Novel Computational Methods for Bayesian Hierarchical Modeling in the Biomedical Domain

The recent growth in the availability of biomedical data promises to reshape healthcare by ushering in an era of personalized medicine where data can be used to diagnose and treat patients with pinpoint accuracy. Truly realizing this goal requires building statistical models that individually model patient variations such as age, sex, and genetic makeup, which leads to a combinatorial growth in the number of parameters in a model and noisy estimates. Fortunately, Bayesian hierarchical models, along with recent computational advances, provide a solution to this issue. By naturally embedding the hierarchical structure that many datasets exhibit into the model, these models allow for separate estimates that capture population-level variation and simultaneously avoid noise via regularization to a population mean.In this thesis, we describe novel models and computational methods for Bayesian hierarchical modeling of biomedical data. We begin by describing our contributions to various areas of Bayesian modeling, along with the problems from our applied work that motivated these contributions.Specifically, we describe our disease progression model, which hierarchically models patient disease trajectories. The model, which was motivated by our applied work on Alzheimer's Disease, utilizes I-splines to capture the characteristic monotonic shape of dementia disease trajectories, along with Dirichlet distributions over the coefficients of these I-splines to hierarchically model these trajectories. Next we describe our work on using the Givens Representation of orthogonal matrices to infer models with orthogonal matrix parameters, such as factor models, in a general Bayesian framework. We describe the innovations in our method along with our motivating hierarchical example based on the analysis of protein biomarkers of coagulopathic trauma patients. Next, we describe a mechanistic model of coagulopathy that relates clotting assay data to protein concentrations, effectively providing a fast and convenient way for clinicians to understand key protein markers involved in clotting.Next we transition specifically to Hamiltonian Monte Carlo (HMC) and elucidate the connection between multiscale posterior distributions and the efficiency of HMC. We describe the issue of numerical stability inside HMC and present our implicit HMC algorithm for efficiently sampling non-Gaussian posterior distributions.Lastly, we provide a summary of our contributions along with ideas for future work

On the Inference of Functional Circadian Networks Using Granger Causality.

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals

On the Inference of Functional Circadian Networks Using Granger Causality.

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals

On the Inference of Functional Circadian Networks Using Granger Causality.

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals

Histogram of average weight change for users during adherent and non-adherent periods of activity tracking.

<p>The histograms depict the association between logging adherence and weight change while controlling for all user variation (gender, age, weight, etc.). For each user in the secondary analysis, average weight change is computed first for their adherent tracking periods and then for their non-adherent periods. Both averages are histogrammed for each activity type. The graph shows a positive association between logging adherence and weight loss, as the adherent weight-change distribution is shifted left relative to the non-adherent weight-change distribution.</p

Adherent Use of Digital Health Trackers Is Associated with Weight Loss

<div><p>We study the association between weight fluctuation and activity tracking in an on-line population of thousands of individuals using digital health trackers (1,749 ≤ <i>N</i> ≤ 14,411, depending on the activity tracker considered) with millions of recorded activities (119,292 ≤ <i>N</i> ≤ 2,221,382) over the years 2013–2015. In a first between-subject analysis, we found a positive association between activity tracking frequency and weight loss. Users who log food with moderate frequency lost an additional 0.63% (CI [0.55, 0.72]; <i>p</i> < .001) of their body weight per month relative to low frequency loggers. Frequent workout loggers lost an additional 0.38% (CI [0.20, 0.56]; <i>p</i> < .001) and frequent weight loggers lost an additional 0.40% (CI [0.33, 0.47]; <i>p</i> < .001) as compared to infrequent loggers. In a subsequent within-subject analysis on a subset of the population (799 ≤ <i>N</i> ≤ 6,052) with sufficient longitudinal data, we used fixed effect models to explore the temporal relationship between a change in tracking adherence and weight change. We found that for the same individual, weight loss is significantly higher during periods of high adherence to tracking vs. periods of low adherence: +2.74% of body weight lost per month (CI [2.68, 2.81]; <i>p</i> < .001) during adherent weight tracking, +1.35% per month (CI [1.26, 1.43]; <i>p</i> < .001) during adherent food tracking, and +0.60% per month (CI [0.44, 0.76]; <i>p</i> < .001) during adherent workout tracking. The findings suggest that adherence to activity tracking can be utilized as a convenient real-time predictor of weight fluctuations, enabling large-scale, personalized intervention strategies.</p></div

Population characteristics for the primary analysis: mean (standard deviation) [number not reported].

<p>Population characteristics for the primary analysis: mean (standard deviation) [number not reported].</p

Average weight change during adherent and non-adherent periods for various definitions of adherent period.

<p>We observe that non-adherent periods have higher weight loss, regardless of the value of max gap or period length. The secondary analysis was performed with a max gap of 4 days, and including periods of 7–28 days in length.</p