Electronic medical records (EMR) contain a longitudinal collection of laboratory data that contains valuable phenotypic information on disease progression of a large collection of patients. These data can be potentially used in medical research or patient care; finding disease progression subtypes is a particularly important application. There are, however, two significant difficulties in utilizing this data for statistical analysis: (a) a large proportion of data is missing and (b) patients are in very different stages of disease progression and there are no well-defined start points of the time series. We present a Bayesian machine learning model that overcomes these difficulties. The method can use highly incomplete time-series measurement of varying lengths, it aligns together similar trajectories in different phases and is capable of finding consistent disease progression subtypes. We demonstrate the method on finding chronic kidney disease progression subtypes.