arXiv subjects

Benny Ren

Publications and source records attributed to Benny Ren.

5 recordsLinked to original sources

arXiv2024

Semiparametric quantile functional regression analysis of adolescent physical activity distributions in the presence of missing data

In the age of digital healthcare, passively collected physical activity profiles from wearable sensors are a preeminent tool for evaluating health outcomes. In order to fully leverage the vast amounts of data collected through wearable accelerometers, we propose to use quantile functional regression to model activity profiles as distributional outcomes through quantile responses, which can be used to evaluate activity level differences across covariates based on any desired distributional summary. Our proposed framework addresses two key problems not handled in existing distributional regression literature. First, we use spline mixed model formulations in the basis space to model nonparametric effects of continuous predictors on the distributional response. Second, we address the underlying missingness problem that is common in these types of wearable data but typically not addressed. We show that the missingness can induce bias in the subject-specific distributional summaries that leads to biased distributional regression estimates and even bias the frequently used scalar summary measures, and introduce a nonparametric function-on-function modeling approach that adjusts for each subject's missingness profile to address this problem. We evaluate our nonparametric modeling and missing data adjustment using simulation studies based on realistically simulated activity profiles and use it to gain insights into adolescent activity profiles from the Teen Environment and Neighborhood study.

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arXiv2024

The Cox-Polya-Gamma Algorithm for Flexible Bayesian Inference of Multilevel Survival Models

Bayesian Cox semiparametric regression is an important problem in many clinical settings. Bayesian procedures provide finite-sample inference and naturally incorporate prior information if MCMC algorithms and posteriors are well behaved. Survival analysis should also be able to incorporate multilevel modeling such as case weights, frailties and smoothing splines, in a straightforward manner. To tackle these modeling challenges, we propose the Cox-Polya-Gamma (Cox-PG) algorithm for Bayesian multilevel Cox semiparametric regression and survival functions. Our novel computational procedure succinctly addresses the difficult problem of monotonicity constrained modeling of the nonparametric baseline cumulative hazard along with multilevel regression. We develop two key strategies. First, we exploit an approximation between Cox models and negative binomial processes through the Poisson process to reduce Bayesian computation to iterative Gaussian sampling. Next, we appeal to sufficient dimension reduction to address the difficult computation of nonparametric baseline cumulative hazard, allowing for the collapse of the Markov transition within the Gibbs sampler based on beta sufficient statistics. In addition, we explore conditions for uniform ergodicity of the Cox-PG algorithm. We demonstrate our multilevel modeling approach using open source data and simulations. We provide software for our Bayesian procedure in the supplement.

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arXiv2022

Analysis of block slice samplers for Bayesian GLMMs and GAMs with linear inequality and shape constraints

Exponential family models, generalized linear models (GLMs), generalized linear mixed models (GLMMs) and generalized additive models (GAMs) are widely used methods in statistics. However, many scientific applications necessitate constraints be placed on model parameters such as shape and linear inequality constraints. Constrained estimation and inference of parameters remains a pervasive problem in statistics where many methods rely on modifying rigid large sample theory assumptions for inference. We propose a flexible slice sampler Gibbs algorithm for Bayesian GLMMs and GAMs with linear inequality and shape constraints. We prove our posterior samples follow a Markov chain central limit theorem (CLT) by proving uniform ergodicity of our Markov chain and existence of the a moment generating function for our posterior distributions. We use our CLT results to derive joint bands and multiplicity adjusted Bayesian inference for nonparametric functional effects. Our rigorous CLT results address a shortcoming in the literature by obtaining valid estimation and inference on constrained parameters in finite sample settings. Our algorithmic and proof techniques are adaptable to a myriad of important statistical modeling problems. We apply our Bayesian GAM to a real data analysis example involving proportional odds regression for concussion recovery in children with shape constraints and smoothed nonparametric effects. We obtain multiplicity adjusted inference on monotonic nonparametric time effect to elucidate recovery trends in children as a function of time.

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arXiv2022

Combining Mixed Effects Hidden Markov Models with Latent Alternating Recurrent Event Processes to Model Diurnal Active-Rest Cycles

Data collected from wearable devices and smartphones can shed light on an individual's pattern of behavioral and circadian routine. Phone use can be modeled as alternating event process, between the state of active use and the state of being idle. Markov chains and alternating recurrent event models are commonly used to model state transitions in cases such as these, and the incorporation of random effects can be used to introduce diurnal effects. While state labels can be derived prior to modeling dynamics, this approach omits informative regression covariates that can influence state memberships. We instead propose an alternating recurrent event proportional hazards (PH) regression to model the transitions between latent states. We propose an Expectation-Maximization (EM) algorithm for imputing latent state labels and estimating regression parameters. We show that our E-step simplifies to the hidden Markov model (HMM) forward-backward algorithm, allowing us to recover a HMM with logistic regression transition probabilities. In addition, we show that PH modeling of discrete-time transitions implicitly penalizes the logistic regression likelihood and results in shrinkage estimators for the relative risk. We derive asymptotic distributions for our model parameter estimates and compare our approach against competing methods through simulation as well as in a digital phenotyping study that followed smartphone use in a cohort of adolescents with mood disorders.

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arXiv2022

Autoregressive Mixture Models for Serial Correlation Clustering of Time Series Data

Clustering time series into similar groups can improve models by combining information across like time series. While there is a well developed body of literature for clustering of time series, these approaches tend to generate clusters independently of model training which can lead to poor model fit. We propose a novel distributed approach that simultaneously clusters and fits autoregression models for groups of similar individuals. We apply a Wishart mixture model so as to cluster individuals while modeling the corresponding autocovariance matrices at the same time. The fitted Wishart scale matrices map to cluster-level autoregressive coefficients through the Yule-Walker equations, fitting robust parsimonious autoregressive mixture models. This approach is able to discern differences in underlying autocorrelation variation of time series in settings with large heterogeneous datasets. We prove consistency of our cluster membership estimator, asymptotic distributions of coefficients and compare our approach against competing methods through simulation as well as by fitting a COVID-19 forecast model.

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