Besides the traditional indices such as biochemistry, arterial blood gas, rapid shallow breathing index (RSBI), acute physiology and chronic health evaluation (APACHE) II score, this study suggests a data science framework for extubation prediction in the surgical intensive care unit (SICU) and investigates the value of the information our prediction model provides. A data science framework including variable selection (e.g., multivariate adaptive regression splines, stepwise logistic regression and random forest), prediction models (e.g., support vector machine, boosting logistic regression and backpropagation neural network (BPN)) and decision analysis (e.g., Bayesian method) is proposed to identify the important variables and support the extubation decision. An empirical study of a leading hospital in Taiwan in 2015–2016 is conducted to validate the proposed framework. The results show that APACHE II and white blood cells (WBC) are the two most critical variables, and then the priority sequence is eye opening, heart rate, glucose, sodium and hematocrit. BPN with selected variables shows better prediction performance (sensitivity: 0.830; specificity: 0.890; accuracy 0.860) than that with APACHE II or RSBI. The value of information is further investigated and shows that the expected value of experimentation (EVE), 0.652 days (patient staying in the ICU), is saved when comparing with current clinical experience. Furthermore, the maximal value of information occurs in a failure rate around 7.1% and it reveals the “best applicable condition” of the proposed prediction model. The results validate the decision quality and useful information provided by our predicted model.