Method 2: A likelihood-based approach. The second approach estimates the probabilities q ijt using maximum likelihood estimation (MLE). With two MRSA types, we assume that patients susceptible to type 1 are also susceptible to type 2, so S i1t~Si2t~Sit . This implicitly assumes complete bacterial interference (i.e. that colonisation with one type of MRSA prevents acquisition of another type one or more days after the first acquisition [48] ). As a sensitivity analysis we also considered the other extreme: complete lack of bacterial interference, so that a patient colonized with one MRSA type had the same daily risk of acquiring a different subtype as an uncolonized patient. With the additional assumption that new MRSA acquisitions occur the day before they are detected, the log likelihood of the new MRSA acquisition data in ward i on day t is given by: