Data_Sheet_1_Estimating the Minimal Number of Repeated Examinations for Random Responsiveness With the Coma Recovery Scale—Revised as an Example.docx

Objective: The aim of this study was to develop a general method to estimate the minimal number of repeated examinations needed to detect patients with random responsiveness, given a limited rate of missed diagnosis.
Methods: Basic statistical theory was applied to develop the method. As an application, 100 patients with disorders of consciousness (DOC) were assessed with the Coma Recovery Scale–Revised (CRS-R). DOC patients were supposed to be examined for 13 times over 20 days, while anyone who was diagnosed as a minimally conscious state (MCS) in a round would no longer be examined in the subsequent rounds. To test the validation of this method, a series of the stochastic simulation was completed by computer software under all the conditions of possible combinations of three kinds of distributions for p, five values of p, and four sizes of the sample and repeated for 100 times.
Results: A series of formula was developed to estimate the probability of a positive response to a single examination given by a patient and the minimal number of successive examinations needed based on the numbers of patients detected in the first i (i =1, 2,.) rounds of repeated examinations. As applied to the DOC patients assessed with the CRS-R, with a rate of missed diagnosis < 0.0001, the estimate of the minimal number of examinations was six in traumatic brain injury patients and five in non-traumatic brain injury patients. The outcome of the simulation showed that this method performed well under various conditions possibly occurring in practice.
Interpretation: The method developed in this paper holds in theory and works well in application and stochastic simulation. It could be applied to any other kind of examinations for random responsiveness, not limited to CRS-R for detecting MCS; this should be validated in further research.