arXiv subjects

David A. Stephens

Publications and source records attributed to David A. Stephens.

At least 37 records · Page 2Linked to original sources

arXiv2023

A time-dependent Poisson-Gamma model for recruitment forecasting in multicenter studies

Forecasting recruitments is a key component of the monitoring phase of multicenter studies. One of the most popular techniques in this field is the Poisson-Gamma recruitment model, a Bayesian technique built on a doubly stochastic Poisson process. This approach is based on the modeling of enrollments as a Poisson process where the recruitment rates are assumed to be constant over time and to follow a common Gamma prior distribution. However, the constant-rate assumption is a restrictive limitation that is rarely appropriate for applications in real studies. In this paper, we illustrate a flexible generalization of this methodology which allows the enrollment rates to vary over time by modeling them through B-splines. We show the suitability of this approach for a wide range of recruitment behaviors in a simulation study and by estimating the recruitment progression of the Canadian Co-infection Cohort (CCC).

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arXiv2022

The role of exchangeability in causal inference

Though the notion of exchangeability has been discussed in the causal inference literature under various guises, it has rarely taken its original meaning as a symmetry property of probability distributions. As this property is a standard component of Bayesian inference, we argue that in Bayesian causal inference it is natural to link the causal model, including the notion of confounding and definition of causal contrasts of interest, to the concept of exchangeability. Here we propose a probabilistic between-group exchangeability property as an identifying condition for causal effects, relate it to alternative conditions for unconfounded inferences (commonly stated using potential outcomes) and define causal contrasts in the presence of exchangeability in terms of posterior predictive expectations for further exchangeable units. While our main focus is on a point treatment setting, we also investigate how this reasoning carries over to longitudinal settings.

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arXiv2022

Targeting functional parameters with semiparametric Bayesian inference

Typical Bayesian inference requires parameter identification via likelihood parameterization, which has invited criticism for being less flexible than the Frequentist framework and subject to misspecification. Though misspecification may be avoided by functional parameter inference under a nonparametric model space, there does not exist a flexible Bayesian semiparametric model that would allow full control over the marginal prior over any general functional parameter. We present the technique of $θ$-augmentation which helps us manipulate nonparametric models into semiparametric ones that directly target any functional parameter. The method allows Bayesian probabilistic statements to be drawn for any estimator that is defined as a functional of the empirical distribution without requiring a likelihood function, thus providing a path to Bayesian analysis in problems like causal inference and censoring where there do not exist well-accepted likelihood functions.

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arXiv2022

Estimation of Optimal Dynamic Treatment Regimes using Gaussian Process Emulation

In precision medicine, identifying optimal sequences of decision rules, termed dynamic treatment regimes (DTRs), is an important undertaking. One approach investigators may take to infer about optimal DTRs is via Bayesian dynamic Marginal Structural Models (MSMs). These models represent the expected outcome under adherence to a DTR for DTRs in a family indexed by a parameter $ ψ$; the function mapping regimes in the family to the expected outcome under adherence to a DTR is known as the value function. Models that allow for the straightforward identification of an optimal DTR may lead to biased estimates. If such a model is computationally tractable, common wisdom says that a grid-search for the optimal DTR may obviate this difficulty. In a Bayesian context, computational difficulties may be compounded if a posterior mean must be calculated at each grid point. We seek to alleviate these inferential challenges by implementing Gaussian Process ($ \mathcal{GP} $) optimization methods for estimators for the causal effect of adherence to a specified DTR. We examine how to identify optimal DTRs in settings where the value function is multi-modal, which are often not addressed in the DTR literature. We conclude that a $ \mathcal{GP} $ modeling approach that acknowledges noise in the estimated response surface leads to improved results. Additionally, we find that a grid-search may not always yield a robust solution and that it is often less efficient than a $ \mathcal{GP} $ approach. We illustrate the use of the proposed methods by analyzing a clinical dataset with the aim of quantifying the effect of different patterns of HIV therapy.

