Mathematical study of the contamination phenomenon in the culture of tubercle bacilli.

This paper demonstrates that when 'spot' specimens of sputum are cultured for tubercle bacilli on Löwenstein-Jensen medium, bacterial contamination occurs at random and follows a Poisson distribution. Over a period of 14 years, contamination rates with overnight 'collection' specimens (4.5 to 10.2%) were substantially higher than with spot specimens (1.3 to 4.0%), but the correlation between the two was very high (r = 0.98). In contrast to spot specimens, the incidence of contamination with collection specimens was significantly higher for females than for males, and significant variation was also found between patients of the same sex. In consequence, the Poisson distribution, which assumes a constant contamination rate for all patients, did not provide a satisfactory fit to the data on collection specimens. However, a negative binomial distribution, which incorporates individual variability in contamination rate, provided a good fit. The reasons for individual variability are discussed.