Drowsy driving is a major factor in many vehicle crashes around the world. Sleep disorders, such as obstructive sleep apnea (OSA), underpin many of these crashes. Continuous positive airway pressure (CPAP) therapy is an effective treatment for sleep apnea but it requires consistent use and is often rejected by OSA patients. Rejection of CPAP treatment creates a dangerous on-road environment for both OSA sufferers and the general public. Algorithms capable of detecting CPAP use and its effects on driving are integral to identifying and mitigating this danger. This work uses naturalistic kinematic driving data to develop an algorithm which can detect nightly CPAP abstinence and adequate CPAP use. Speed and lateral acceleration data were collected using a data recorder in participant's primary vehicle and CPAP data were collected by downloading adherence data from participant CPAP machines. The speed and acceleration data were reduced to a set of symbols using Symbolic Aggregate approximation (SAX) time-series analysis. The symbols were converted into a sequence frequency dataset using sliding windows of size 1 to 10 s with a 1 Hz sampling rate. A Random Forest classifier was trained on the data to create a classification algorithm. On a held aside testing set, the Random Forest algorithm correctly identified 71% of the instances and had an area under the receiver operating characteristic curve of 0.76. The variable importance of the algorithm suggested that kinematic patterns associated with common drowsy driver crash types were key features in the algorithm's prediction performance.