Home monitoring of medication levels in saliva promises a "precision medicine" approach for improving management of chronic diseases. However, saliva's high variability poses a signal processing challenge for miniaturized field-use drug assays. In the context of electrochemical detection of the epilepsy medication carbamazepine, we measured the performance of linear univariate, linear multivariate, and machine-learning (kappa-nearest neighbors (KNN), Random Forest (RF), and Gaussian process (GP)) regression models. For model training and testing, we used a large dataset that we generated by electrochemically assaying 246 saliva samples into which carbamazepine had been spiked at defined concentrations. For each sample, we extracted thirteen quantitative features of the voltammogram peak corresponding to the target drug, carbamazepine, and used wrapper feature selection for the multivariate models. We assessed the models using two independent performance measures applied to hold-out data and statistically compared models for test-set performance using permutation testing. The multivariate linear model using multiple analyte (carbamazepine) peak features was significantly more accurate than the best univariate linear model, decreasing relative prediction error by 19.4%. Further, all three machine-learning models outperformed the multivariate linear model, decreasing relative error by 15.9%, 13.9%, and 10.5% for KNN, RF, and GP, respectively. Our findings underscore the importance and benefit of using multivariate machine-learning models for electrochemical measurement of drug levels in saliva.