BackgroundSporadic lymphangioleiomyomatosis (S-LAM) is a rare low-grade neoplasm of young women characterized by multiple pulmonary cysts leading to progressive dyspnea and recurrent spontaneous pneumothorax (SP). The diagnosis of S-LAM may be delayed by several years. To reduce this delay, chest computed tomography (CT) screening has been proposed to uncover cystic lung disease in women presenting with SP. However, the probability to discover S-LAM in this population has not been determined precisely. The aim of this study was to calculate the probability of finding S-LAM in women presenting with (a) SP, and (b) apparent primary SP (PSP) as first manifestation of S-LAM.MethodsCalculations were made by applying the Bayes theorem to published epidemiological data on S-LAM, SP and PSP. Each term of the Bayes equation was determined by meta-analysis, and included: (1) the prevalence of S-LAM in the general female population, (2) the incidence rate of SP and PSP in the general female population, and (3) the incidence rate of SP and apparent PSP in women with S-LAM.ResultsThe prevalence of S-LAM in the general female population was 3.03 per million (95% confidence interval 2.48, 3.62). The incidence rate of SP in the general female population was 9.54 (8.15, 11.17) per 100,000 person-years (p-y). The incidence rate of SP in women with S-LAM was 0.13 (0.08, 0.20). By combining these data in the Bayes theorem, the probability of finding S-LAM in women presenting with SP was 0.0036 (0.0025, 0.0051). For PSP, the incidence rate in the general female population was 2.70 (1.95, 3.74) per 100,000 p-y. The incidence rate of apparent PSP in women with S-LAM was 0.041 (0.030, 0.055). With the Bayes theorem, the probability of finding S-LAM in women presenting with apparent PSP as first disease manifestation was 0.0030 (0.0020, 0.0046). The number of CT scans to perform in women to find one case of S-LAM was 279 for SP and 331 for PSP.ConclusionThe probability of discovering S-LAM at chest CT in women presenting with apparent PSP as first disease manifestation was low (0.3%). Recommending chest CT screening in this population should be reconsidered.Supplementary InformationThe online version contains supplementary material available at 10.1186/s13023-023-02784-5.