arXiv subjects

Luke Duttweiler

Publications and source records attributed to Luke Duttweiler.

6 recordsLinked to original sources

arXiv2025

SkipTrack: A Bayesian Hierarchical Model for Self-tracked Menstrual Cycle Length and Regularity in Large Mobile Health Cohorts

Menstrual cycle length and regularity are important vital signs with implications for a variety of acute and chronic health conditions. Large datasets derived from cycle-tracking mobile health apps are being used to investigate the effects of various covariates on menstrual cycle length and regularity. One limitation on these analyses is that recorded cycle lengths can be incorrectly inflated if users skip tracking any cycle related bleeding days in the app. Here we present SkipTrack, a novel Bayesian hierarchical framework for examining baseline and time-varying effects on menstrual cycle length and regularity while accounting for the uncertainty of possible skips in cycle tracking. In simulations we demonstrate the superiority of the SkipTrack model by showing that competing methods which specify cycle skips a priori are more susceptible to issues of estimation bias and overconfidence than the SkipTrack model. Finally, we apply the SkipTrack framework to data from the Apple Women's Healthy Study, a US-based digital cohort (consent provided at study enrollment) to examine patterns of association between age, BMI and race/ethnicity, and menstrual cycle length and regularity.

stat.AP↗

arXiv2024

Constructing optimal treatment length strategies to maximize quality-adjusted lifetimes

Real-world clinical decision making is a complex process that involves balancing the risks and benefits of treatments. Quality-adjusted lifetime is a composite outcome that combines patient quantity and quality of life, making it an attractive outcome in clinical research. We propose methods for constructing optimal treatment length strategies to maximize this outcome. Existing methods for estimating optimal treatment strategies for survival outcomes cannot be applied to a quality-adjusted lifetime due to induced informative censoring. We propose a weighted estimating equation that adjusts for both confounding and informative censoring. We also propose a nonparametric estimator of the mean counterfactual quality-adjusted lifetime survival curve under a given treatment length strategy, where the weights are estimated using an undersmoothed sieve-based estimator. We show that the estimator is asymptotically linear and provide a data-dependent undersmoothing criterion. We apply our method to obtain the optimal time for percutaneous endoscopic gastrostomy insertion in patients with amyotrophic lateral sclerosis.

math.ST↗

arXiv2024

The Traceplot Thickens: Developing All-Purpose Convergence Diagnostics for any Markov Chain Monte Carlo Algorithm

Markov Chain Monte Carlo (MCMC) algorithms are frequently used to perform inference under a Bayesian modeling framework. Convergence diagnostics, such as traceplots, the Gelman-Rubin potential scale reduction factor, and effective sample size, are used to visualize and monitor how well the sampler has explored the parameter space and the mixing of multiple chains. However, these classic diagnostics can be undefined or ineffective when the sample space of the algorithm varies in dimension or has a large number of discrete parameters. In this article, we develop a novel approach to produce convergence diagnostics in these difficult scenarios by mapping the original sample space to the real-line and then evaluating the convergence diagnostics on the mapped values. The effectiveness of our method is demonstrated on a MCMC algorithm sampling from a Dirichlet process mixture model. The proposed diagnostics are also used to evaluate the performance of a Bayesian kernel machine regression model for estimating the health effect of multi-pollutant mixtures in the Study of Environment, Lifestyle, and Fibroids. Based on diagnostics for the latter dataset, we then explain how we modify the MCMC sampler to improve convergence.

stat.CO↗

arXiv2023

Nonparametric estimation of a covariate-adjusted counterfactual treatment regimen response curve

Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which we refer to as a stratum based value function. We focus on semiparametric class of decision rules and propose a sieve based nonparametric covariate adjusted regimen-response curve estimator within that class. Our work contributes in several ways. First, we propose an inverse probability weighted nonparametrically efficient estimator of the smoothed regimen-response curve function. We show that asymptotic linearity is achieved when the nuisance functions are undersmoothed sufficiently. Asymptotic and finite sample criteria for undersmoothing are proposed. Second, using Gaussian process theory, we propose simultaneous confidence intervals for the smoothed regimen-response curve function. Third, we provide consistency and convergence rate for the optimizer of the regimen-response curve estimator; this enables us to estimate an optimal semiparametric rule. The latter is important as the optimizer corresponds with the optimal dynamic treatment regimen. Some finite-sample properties are explored with simulations.

math.ST↗

arXiv2023

Testing Sparsity Assumptions in Bayesian Networks

Bayesian network (BN) structure discovery algorithms typically either make assumptions about the sparsity of the true underlying network, or are limited by computational constraints to networks with a small number of variables. While these sparsity assumptions can take various forms, frequently the assumptions focus on an upper bound for the maximum in-degree of the underlying graph $\nabla_G$. Theorem 2 in Duttweiler et. al. (2023) demonstrates that the largest eigenvalue of the normalized inverse covariance matrix ($\Omega$) of a linear BN is a lower bound for $\nabla_G$. Building on this result, this paper provides the asymptotic properties of, and a debiasing procedure for, the sample eigenvalues of $\Omega$, leading to a hypothesis test that may be used to determine if the BN has max in-degree greater than 1. A linear BN structure discovery workflow is suggested in which the investigator uses this hypothesis test to aid in selecting an appropriate structure discovery algorithm. The hypothesis test performance is evaluated through simulations and the workflow is demonstrated on data from a human psoriasis study.

stat.ML↗

arXiv2022

Spectral Bayesian Network Theory

A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often lead to many `likely' network structures. In this paper, we lay the groundwork for an approach that focuses on learning global properties of the DAG rather than exact edges. This is done by defining the structural hypergraph of a BN, which is shown to be related to the inverse-covariance matrix of the network. Spectral bounds are derived for the normalized inverse-covariance matrix, which are shown to be closely related to the maximum indegree of the associated BN.

math.CO↗