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Overlapping asymmetric datasets are common in data science and pose questionsof how they can be incorporated together into a predictive analysis. Inhealthcare datasets there is often a small amount of information that isavailable for a larger number of patients such as an electronic health record,however a small number of patients may have had extensive further testing.Common solutions such as missing imputation can often be unwise if the smallercohort is significantly different in scale to the larger sample, therefore theaim of this research is to develop a new method which can model the smallercohort against a particular response, whilst considering the larger cohortalso. Motivated by non-parametric models, and specifically flexible smoothingtechniques via generalized additive models, we model a twice penalized P-Splineapproximation method to firstly prevent over/under-fitting of the smallercohort and secondly to consider the larger cohort. This second penalty iscreated through discrepancies in the marginal value of covariates that exist inboth the smaller and larger cohorts. Through data simulations, parametertunings and model adaptations to consider a continuous and binary response, wefind our twice penalized approach offers an enhanced fit over a linear B-Splineand once penalized P-Spline approximation. Applying to a real-life datasetrelating to a person's risk of developing Non-Alcoholic Steatohepatitis, we seean improved model fit performance of over 65%. Areas for future work withinthis space include adapting our method to not require dimensionality reductionand also consider parametric modelling methods. However, to our knowledge thisis the first work to propose additional marginal penalties in a flexibleregression of which we can report a vastly improved model fit that is able toconsider asymmetric datasets, without the need for missing data imputation.

Handling Overlapping Asymmetric Datasets -- A Twice Penalized P-Spline Approach