Semiparametric Bayesian inference for optimal dynamic treatment regimes via dynamic marginal structural models.

Considerable statistical work done on dynamic treatment regimes (DTRs) is in the frequentist paradigm, but Bayesian methods may have much to offer in this setting as they allow for the appropriate representation and propagation of uncertainty, including at the individual level. In this work, we extend the use of recently developed Bayesian methods for Marginal Structural Models to arrive at inference of DTRs. We do this (i) by linking the observational world with a world in which all patients are randomized to a DTR, thereby allowing for causal inference and then (ii) by maximizing a posterior predictive utility, where the posterior distribution has been obtained from nonparametric prior assumptions on the observational world data-generating process. Our approach relies on Bayesian semiparametric inference, where inference about a finite-dimensional parameter is made all while working within an infinite-dimensional space of distributions. We further study Bayesian inference of DTRs in the double robust setting by using posterior predictive inference and the nonparametric Bayesian bootstrap. The proposed methods allow for uncertainty quantification at the individual level, thereby enabling personalized decision-making. We examine the performance of these methods via simulation and demonstrate their utility by exploring whether to adapt HIV therapy to a measure of patients' liver health, in order to minimize liver scarring.

Bayesian sample size calculations for comparing two strategies in SMART studies.

In the management of most chronic conditions characterized by the lack of universally effective treatments, adaptive treatment strategies (ATSs) have grown in popularity as they offer a more individualized approach. As a result, 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, sample size and design considerations have generally been carried out in frequentist settings. However, standard frequentist formulae require assumptions on interim response rates and variance components. Misspecifying these can lead to incorrect sample size calculations and correspondingly inadequate levels of power. 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 frequentist 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 MDD. 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 on cardiovascular disease patients using data from its pilot study conducted in two Canadian provinces.

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.

The evolution of SARS-CoV-2 seroprevalence in Canada: a time-series study, 2020-2023.

BACKGROUND: During the first year of the COVID-19 pandemic, the proportion of reported cases of COVID-19 among Canadians was under 6%. Although high vaccine coverage was achieved in Canada by fall 2021, the Omicron variant caused unprecedented numbers of infections, overwhelming testing capacity and making it difficult to quantify the trajectory of population immunity. METHODS: Using a time-series approach and data from more than 900 000 samples collected by 7 research studies collaborating with the COVID-19 Immunity Task Force (CITF), we estimated trends in SARS-CoV-2 seroprevalence owing to infection and vaccination for the Canadian population over 3 intervals: prevaccination (March to November 2020), vaccine roll-out (December 2020 to November 2021), and the arrival of the Omicron variant (December 2021 to March 2023). We also estimated seroprevalence by geographical region and age. RESULTS: By November 2021, 9.0% (95% credible interval [CrI] 7.3%-11%) of people in Canada had humoral immunity to SARS-CoV-2 from an infection. Seroprevalence increased rapidly after the arrival of the Omicron variant - by Mar. 15, 2023, 76% (95% CrI 74%-79%) of the population had detectable antibodies from infections. The rapid rise in infection-induced antibodies occurred across Canada and was most pronounced in younger age groups and in the Western provinces: Manitoba, Saskatchewan, Alberta and British Columbia. INTERPRETATION: Data up to March 2023 indicate that most people in Canada had acquired antibodies against SARS-CoV-2 through natural infection and vaccination. However, given variations in population seropositivity by age and geography, the potential for waning antibody levels, and new variants that may escape immunity, public health policy and clinical decisions should be tailored to local patterns of population immunity.

Survival Modelling For Data From Combined Cohorts: Opening the Door to Meta Survival Analyses and Survival Analysis using Electronic Health Records.

Non-parametric estimation of the survival function using observed failure time data depends on the underlying data generating mechanism, including the ways in which the data may be censored and/or truncated. For data arising from a single source or collected from a single cohort, a wide range of estimators have been proposed and compared in the literature. Often, however, it may be possible, and indeed advantageous, to combine and then analyze survival data that have been collected under different study designs. We review non-parametric survival analysis for data obtained by combining the most common types of cohort. We have two main goals: (i) To clarify the differences in the model assumptions, and (ii) to provide a single lens through which some of the proposed estimators may be viewed. Our discussion is relevant to the meta analysis of survival data obtained from different types of study, and to the modern era of electronic health records.

Predicting missing links in global host-parasite networks.

