@Article{math12050777,
AUTHOR = {McTeer, Matthew and Henderson, Robin and Anstee, Quentin M. and Missier, Paolo},
TITLE = {Handling Overlapping Asymmetric Data Sets—A Twice Penalized P-Spline Approach},
JOURNAL = {Mathematics},
VOLUME = {12},
YEAR = {2024},
NUMBER = {5},
ARTICLE-NUMBER = {777},
URL = {https://www.mdpi.com/2227-7390/12/5/777},
ISSN = {2227-7390},
ABSTRACT = {Aims: Overlapping asymmetric data sets are where a large cohort of observations have a small amount of information recorded, and within this group there exists a smaller cohort which have extensive further information available. Missing imputation is unwise if cohort size differs substantially; therefore, we aim to develop a way of modelling the smaller cohort whilst considering the larger. Methods: Through considering traditionally once penalized P-Spline approximations, we create a second penalty term through observing discrepancies in the marginal value of covariates that exist in both cohorts. Our now twice penalized P-Spline is designed to firstly prevent over/under-fitting of the smaller cohort and secondly to consider the larger cohort. Results: Through a series of data simulations, penalty parameter tunings, and model adaptations, our twice penalized model offers up to a 58% and 46% improvement in model fit upon a continuous and binary response, respectively, against existing B-Spline and once penalized P-Spline methods. Applying our model to an individual’s risk of developing steatohepatitis, we report an over 65% improvement over existing methods. Conclusions: We propose a twice penalized P-Spline method which can vastly improve the model fit of overlapping asymmetric data sets upon a common predictive endpoint, without the need for missing data imputation.},
DOI = {10.3390/math12050777}
}

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