Background: Electronic health records represent a large data source for outcomes research, but the majority of EHR data is unstructured (e.g. free text of clinical notes) and not conducive to computational methods. While there are currently approaches to handle unstructured data, such as manual abstraction, structured proxy variables, and model-assisted abstraction, these methods are time-consuming, not scalable, and require clinical domain expertise. This paper aims to determine whether selective prediction, which gives a model the option to abstain from generating a prediction, can improve the accuracy and efficiency of unstructured clinical data abstraction. Methods: We trained selective prediction models to identify the presence of four distinct clinical variables in free-text pathology reports: primary cancer diagnosis of glioblastoma (GBM, n = 659), resection of rectal adenocarcinoma (RRA, n = 601), and two procedures for resection of rectal adenocarcinoma: abdominoperineal resection (APR, n = 601) and low anterior resection (LAR, n = 601). Data were manually abstracted from pathology reports and used to train L1-regularized logistic regression models using term-frequency-inverse-document-frequency features. Data points that the model was unable to predict with high certainty were manually abstracted. Findings: All four selective prediction models achieved a test-set sensitivity, specificity, positive predictive value, and negative predictive value above 0.91. The use of selective prediction led to sizable gains in automation (anywhere from 57% to 95% reduction in manual abstraction of charts across the four outcomes). For our GBM classifier, the selective prediction model saw improvements to sensitivity (0.94 to 0.96), specificity (0.79 to 0.96), PPV (0.89 to 0.98), and NPV (0.88 to 0.91) when compared to a non-selective classifier. Interpretation: Selective prediction using utility-based probability thresholds can facilitate unstructured data extraction by giving "easy" charts to a model and "hard" charts to human abstractors, thus increasing efficiency while maintaining or improving accuracy.