The Centers for Disease Control and Prevention (CDC) coordinates a labor-intensive process to measure the prevalence of autism spectrum disorder (ASD) among children in the United States. Random forests methods have shown promise in speeding up this process, but they lag behind human classification accuracy by about 5 percent. We explore whether newer document classification algorithms can close this gap. We applied 6 supervised learning algorithms to predict whether children meet the case definition for ASD based solely on the words in their evaluations. We compared the algorithms? performance across 10 random train-test splits of the data, and then, we combined our top 3 classifiers to estimate the Bayes error rate in the data. Across the 10 train-test cycles, the random forest, neural network, and support vector machine with Naive Bayes features (NB-SVM) each achieved slightly more than 86.5 percent mean accuracy. The Bayes error rate is estimated at approximately 12 percent meaning that the model error for even the simplest of our algorithms, the random forest, is below 2 percent. NB-SVM produced significantly more false positives than false negatives. The random forest performed as well as newer models like the NB-SVM and the neural network. NB-SVM may not be a good candidate for use in a fully-automated surveillance workflow due to increased false positives. More sophisticated algorithms, like hierarchical convolutional neural networks, would not perform substantially better due to characteristics of the data. Deep learning models performed similarly to traditional machine learning methods at predicting the clinician-assigned case status for CDC's autism surveillance system. While deep learning methods had limited benefit in this task, they may have applications in other surveillance systems.