The Pseudotemporal Bootstrap for Predicting Glaucoma From Cross-Sectional Visual Field Data

Abstract

Abstract-Progressive loss of the field of vision is characteristic of a number of eye diseases such as glaucoma, a leading cause of irreversible blindness in the world. Recently, there has been an explosion in the amount of data being stored on patients who suffer from visual deterioration, including visual field (VF) test, retinal image, and frequent intraocular pressure measurements. Like the progression of many biological and medical processes, VF progression is inherently temporal in nature. However, many datasets associated with the study of such processes are often cross sectional and the time dimension is not measured due to the expensive nature of such studies. In this paper, we address this issue by developing a method to build artificial time series, which we call pseudo time series from cross-sectional data. This involves building trajectories through all of the data that can then, in turn, be used to build temporal models for forecasting (which would otherwise be impossible without longitudinal data). Glaucoma, like many diseases, is a family of conditions and it is, therefore, likely that there will be a number of key trajectories that are important in understanding the disease. In order to deal with such situations, we extend the idea of pseudo time series by using resampling techniques to build multiple sequences prior to model building. This approach naturally handles outliers and multiple possible disease trajectories. We demonstrate some key properties of our approach on synthetic data and present very promising results on VF data for predicting glaucoma.

Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of1/fNoise Type

“…In fact, if specific biomedical signals are in the class of 1/ f noise, the variances of their prediction errors may not exist or large [72]. Tucker and Garway-Heath used to state that their prediction errors with either prediction model they used are large [74]. The result in this paper may in a way provide their research with an explanation.…”

Integrating Clinical Data from Cross-Sectional and Longitudinal Studies

“…The trajectory is determined by the Floyd-Warshall algorithm [6], a wellestablished algorithm for finding the shortest path in weighted graphs. A full description of the algorithm to generate PTS appears in [3] and example PTS generated from simulated cross-sectional data are shown in Figure 2. We explore whether adding a small number of longitudinal data samples to models learnt from crosssectional data (via the PTS approach) improves them.…”

“…The main disadvantage of such studies is that the progression of disease is inherently temporal in nature and the time dimension is not captured. Previously, we developed a resampling approach known as the temporal bootstrap [3] that builds multiple trajectories through cross sectional data to approximate genuine longitudinal data. These pseudo time-series can be used to build approximate temporal models for prediction and for identifying stages in disease progression [4].…”

Uncovering genomic trajectories with heterogeneous genetic and environmental backgrounds across single-cells and populations

“…Using advanced machine learning techniques, these methods can be applied to characterise complex, nonlinear behaviours, such as cell cycle, and modelling branching behaviours to allow, for example, the possibility of cell fate decision making. Historically, single cell applications were pre-dated by more general applications in modelling cancer progression from gene expression profiling of tumours [Qiu et al, 2011, Magwene et al, 2003, Gupta and Bar-Joseph, 2008] as well as in other progressive disease contexts such as glaucoma [Tucker and Garway-Heath, 2010, Tucker et al, 2017, Tucker and Li, 2015, Tucker et al, 2015]. However, to date, there has been little cross-over between these domains in terms of methodological development due to the differing contexts in which methods are applied.…”