Maintaining adequate and stable blood oxygen level is important for preterm babies to avoid the risk of brain, lung and retinal injury such as retinopathy of prematurity (ROP). However, wide disparities in policies and practices of oxygenation in preterm babies exist among neonatal care providers as it is still unclear which best method of monitoring and what features of oxygen measurements are important to clinician’s interpretations for assessing preterm babies at risk of developing severe ROP or unstable health condition. This thesis consists of two projects: NZ-ROP that examines multiple factors of severe ROP including summary statistics (mean, standard deviation (SD), coefficient of variation (CV) and desaturation) for oxygen saturation (OS) features in very extreme preterm babies, and NZ-LP that investigates the efficacy of some of these statistics for health monitoring of late preterm babies. The OS data in NZ-ROP were recorded using modified oximeters that have offsets and inherent software artefact, both of which mask the actual saturation for certain OS ranges and may complicate the choice of methods in the analyses. Therefore, novel algorithms involving linear and quadratic interpolations are developed, implemented on the New Zealand data, and validated using the data of a UK preterm baby, as recorded from offsets and non-offsets oximeters. For all data sets, the algorithms produced saturation distributions that were very close to those obtained from the non-offset oximeter. The algorithms perform within the recommended standards of commercial oximeters currently used in the clinical practice. ROP is a multifactorial disease, with oxygenation fluctuations as one of the key contributors. The all-subsets logistic regression, robust and generalised additive statistical modelling, along with a model averaging approach, are applied in NZ-ROP to determine the relationship of variability and level of OS with severe ROP, and the extent of contribution of various clinical predictors to the severity of this eye disease. Desaturation, as a measure of OS variability, has the strongest association with severe ROP among all OS statistics, in particular, the risk of severe ROP is almost three times higher in babies that exhibit greater occurrences of desaturation episodes. Additionally, this study identifies longer periods of ventilation support, frequent desaturation events, extreme prematurity and low birth weight as the most important factors that substantially exacerbate the severity of ROP, and therefore signify babies’ underlying condition of being severely ill. Persistent cardiorespiratory instabilities prior to hospital discharge may expose preterm babies to a greater risk of neuro-developmental impairments. In NZ-LP, the statistical summaries of mean, SD and CV are computed from the OS measurements of healthy stable and unstable babies, and the performance of these statistics in detecting the unstable babies is evaluated using an extremeness index for outlying data and a hierarchical clustering technique. With SD and CV, the clinically unstable babies were very well separated from the group of stable babies, wherein, the separation was even more apparent with the use of CV. These suggest that measures of variability could be better than saturation level for highlighting babies’ underlying instability due to immature physiological systems, but the combination of variability and level through the CV are believed to be even better. Identification and summarisation of useful OS features quantitatively hold great promise for improved monitoring of oxygenation instability and diagnosis of severe ROP for preterm babies.