where i is the status to pathogen 1 (0 for seronegative and 1 for seropositive) and j is the status to pathogen 2. To calculate the E i,j , for each pathogen taken separately, a logistic regression including K risk factors (see previous section) is run to estimate the probability of being seropositive for each individual (termedp p p,x for individual x and pathogen p, p[ 1,2 f g):