The data of Casale and associates for nonatopic asymptomatic cigarette smokers and nonsmokers with and without asthma were used for the analysis. The nonsmoking nonasthmatic group excluded patients with an atopic or allergic background or with positive skin tests.

Sensitivity (SE) is defined as the fraction of patients with the disease who have a positive test. Specificity (SP) is defined as the fraction of patients without the disease who have a negative test. The pretest probability (P) is the physicians estimate (in fractional terms) of the likelihood that the patient has the disease before the test results are considered. Thus, a pretest probability of 0.6 means in this case that the physician estimates a 60 percent likelihood of asthma on the basis of all available information but before he sees the test results. The post-test probability (PP) is the likelihood of asthma considering the pretest probability and the test results. The difference between P and PP represents the contribution of the test (which could be helpful or misleading) to the final diagnosis.

The post-test probability of asthma after a positive provocation test was calculated using the following form of Bayes’ theorem:

PP = (P x SE)/[P xSE + (l-P)x(l- SP)]

The post-test probability of asthma after a negative provocation test was calculated as follows:

PP = 1 – {[(1 – P) x SP]/[(1 – P) x SP + P x (1 – SE)]}

A breath unit is one inhalation of an aerosol of a 1 mg/ml solution of methacholine. Curves were calculated for a positive test (defined as a 20 percent fall in one second forced expiratory volume) occurring after the following cumulative breath units (CBU): 0.375, 1.125, 2.675, 5.77, 12.025, 24.5, 49.5, 99.5, and 224. The CBU producing the 20 percent fall is referred to as PD20. A separate set of curves was constructed for smokers and nonsmokers.