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arXiv2022

Causal inference under mis-specification: adjustment based on the propensity score

We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional `likelihood times prior' posterior inference; in addition, most methods rely on parametric and distributional assumptions, and presumed correct specification. We emphasize that causal inference is typically carried out in settings of mis-specification, and develop strategies for fully Bayesian inference that reflect this. We focus on methods based on decision-theoretic arguments, and show how inference based on loss-minimization can give valid and fully Bayesian inference. We propose a computational approach to inference based on the Bayesian bootstrap which has good Bayesian and frequentist properties.

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arXiv2021

Bayesian Sample Size Calculations for SMART Studies

In the management of most chronic conditions characterized by the lack of universally effective treatments, adaptive treatment strategies (ATSs) have been growing in popularity as they offer a more individualized approach, and sequential multiple assignment randomized trials (SMARTs) have gained attention as the most suitable clinical trial design to formalize the study of these strategies. While the number of SMARTs has increased in recent years, their design has remained limited to the frequentist setting, which may not fully or appropriately account for uncertainty in design parameters and hence not yield appropriate sample size recommendations. Specifically, standard frequentist formulae rely on several assumptions that can be easily misspecified. The Bayesian framework offers a straightforward path to alleviate some of these concerns. In this paper, we provide calculations in a Bayesian setting to allow more realistic and robust estimates that account for uncertainty in inputs through the `two priors' approach. Additionally, compared to the standard formulae, this methodology allows us to rely on fewer assumptions, integrate pre-trial knowledge, and switch the focus from the standardized effect size to the minimal detectable difference. The proposed methodology is evaluated in a thorough simulation study and is implemented to estimate the sample size for a full-scale SMART of an Internet-Based Adaptive Stress Management intervention based on a pilot SMART conducted on cardiovascular disease patients from two Canadian provinces.

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arXiv2021

Bayesian inference for continuous-time hidden Markov models with an unknown number of states

We consider the modeling of data generated by a latent continuous-time Markov jump process with a state space of finite but unknown dimensions. Typically in such models, the number of states has to be pre-specified, and Bayesian inference for a fixed number of states has not been studied until recently. In addition, although approaches to address the problem for discrete-time models have been developed, no method has been successfully implemented for the continuous-time case. We focus on reversible jump Markov chain Monte Carlo which allows the trans-dimensional move among different numbers of states in order to perform Bayesian inference for the unknown number of states. Specifically, we propose an efficient split-combine move which can facilitate the exploration of the parameter space, and demonstrate that it can be implemented effectively at scale. Subsequently, we extend this algorithm to the context of model-based clustering, allowing numbers of states and clusters both determined during the analysis. The model formulation, inference methodology, and associated algorithm are illustrated by simulation studies. Finally, We apply this method to real data from a Canadian healthcare system in Quebec.

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arXiv2021

Bayesian Clustering for Continuous-Time Hidden Markov Models

We develop clustering procedures for longitudinal trajectories based on a continuous-time hidden Markov model (CTHMM) and a generalized linear observation model. Specifically in this paper, we carry out finite and infinite mixture model-based clustering for a CTHMM and achieve inference using Markov chain Monte Carlo (MCMC). For a finite mixture model with prior on the number of components, we implement reversible-jump MCMC to facilitate the trans-dimensional move between different number of clusters. For a Dirichlet process mixture model, we utilize restricted Gibbs sampling split-merge proposals to expedite the MCMC algorithm. We employ proposed algorithms to the simulated data as well as a real data example, and the results demonstrate the desired performance of the new sampler.

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arXiv2021

Adaptive Importance Sampling for Finite-Sum Optimization and Sampling with Decreasing Step-Sizes

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies. Recently, the problem of designing such schemes was formulated as an online learning problem with bandit feedback, and algorithms with sub-linear static regret were designed. In this work, we build on this framework and propose Avare, a simple and efficient algorithm for adaptive importance sampling for finite-sum optimization and sampling with decreasing step-sizes. Under standard technical conditions, we show that Avare achieves $\mathcal{O}(T^{2/3})$ and $\mathcal{O}(T^{5/6})$ dynamic regret for SGD and SGLD respectively when run with $\mathcal{O}(1/t)$ step sizes. We achieve this dynamic regret bound by leveraging our knowledge of the dynamics defined by the algorithm, and combining ideas from online learning and variance-reduced stochastic optimization. We validate empirically the performance of our algorithm and identify settings in which it leads to significant improvements.