1. Parasites that infect multiple species cause major health burdens globally, but for many, the full suite of susceptible hosts is unknown. Predicting undocumented host-parasite associations will help expand knowledge of parasite host specificities, promote the development of theory in disease ecology and evolution, and support surveillance of multi-host infectious diseases. The analysis of global species interaction networks allows for leveraging of information across taxa, but link prediction at this scale is often limited by extreme network sparsity and lack of comparable trait data across species. 2. Here we use recently developed methods to predict missing links in global mammal-parasite networks using readily available data: network properties and evolutionary relationships among hosts. We demonstrate how these link predictions can efficiently guide the collection of species interaction data and increase the completeness of global species interaction networks. 3. We amalgamate a global mammal host-parasite interaction network (>29,000 interactions) and apply a hierarchical Bayesian approach for link prediction that leverages information on network structure and scaled phylogenetic distances among hosts. We use these predictions to guide targeted literature searches of the most likely yet undocumented interactions, and identify empirical evidence supporting many of the top 'missing' links. 4. We find that link prediction in global host-parasite networks can successfully predict parasites of humans, domesticated animals and endangered wildlife, representing a combination of published interactions missing from existing global databases, and potential but currently undocumented associations. 5. Our study provides further insight into the use of phylogenies for predicting host-parasite interactions, and highlights the utility of iterated prediction and targeted search to efficiently guide the collection of information on host-parasite interactions. These data are critical for understanding the evolution of host specificity, and may be used to support disease surveillance through a process of predicting missing links, and targeting research towards the most likely undocumented interactions.

Adaptive treatment strategies for chronic conditions: shared-parameter G-estimation with an application to rheumatoid arthritis.

Most estimation algorithms for adaptive treatment strategies assume that treatment rules at each decision point are independent from one another in the sense that they do not possess any common parameters. This is often unrealistic, as the same decisions may be made repeatedly over time. Sharing treatment-decision parameters across decision points offers several advantages, including estimation of fewer parameters and the clinical ease of a single, time-invariant decision to implement. We propose a new computational approach to estimation of shared-parameter G-estimation, which is efficient and shares the double robustness of the "unshared" sequential G-estimation. We use this approach to analyze data from the Scottish Early Rheumatoid Arthritis (SERA) Inception Cohort.

Bayesian latent multi-state modeling for nonequidistant longitudinal electronic health records.

Large amounts of longitudinal health records are now available for dynamic monitoring of the underlying processes governing the observations. However, the health status progression across time is not typically observed directly: records are observed only when a subject interacts with the system, yielding irregular and often sparse observations. This suggests that the observed trajectories should be modeled via a latent continuous-time process potentially as a function of time-varying covariates. We develop a continuous-time hidden Markov model to analyze longitudinal data accounting for irregular visits and different types of observations. By employing a specific missing data likelihood formulation, we can construct an efficient computational algorithm. We focus on Bayesian inference for the model: this is facilitated by an expectation-maximization algorithm and Markov chain Monte Carlo methods. Simulation studies demonstrate that these approaches can be implemented efficiently for large data sets in a fully Bayesian setting. We apply this model to a real cohort where patients suffer from chronic obstructive pulmonary disease with the outcome being the number of drugs taken, using health care utilization indicators and patient characteristics as covariates.

Model selection for G-estimation of dynamic treatment regimes.

Dynamic treatment regimes (DTRs) aim to formalize personalized medicine by tailoring treatment decisions to individual patient characteristics. G-estimation for DTR identification targets the parameters of a structural nested mean model, known as the blip function, from which the optimal DTR is derived. Despite its potential, G-estimation has not seen widespread use in the literature, owing in part to its often complex presentation and implementation, but also due to the necessity for correct specification of the blip. Using a quadratic approximation approach inspired by iteratively reweighted least squares, we derive a quasi-likelihood function for G-estimation within the DTR framework, and show how it can be used to form an information criterion for blip model selection. We outline the theoretical properties of this model selection criterion and demonstrate its application in a variety of simulation studies as well as in data from the Sequenced Treatment Alternatives to Relieve Depression study.

A hidden markov model for identifying differentially methylated sites in bisulfite sequencing data.

DNA methylation studies have enabled researchers to understand methylation patterns and their regulatory roles in biological processes and disease. However, only a limited number of statistical approaches have been developed to provide formal quantitative analysis. Specifically, a few available methods do identify differentially methylated CpG (DMC) sites or regions (DMR), but they suffer from limitations that arise mostly due to challenges inherent in bisulfite sequencing data. These challenges include: (1) that read-depths vary considerably among genomic positions and are often low; (2) both methylation and autocorrelation patterns change as regions change; and (3) CpG sites are distributed unevenly. Furthermore, there are several methodological limitations: almost none of these tools is capable of comparing multiple groups and/or working with missing values, and only a few allow continuous or multiple covariates. The last of these is of great interest among researchers, as the goal is often to find which regions of the genome are associated with several exposures and traits. To tackle these issues, we have developed an efficient DMC identification method based on Hidden Markov Models (HMMs) called "DMCHMM" which is a three-step approach (model selection, prediction, testing) aiming to address the aforementioned drawbacks. Our proposed method is different from other HMM methods since it profiles methylation of each sample separately, hence exploiting inter-CpG autocorrelation within samples, and it is more flexible than previous approaches by allowing multiple hidden states. Using simulations, we show that DMCHMM has the best performance among several competing methods. An analysis of cell-separated blood methylation profiles is also provided.

Should a propensity score model be super? The utility of ensemble procedures for causal adjustment.

