Predicting disease progression from short biomarker series using expert advice algorithm

Abstract

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of “prediction with expert advice” to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

Variable Responses to Corneal Grafts: Insights from Immunology and Systems Biology

“…Extracting information from a large number of biomarkers is a challenge; however, well-trained clinicians may be able to glean diagnostic and prognostic information from a smaller number of markers. Mathematical technologies are being developed to estimate the patient state from a large set of biomarkers [161] or from a very short time-series of single biomarker [162,163]. Technologies like Bayesian belief networks and random survival forests constructed from conditional inference trees [162] have been recently developed to predict solid organ graft failure and can in principle be applied to corneal grafts [164].…”

Twenty years after “The Impact of Chaos”: what have been achieved and what should be answered

“…Moreover, we should consider how to combine the "chaos theory" or more generally the dynamical systems theory, with the other fields including machine learning, statistics, signal processing, control theory, and information theory. Especially, combining multiple predictions [105] will provide new scopes for machine learning, statistics, and signal processing. Although we have used an idea of stabilizing a piecewise linear system and obtaining an optimal treatment schedule for prostate cancer, we need to extend this idea for a piecewise smooth (nonlinear) system [106].…”

System identification and parameter estimation in mathematical medicine: examples demonstrated for prostate cancer

“…The methods of the bootstrapping [17], the cross entropy [19], the variational Bayes [20], and the Gaussian process [20] can provide the parameter distribution, and thus the prediction interval as well. The method of the temporal expert advice [11] can provide the prediction interval by weighting predictions according to each expert with Gaussian distributions, although this method cannot provide the parameter distribution itself. The second aspect is whether we use constraints for the parameters.…”

“…These assumptions came from general common observations made by urologists [3]. A summary of recent methods [11,12,17,19,20] for the system identification and parameter estimation is pre-sented in Table 1. The methods are roughly classified into three classes: parametric estimation, semi-parametric estimation, and non-parametric estimation.…”

“…Bootstrapping [17] Cross entropy [19] Variational Bayes [20] Gaussian process [20] Temporal expert advice [11] Bayes with past patients' prior [12] Parametric…”