CD4 and infection: 1994; Farewell et al. 1994), particularly within a multi-state model (Aalen et al. 1997; Sweeting et al. 2005), have been fundamental. These ideas have been central to the development of multi-state back-calculation, where the incorporation of information on CD4 count data around HIV diagnosis, has also enabled estimation of trends in diagnosis probabilities and, consequently, trends in the number of undiagnosed infections (Birrell et al. 2012).