Selected Ion Flow Tube-Mass spectrometry (SIFT-MS) is an analytical measurement technology for the real-time quantification of volatile organic compounds in gaseous samples. This technology has current and potential applications in a wide variety of industries, although the focus of this research is in medical science. In this field, SIFT-MS has potential as a diagnostic device, capable of determining the presence of a particular disease or condition. In addition, SIFT-MS can be used to monitor the progression of a disease state, or predict deviations from expected behaviour. Lastly, SIFT-MS can be used for the identification of biomarkers of a particular disease state. All these possibilities are available non-invasively and in real-time, by analysing breath samples. SIFT-MS produces an extensive amount of data, requiring specific mathematical methods to identify biomarker masses that differ significantly between populations or time-points. Two classification methods are presented for the analysis of SIFT-MS mass scan data. The first method is a cross-sectional classification model, intended to differentiate between the diseased and non-diseased state. This model was validated in a simple test case. The second method is a longitudinal classification model, intended to identify key biomarkers that change over time, or in response to treatment. Both of these classification models were validated in 2 clinical trials, investigating renal function in humans and rats. The first clinical trial monitored changes in breath ammonia, TMA and acetone concentrations over the course of dialysis treatment. Correlations with the current gold standard plasma creatinine, and blood urea nitrogen were reported. Finally, biomarkers of renal function were identified that change predictably over the course of treatment. The second trial induced acute renal failure in rats, and monitored the change in renal function observed during recovery. For comparison and validation of the result, a 2-compartment model was developed for estimating renal function via a bolus injection of a radio-labelled inulin tracer, and was compared with the current gold standard plasma creatinine measurement, modified using the Cockcroft-Gault equation for rats. These two methods were compared with SIFT-MS monitoring of breath analytes, to examine the potential for non-invasive biomarkers of kidney function. Results show good promise for the non-invasive, real-time monitoring of breath analytes for diagnosis and monitoring of kidney function, and, potentially, other disease states.