A chain-binomial model for intra-household spread of Mycobacterium tuberculosis in a low socio-economic setting in Pakistan

A simulation study using Greenwood's chain-binomial model was carried out to elucidate the spread and control of Mycobacterium tuberculosis among the household contacts of infectious pulmonary tuberculosis (TB) patients. Based on the observed data, the maximum-likelihood estimates (±S.E.) of chain-binomial probabilities of intra-household M. tuberculosis transmission from an index case in 3-person and 4-person households were 0·313±0·008 and 0·325±0·009 respectively. The χ2 goodness-of-fit test of observed and simulated mean expected frequencies of cases revealed good fit for 3-person (P=0·979) and 4-person (P=0·546) households. With the assumption of varying risk of M. tuberculosis transmission across the households under β-distribution, goodness-of-fit tests of observed and mean simulated expected frequencies revealed the inadequacy of Greenwood's chain-binomial model both for 3-person (P=0·0185) and 4-person (P