Logistic regression (LR) is widely used in clinical prediction because it is simple to deploy and easy to interpret. Nevertheless, being a linear model, LR has limited expressive capability and often has unsatisfactory performance. Generalized additive models (GAMs) extend the linear model with transformations of input features, though feature interaction is not allowed for all GAM variants. In this paper, we propose a factored generalized additive model (F-GAM) to preserve the model interpretability for targeted features while allowing a rich model for interaction with features fixed within the individual. We evaluate F-GAM on prediction of two targets, postoperative acute kidney injury and acute respiratory failure, from a single-center database. We find superior model performance of F-GAM in terms of AUPRC and AUROC compared to several other GAM implementations, random forests, support vector machine, and a deep neural network. We find that the model interpretability is good with results with high face validity.