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.

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A single curve was constructed for a negative test result after 224 CBU. For this curve, a sensitivity of 0.9 was used with the specificities of Casale et al.

A sample calculation for a single point is as follows: For 49.5 CBU,^{)} a 90 percent positive response in asthma is shown, and a 6 percent positive response in nonasthmatic, nonsmokers. This represents a sensitivity of 90 percent and a specificity of 94 percent. For a pretest probability of 0.4, equation (1) is solved as follows:

PP = (0.4 x 0.9)40.4 x 0.9 + (1 – 0.4) x (1 – 0.94)] = 0.91

This value was used as the post-test probability for a pretest probability of 0.4 on the nonsmoking curve.

We are unaware of any data on the sensitivity of methacholine challenge for smoking asthmatic patients. To construct the curves for positive tests in smokers, we used the data of Casale assuming that the sensitivity for smoking asthmatic patients would be the same as for non-smoking asthmatic patients. It seems reasonable to assume that the sensitivity in the smokers will be at least as high as in the nonsmokers. We made sample calculations using a value for sensitivity 50 percent higher than the reported values for nonsmoking asthmatic patients (up to a value of 1.0 sensitivity). The curves for values of pretest probabilities of 0.3 and greater were virtually identical to those for the lower sensitivities. At pretest probabilities of 0.1 and 0.2, the maximum differences in the post-test probabilities was 20 percent, and this only for the curves for CBU of 5.77 and 12.025. silagra tablets