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End-stage renal disease (ESRD) is one of the leading causes of morbidity and mortality worldwide and its prevalence is only projected to increase as the average age and global population rises. By far the most effective treatment for ESRD is kidney transplantation with fully compatible donor and recipient human leukocyte antigen (HLA). Practically however, full compatibility is not always possible. Where a mismatch in HLA occurs an immune response may take place, leading to the formation of donor specific antibodies (DSA) which target the kidney. In this thesis analysis is performed on 110 HLA incompatible kidney transplants performed between 2003 and 2014 at the University Hospitals of Coventry and Warwickshire. The analysis aimed to address four main tasks: data processing, exploratory analysis, immune response classification, and dynamical modelling of DSA immune response. Under the exploratory analysis statistical techniques were utilised to investigate relationships between characteristic variables and daily posttransplant DSA levels with graft survival. Results of this work highlighted the significance of certain pre-transplant and post-transplant periods. For classification, a time series clustering technique was used to identify five early post-transplant DSA response types: no-response, fast-modulation, slow-modulation, rise-to-sustained and sustained. This discovery was a new contribution to literature and highlighted improved outcome for modulatory versus sustained outcome. Lastly, a set of parametric models were developed to describe the DSA post-transplant dynamic responses. Findings in this work reinforce the concept of higher DSA levels being associated with worse outcome, however, contribute further by suggesting that this relationship may be dependent on response type. Overall, these findings show that early period post-transplant monitoring can be a beneficial tool for clinicians in the monitoring of patient health. It has provided indicators towards the outcome of an incompatible kidney transplant. Future work should seek to validate these findings with a larger multi-centre cohort.