicated that physical activity volume was particularly important for sleep duration, with the association direction consistent with logistic regression results, demonstrating strong robustness of the positive correlation. The association showed non-linear relationships and threshold effects: the marginal effects of physical activity volume changes were relatively low below 7,000 MIMS and above 15,000 MIMS, with 11461.51 MIMS being the key threshold point for predicting whether older adults would have good sleep duration. Conclusion In studies targeting sleep duration improvement in older adults, physical activity may be considered as a non-invasive intervention. When designing such programs, special attention should be given to critical thresholds and zone effects of physical activity volume. We recommend that older adults maintain a daily activity level of at least 12,000 MIMS, with 15,000 MIMS representing the optimal standard. However, potential risks associated with excessive exercise should be noted.