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%. We explore whether more recently available document classification algorithms can close this gap. Using data gathered from a single surveillance site, we applied 8 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, using classification accuracy, F1 score, and number of positive calls to evaluate their potential use for surveillance. Across the 10 train-test cycles, the random forest and support vector machine with Naive Bayes features (NB-SVM) each achieved slightly more than 87% mean accuracy. The NB-SVM produced significantly more false negatives than false positives (P = 0.027), but the random forest did not, making its prevalence estimates very close to the true prevalence in the data. The best-performing neural network performed similarly to the random forest on both measures. The random forest performed as well as more recently available models like the NB-SVM and the neural network, and it also produced good prevalence estimates. NB-SVM may not be a good candidate for use in a fully-automated surveillance workflow due to increased false negatives. More sophisticated algorithms, like hierarchical convolutional neural networks, may not be feasible to train due to characteristics of the data. Current algorithms might perform better if the data are abstracted and processed differently and if they take into account information about the children in addition to their evaluations. 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.