Breath mass spectrometry is a useful tool for identifying important compounds associated with health. However, there have been few studies that have explored human exhaled breath by full-scan mass spectrometry as a non-invasive method for medical diagnosis, which may be attributed to the difficulties resulting from multicollinearity and small sample sizes relative to a large number of product ions. In this study, breath samples from 54 chronic kidney disease patients were analyzed by selected ion flow tube mass spectrometry in the full-scan mode. With the signal intensities of product ions, we developed a novel and robust algorithm, iterative PCA with intensity screening (IPS), to build linear models for estimating important clinical parameters of chronic kidney disease. It has been shown that IPS provided good estimations in cross-validated samples, and furthermore the identified product ions could have direct medical relevance to the disease. The study demonstrated the potential of quantitative breath analysis using mass spectrometry for medical diagnosis, and the importance of applying appropriate statistical tools to unveil the rich information in this type of data.