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.

本研究旨在开发一种新方法，能够模拟较小样本与特定响应之间的关系，并考虑较大样本。通过非参数模型和柔性平滑技术，我们提出了一个经过两次惩罚的 P-Spline 逼近方法，通过对较大和较小样本中已存在的协变量的边际值的差异进行惩罚，得到了比线性 B-Spline 和一次惩罚 P-Spline 逼近更好的模型拟合效果。在将其应用于非酒精性脂肪肝风险相关的真实数据集时，我们发现我们的方法可以显著改善模型拟合性能超过 65%。未来的工作包括对方法进行维度约减和考虑参数建模方法的改进，但据我们所知，这是第一个在柔性回归中提出额外边际惩罚的研究，能够考虑到不对称数据集而无需缺失数据插补。