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arXiv2021

Stochastic Reweighted Gradient Descent

Despite the strong theoretical guarantees that variance-reduced finite-sum optimization algorithms enjoy, their applicability remains limited to cases where the memory overhead they introduce (SAG/SAGA), or the periodic full gradient computation they require (SVRG/SARAH) are manageable. A promising approach to achieving variance reduction while avoiding these drawbacks is the use of importance sampling instead of control variates. While many such methods have been proposed in the literature, directly proving that they improve the convergence of the resulting optimization algorithm has remained elusive. In this work, we propose an importance-sampling-based algorithm we call SRG (stochastic reweighted gradient). We analyze the convergence of SRG in the strongly-convex case and show that, while it does not recover the linear rate of control variates methods, it provably outperforms SGD. We pay particular attention to the time and memory overhead of our proposed method, and design a specialized red-black tree allowing its efficient implementation. Finally, we present empirical results to support our findings.

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arXiv2020

Estimating Sparse Networks with Hubs

Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks in such applications that poses a challenge for statistical inference is the presence of a small number of strongly interconnected nodes in a network which are called hubs. For example, in microbiome research hubs or microbial taxa play a significant role in maintaining stability of the microbial community structure. In this paper, we investigate the problem of estimating sparse networks in which there are a few highly connected hub nodes. Methods based on L1-regularization have been widely used for performing sparse selection in the graphical modelling context. However, while these methods encourage sparsity, they do not take into account structural information of the network. We introduce a new method for estimating networks with hubs that exploits the ability of (inverse) covariance selection methods to include structural information about the underlying network. Our proposed method is a weighted lasso approach with novel row/column sum weights, which we refer to as the hubs weighted graphical lasso. We establish large sample properties of the method when the number of parameters diverges with the sample size, and evaluate its finite sample performance via extensive simulations. We illustrate the method with an application to microbiome data.

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arXiv2019

A hierarchical Bayesian model for predicting ecological interactions using scaled evolutionary relationships

Identifying undocumented or potential future interactions among species is a challenge facing modern ecologists. Recent link prediction methods rely on trait data, however large species interaction databases are typically sparse and covariates are limited to only a fraction of species. On the other hand, evolutionary relationships, encoded as phylogenetic trees, can act as proxies for underlying traits and historical patterns of parasite sharing among hosts. We show that using a network-based conditional model, phylogenetic information provides strong predictive power in a recently published global database of host-parasite interactions. By scaling the phylogeny using an evolutionary model, our method allows for biological interpretation often missing from latent variable models. To further improve on the phylogeny-only model, we combine a hierarchical Bayesian latent score framework for bipartite graphs that accounts for the number of interactions per species with the host dependence informed by phylogeny. Combining the two information sources yields significant improvement in predictive accuracy over each of the submodels alone. As many interaction networks are constructed from presence-only data, we extend the model by integrating a correction mechanism for missing interactions, which proves valuable in reducing uncertainty in unobserved interactions.

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arXiv2017

DM-PhyClus: A Bayesian phylogenetic algorithm for infectious disease transmission cluster inference

Background. Conventional phylogenetic clustering approaches rely on arbitrary cutpoints applied a posteriori to phylogenetic estimates. Although in practice, Bayesian and bootstrap-based clustering tend to lead to similar estimates, they often produce conflicting measures of confidence in clusters. The current study proposes a new Bayesian phylogenetic clustering algorithm, which we refer to as DM-PhyClus, that identifies sets of sequences resulting from quick transmission chains, thus yielding easily-interpretable clusters, without using any ad hoc distance or confidence requirement. Results. Simulations reveal that DM-PhyClus can outperform conventional clustering methods, as well as the Gap procedure, a pure distance-based algorithm, in terms of mean cluster recovery. We apply DM-PhyClus to a sample of real HIV-1 sequences, producing a set of clusters whose inference is in line with the conclusions of a previous thorough analysis. Conclusions. DM-PhyClus, by eliminating the need for cutpoints and producing sensible inference for cluster configurations, can facilitate transmission cluster detection. Future efforts to reduce incidence of infectious diseases, like HIV-1, will need reliable estimates of transmission clusters. It follows that algorithms like DM-PhyClus could serve to better inform public health strategies.

