In order to determine the sensitivity and specificity of a test for extubation success, we will need to ascertain the outcome in all patients regardless of their performance on the test of interest. That means we would have to extubate patients that failed the weaning parameter test. In the original Yang & Tobin article, their cohort consisted of 100 patients. 60(%) of the 100 were said to have passed the weaning test and were extubated, and 40(%) failed and were not extubated. (There is some over-simplification here based on how Yang & Tobin classified and reported events - its not at all transparent in their article - the data to resolve the issues are not reported and the differences are likely to be small. Suffice it to say that about 60% of their patients were successfully weaned and the remainder were not.) Let's try to construct a 2x2 table to determine the sensitivity and specificity of a weaning parameter using a population like theirs. The top row of the 2x2 table would look something like this, assuming an 85% extubation success rate - that is, of the 60 patients with a positive or "passing" SBT score (based on whatever parameter), all were extubated and the positive predictive value of the test is 85% (the actual rate of reintubation in patients with a passing weaning test is not reported, so this is a guess):
Note that without the data relating to how many who fail the SBT could have been successfully extubated, we cannot determine either sensitivity or specificity - only the positive predictive value. Now, if we had a population in whom all the patients passed the SBT or the weaning parameter, we could determine the sensitivity (100%), the specificity (zero%) and the positive predictive value. Note that in this scenario, the positive likelihood ratio (sensitivity/1-specificity) is 1, meaning that the test has no predictive value whatsoever; the negative likelihood ratio (1-sensitivity/specificity) is 0, but it is a meaningless value because it is based on no data.
Similarly, if the proportion of patients who pass a weaning test and are extubated is high, and most of the patients with a positive test are successfully extubated, the sensitivity will approach 100% but the specificity will still be low. This yields a positive likelihood ratio (LR+) of 1.25 which is nearly uninformative, and a negative likelihood ratio (LR-) of 0.22 which is slightly informative, taking a prior from 90% to 67%:
[Afterthought: Yang and Tobin used both "objective" and "subjective" criteria for weaning failure and presumably (the reporting is vague) reintubation:
Twenty-eight patients met objective criteria for weaning failure because they had one or more of the following: a partial pressure of carbon dioxide ≥50 torr (7 kPa) (17 patients), an increase in partial pressure of carbon dioxide of ≥8 torr (1 kPa) (18 patients), a pH of arterial blood ≤7.33 (16 patients), a decrease in pH of ≥0.07 (19 patients), or a partial pressure of oxygen ≤60 torr (8 kPa) with a fraction of inspired oxygen ≥0.5 (5 patients). The remaining 12 patients met subjective criteria for weaning failure because diaphoresis, evidence of increasing effort, tachycardia, arrhythmias, or hypotension required the reinstitution of mechanical ventilation.Perhaps some patients were reintubated but actually could have continued to breathe spontaneously in spite of meeting these criteria - this is yet another potential misclassification and ascertainment error that undermines the ability of a trial to set a clear path forward for extubation decisions.]