  Overlapping asymmetric datasets are common in data science and pose questions
of how they can be incorporated together into a predictive analysis. In
healthcare datasets there is often a small amount of information that is
available 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 smaller
cohort is significantly different in scale to the larger sample, therefore the
aim of this research is to develop a new method which can model the smaller
cohort against a particular response, whilst considering the larger cohort
also. Motivated by non-parametric models, and specifically flexible smoothing
techniques via generalized additive models, we model a twice penalized P-Spline
approximation method to firstly prevent over/under-fitting of the smaller
cohort and secondly to consider the larger cohort. This second penalty is
created through discrepancies in the marginal value of covariates that exist in
both the smaller and larger cohorts. Through data simulations, parameter
tunings and model adaptations to consider a continuous and binary response, we
find our twice penalized approach offers an enhanced fit over a linear B-Spline
and once penalized P-Spline approximation. Applying to a real-life dataset
relating to a person's risk of developing Non-Alcoholic Steatohepatitis, we see
an improved model fit performance of over 65%. Areas for future work within
this space include adapting our method to not require dimensionality reduction
and also consider parametric modelling methods. However, to our knowledge this
is the first work to propose additional marginal penalties in a flexible
regression of which we can report a vastly improved model fit that is able to
consider asymmetric datasets, without the need for missing data imputation.