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arXiv2017

A Bayesian view of doubly robust causal inference

In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both. The latter approaches, which are based on modelling of the treatment assignment mechanism and their doubly robust extensions have been difficult to motivate using formal Bayesian arguments, in principle, for likelihood-based inferences, the treatment assignment model can play no part in inferences concerning the expected outcomes if the models are assumed to be correctly specified. On the other hand, forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness. In this paper, we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood-based arguments, and demonstrate this through simulations. As an alternative to Bayesian propensity score analysis, we propose a Bayesian posterior predictive approach for constructing doubly robust estimation procedures. Our approach appropriately decouples the outcome and treatment assignment models by incorporating the inverse treatment assignment probabilities in Bayesian causal inferences as importance sampling weights in Monte Carlo integration.

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arXiv2015

Doubly robust dose-response estimation for continuous treatments via generalized propensity score augmented outcome regression

This paper constructs a doubly robust estimator for continuous dose-response estimation. An outcome regression model is augmented with a set of inverse generalized propensity score covariates to correct for potential misspecification bias. From the augmented model we can obtain consistent estimates of mean average potential outcomes for distinct strata of the treatment. A polynomial regression is then fitted to these point estimates to derive a Taylor approximation to the continuous dose-response function. The bootstrap is used for variance estimation. Analytical results and simulations show that our approach can provide a good approximation to linear or nonlinear dose-response functions under various sources of misspecification of the outcome regression or propensity score models. Efficiency in finite samples is good relative to minimum variance consistent estimators.

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arXiv2015

Two-sample Bayesian Nonparametric Hypothesis Testing

In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2 )}\;$\stackrel{\scriptscriptstyle{iid}}{\sim}$\;F^{\scriptscriptstyle( 2)}$, with $F^{\scriptscriptstyle(1)},F^{\scriptscriptstyle(2)}$ unknown, we wish to evaluate the evidence for the null hypothesis $H_0:F^{\scriptscriptstyle(1)}\equiv F^{\scriptscriptstyle(2)}$ versus the alternative $H_1:F^{\scriptscriptstyle(1)}\neq F^{\scriptscriptstyle(2)}$. Our method is based upon a nonparametric Pólya tree prior centered either subjectively or using an empirical procedure. We show that the Pólya tree prior leads to an analytic expression for the marginal likelihood under the two hypotheses and hence an explicit measure of the probability of the null $\mathrm{Pr}(H_0|\{\mathbf {y}^{\scriptscriptstyle(1)},\mathbf{y}^{\scriptscriptstyle(2)}\}\mathbf{)}$.

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arXiv2014

Variable Selection in Causal Inference Using Penalization

In the causal adjustment setting, variable selection techniques based on either the outcome or treatment allocation model can result in the omission of confounders or the inclusion of spurious variables in the propensity score. We propose a variable selection method based on a penalized likelihood which considers the response and treatment assignment models simultaneously. The proposed method facilitates confounder selection in high-dimensional settings. We show that under some conditions our method attains the oracle property. The selected variables are used to form a double robust regression estimator of the treatment effect. Simulation results are presented and economic growth data are analyzed.

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arXiv2007

Population-Based Reversible Jump Markov Chain Monte Carlo

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of these population algorithms, under mild assumptions. This result is used to demonstrate the superiority, in terms of convergence rate, of a population transition kernel over a reversible jump sampler for a Bayesian variable selection problem. We also give an example of a population algorithm for a Bayesian multivariate mixture model with an unknown number of components. This is applied to gene expression data of 1000 data points in six dimensions and it is demonstrated that our algorithm out performs some competing Markov chain samplers.

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