Identifying people with Parkinson disease during the prodromal period, including via algorithms in administrative claims data, is an important research and clinical priority. We sought to improve upon an existing penalized logistic regression model, based on diagnosis and procedure codes, by adding prescription medication data or using machine learning. Using Medicare Part D beneficiaries age 66-90 from a population-based case-control study of incident Parkinson disease, we fit a penalized logistic regression both with and without Part D data. We also built a predictive algorithm using a random forest classifier for comparison. In a combined approach, we introduced the probability of Parkinson disease from the random forest, as a predictor in the penalized regression model. We calculated the receiver operator characteristic area under the curve (AUC) for each model. All models performed well, with AUCs ranging from 0.824 (simplest model) to 0.835 (combined approach). We conclude that medication data and random forests improve Parkinson disease prediction, but are not essential.