The performance of an EHR-based deep learning model trained on a small sample can be improved if more data is collected. Instead of collecting more data, the model can be trained on additional data from an analogous external source. However, this risks the model learning patterns in the external data that do not generalize to the target sample. Furthermore, data use agreements often prohibit combining datasets with medical records of different sources. We consider utilizing pre-existing methods in continual learning, namely the elastic weight consolidation (EWC) loss function and variational continual learning (VCL), both of which are regularization-based methods that we use to borrow external data and incorporate parameters from a model on external data into local model training. To investigate the utility of this modeling framework, we consider two binary classification tasks: (1) predicting which children will be diagnosed with autism spectrum disorder (ASD) from medical claims up to 18 months, and (2) predicting which patients with end-stage renal disease (ESRD) will be re-hospitalized within 30 days. Target datasets were derived from Duke University's EHR warehouse, and external datasets were sourced from either NC Medicaid claims for the ASD prediction task, or the United States Renal Data System (USRDS) for the rehospitalization prediction task. For both of these tasks, borrowing models - using either the EWC loss function or VCL - performed similarly to that of a model trained only on the full external data, when the sample size of target data used to train the model was small. That is, while a model that does not borrow using our methods performed poorly in low data regimes, the borrowing model instead matched the performance of a model trained on external data even when sample size of target data was small. In addition, an analysis of model predictions showed that models with small samples are better calibrated and more functionally similar to a model trained only on external data when the sample size is small.