Probabilistic disease progression modeling to characterize diagnostic uncertainty: Application to staging and prediction in Alzheimer's disease

Abstract

Disease progression modeling (DPM) of Alzheimer's disease (AD) aims at revealing long term pathological trajectories from short term clinical data. Along with the ability of providing a data-driven description of the natural evolution of the pathology, DPM has the potential of representing a valuable clinical instrument for automatic diagnosis, by explicitly describing the biomarker transition from normal to pathological stages along the disease time axis. In this work we reformulated DPM within a probabilistic setting to quantify the diagnostic uncertainty of individual disease severity in an hypothetical clinical scenario, with respect to missing measurements, biomarkers, and follow-up information. We show that the staging provided by the model on 582 amyloid positive testing individuals has high face validity with respect to the clinical diagnosis. Using follow-up measurements largely reduces the prediction uncertainties, while the transition from normal to pathological stages is mostly associated with the increase of brain hypo-metabolism, temporal atrophy, and worsening of clinical scores. The proposed formulation of DPM provides a statistical reference for the accurate probabilistic assessment of the pathological stage of de-novo individuals, and represents a valuable instrument for quantifying the variability and the diagnostic value of biomarkers across disease stages.

Introduction

Neurodegenerative disorders (NDDs), such as Alzheimer's disease (AD), are characterized by the progressive pathological alteration of the brain's biochemical processes and morphology, and ultimately lead to the irreversible impairment of cognitive functions (Brookmeyer et al., 2007). The correct understanding of the relationship between the different pathological features is of paramount importance for improving the identification of pathological changes in patients, and for better treatment (Jack et al., 2010).

To this end, ongoing research efforts aim at developing precise models allowing optimal sets of measurements (and combinations of them) to uniquely identify pathological traits in patients. This problem requires the definition of optimal ways to integrate and jointly analyze the heterogeneous multi-modal information available to clinicians (Young et al., 2013, Mwangi et al., 2014, Lorenzi et al., 2016). By consistently analyzing multiple biomarkers that to date have mostly been considered separately, we aim at providing a richer description of the pathological mechanisms and a better understanding of individual disease progressions.

Disease progression modeling (DPM) is a relatively new research direction for the study of NDD data (Fonteijn et al., 2011, Jedynak et al., 2012, Donohue et al., 2014, Younes et al., 2014, Bilgel et al., 2015, Schiratti et al., 2015, Guerrero et al., 2016, Marinescu et al., 2017). The main goal of DPM consists in revealing the natural history of a disorder from collections of imaging and clinical data by: 1) quantifying the dynamics of NDDs along with the related temporal relationship between different biomarkers, and 2) staging patients based on individual observations for diagnostic and interventional purposes. Therefore, this research domain is closely related to the exploitation of advanced statistical/machine-learning approaches for the joint modeling of the heterogeneous and information available to clinicians: imaging, biochemical, and clinical biomarkers. Differently from the several predictive machine-learning approaches proposed in the past in NDD research, disease progression models aim at explicitly estimating the temporal progression of the biomarkers from normal to pathological stages, to provide a better interpretation and understanding of the natural evolution of the pathology. For this reason it represents a very appealing modeling approach in clinical settings.

The main challenge addressed by DPM consists in the general lack a well-defined temporal reference in longitudinal clinical dataset of NDDs. Indeed, age or visit date information are biased time references for the individual longitudinal measurements, since the onset of the pathology may vary across individuals according to genetic and environmental factors (Yang et al., 2011). This is a very specific methodological issue requiring the extension and generalization of the analysis approaches classically used in time-series analysis.

To tackle this problem, it is usually assumed that individual biomarkers are measured relatively to an underlying disease trajectory defined with respect to an absolute time axis describing the natural history of the pathology (Jedynak et al., 2012). Each individual is thus characterized by a specific observation time that needs to be estimated in order to assess the individual pathological stage. According to this statistical setting, we therefore aim at estimating a group-wise disease model defined with respect to an absolute time scale, along with individual time re-parameterisation relative to the group-wise progression. This modeling paradigm has been implemented in a number of approaches proposed in the recent years, either by assuming continuous temporal trajectories of the biomarkers (Jedynak et al., 2012, Donohue et al., 2014, Younes et al., 2014, Bilgel et al., 2015, Schiratti et al., 2015, Guerrero et al., 2016, Marinescu et al., 2017), or by modeling the disease progression as a sequence of discrete events (Fonteijn et al., 2011, Young et al., 2014).

For example, in (Donohue et al., 2014) the authors proposed to model the temporal biomarker trajectories through random effect regression, building on the theory of self-modeling regression (Kneip and Gasser, 1988), while the authors of (Schiratti et al., 2015) re-frame the random effect regression model in a geometrical setting, based on the assumption of a logistic curve shape for the average biomarker trajectories.

Continuous progression models have been recently extended to the modeling of brain images based on the time-reparameterization of voxel/mesh-based measures (Younes et al., 2014, Bilgel et al., 2015, Marinescu et al., 2017).

The use of disease progression models for diagnostic purposes is instead less investigated. Predictive models of patient staging were proposed within the setting of the Event Based Model (Fonteijn et al., 2011), or still through random effect modeling (Guerrero et al., 2016). However, the Event Based Model relies on the coarse binary discretization of the biomarker changes, and does not account for longitudinal observations, while the predictive models proposed in (Guerrero et al., 2016) and (Schmidt-Richberg et al., 2015) require cohorts with known disease onset, and therefore lack flexibility while being prone to bias due to mis-diagnosis and uncertainty of the conversion time.

Furthermore, these methods are generally not formulated in a probabilistic setting, which makes it difficult to account for uncertainties in biomarker progressions and diagnostic predictions. Indeed, the quantification of the variability associated with the biomarkers trajectories, as well as the assessment of the diagnostic uncertainty in de-novo patients, are crucial requirements for decision making in clinical practice (Shinkins and Perera, 2013).

Nonetheless, the ensemble of this research offers a sight of the potential of these approaches in representing a novel and powerful diagnostic instrument: in this study we thus aim at assessing the ability of DPM in providing a statistical reference for the transition from normal to pathological stages, for probabilistic diagnosis in the clinical scenario. To this end, we reformulate classical DPM within a Bayesian setting in order to allow the probabilistic estimate of the biomarker trajectories and the quantification of the uncertainty of predictions of the individual pathological stage. The resulting probabilistic framework is exploited in an hypothetical clinical scenario, for the estimation of the pathological stage in a de-novo cohort of testing individuals, by assessing the influence of missing observations, biomarkers, and follow-up information.

The manuscript is structured as follows. Section 2.1 formulates DPM based on Bayesian Gaussian Process regression (Rasmussen, 2006), while Section 2.2 illustrates the validation of our model on clinical and multivariate imaging measurements from a cohort of 782 amyloid positive individuals extracted from the ADNI database.