The integrated approach of learning tuberculosis transmission within and outside households via random directed graph models

Household contact studies are frequently used in tuberculosis transmission research, and models based on them often focus on transmission within the household. This contradicts recent research which suggests the transmission may be more likely to happen outside the household than within the household in high burden settings where these studies are frequently conducted. Consequently, most models would lead to biased estimates and misleading public health interventions. There is a strong need for developing models that allow concurrent estimation of household and extra-household transmission. In this study, we develop a random directed graph model for tuberculosis transmission, which permits users to concurrently build models for both household and extra-household transmission. Furthermore, our model can estimate the relative frequency of household transmission versus extra-household transmission and consistently produce unbiased estimates for risk factors, regardless of whether community controls are available. We illustrate our approach with a household contact study conducted in Vitoria, Brazil, and our results indicate that extra-household transmission can account for 63% to 98% of M. tuberculosis infections detected during such a study.