In investigations of the effect of treatment on outcome, the propensity score is a tool to eliminate imbalance in the distribution of confounding variables between treatment groups. Recent work has suggested that Super Learner, an ensemble method, outperforms logistic regression in nonlinear settings; however, experience with real-data analyses tends to show overfitting of the propensity score model using this approach. We investigated a wide range of simulated settings of varying complexities including simulations based on real data to compare the performances of logistic regression, generalized boosted models, and Super Learner in providing balance and for estimating the average treatment effect via propensity score regression, propensity score matching, and inverse probability of treatment weighting. We found that Super Learner and logistic regression are comparable in terms of covariate balance, bias, and mean squared error (MSE); however, Super Learner is computationally very expensive thus leaving no clear advantage to the more complex approach. Propensity scores estimated by generalized boosted models were inferior to the other two estimation approaches. We also found that propensity score regression adjustment was superior to either matching or inverse weighting when the form of the dependence on the treatment on the outcome is correctly specified.

A cure-rate model for Q-learning: Estimating an adaptive immunosuppressant treatment strategy for allogeneic hematopoietic cell transplant patients.

Cancers treated by transplantation are often curative, but immunosuppressive drugs are required to prevent and (if needed) to treat graft-versus-host disease. Estimation of an optimal adaptive treatment strategy when treatment at either one of two stages of treatment may lead to a cure has not yet been considered. Using a sample of 9563 patients treated for blood and bone cancers by allogeneic hematopoietic cell transplantation drawn from the Center for Blood and Marrow Transplant Research database, we provide a case study of a novel approach to Q-learning for survival data in the presence of a potentially curative treatment, and demonstrate the results differ substantially from an implementation of Q-learning that fails to account for the cure-rate.

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 (Dirichlet-Multinomial Phylogenetic Clustering), 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.

Reward ignorant modeling of dynamic treatment regimes.

Personalized medicine optimizes patient outcome by tailoring treatments to patient-level characteristics. This approach is formalized by dynamic treatment regimes (DTRs): decision rules that take patient information as input and output recommended treatment decisions. The DTR literature has seen the development of increasingly sophisticated causal inference techniques that attempt to address the limitations of our typically observational datasets. Often overlooked, however, is that in practice most patients may be expected to receive optimal or near-optimal treatment, and so the outcome used as part of a typical DTR analysis may provide limited information. In light of this, we propose considering a more standard analysis: ignore the outcome and elicit an optimal DTR by modeling the observed treatment as a function of relevant covariates. This offers a far simpler analysis and, in some settings, improved optimal treatment identification. To distinguish this approach from more traditional DTR analyses, we term it reward ignorant modeling, and also introduce the concept of multimethod analysis, whereby different analysis methods are used in settings with multiple treatment decisions. We demonstrate this concept through a variety of simulation studies, and through analysis of data from the International Warfarin Pharmacogenetics Consortium, which also serve as motivation for this work.

Model assessment in dynamic treatment regimen estimation via double robustness.

Dynamic treatment regimens (DTRs) recommend treatments based on evolving subject-level data. The optimal DTR is that which maximizes expected patient outcome and as such its identification is of primary interest in the personalized medicine setting. When analyzing data from observational studies using semi-parametric approaches, there are two primary components which can be modeled: the expected level of treatment and the expected outcome for a patient given their other covariates. In an effort to offer greater flexibility, the so-called doubly robust methods have been developed which offer consistent parameter estimators as long as at least one of these two models is correctly specified. However, in practice it can be difficult to be confident if this is the case. Using G-estimation as our example method, we demonstrate how the property of double robustness itself can be used to provide evidence that a specified model is or is not correct. This approach is illustrated through simulation studies as well as data from the Multicenter AIDS Cohort Study.

Optimal individualized dosing strategies: A pharmacologic approach to developing dynamic treatment regimens for continuous-valued treatments.

There have been considerable advances in the methodology for estimating dynamic treatment regimens, and for the design of sequential trials that can be used to collect unconfounded data to inform such regimens. However, relatively little attention has been paid to how such methodology could be used to advance understanding of optimal treatment strategies in a continuous dose setting, even though it is often the case that considerable patient heterogeneity in drug response along with a narrow therapeutic window may necessitate the tailoring of dosing over time. Such is the case with warfarin, a common oral anticoagulant. We propose novel, realistic simulation models based on pharmacokinetic-pharmacodynamic properties of the drug that can be used to evaluate potentially optimal dosing strategies. Our results suggest that this methodology can lead to a dosing strategy that performs well both within and across populations with different pharmacokinetic characteristics, and may assist in the design of randomized trials by narrowing the list of potential dosing strategies to those which are most promising.

The Gap Procedure: for the identification of phylogenetic clusters in HIV-1 sequence data.

BACKGROUND: In the context of infectious disease, sequence clustering can be used to provide important insights into the dynamics of transmission. Cluster analysis is usually performed using a phylogenetic approach whereby clusters are assigned on the basis of sufficiently small genetic distances and high bootstrap support (or posterior probabilities). The computational burden involved in this phylogenetic threshold approach is a major drawback, especially when a large number of sequences are being considered. In addition, this method requires a skilled user to specify the appropriate threshold values which may vary widely depending on the application. RESULTS: This paper presents the Gap Procedure, a distance-based clustering algorithm for the classification of DNA sequences sampled from individuals infected with the human immunodeficiency virus type 1 (HIV-1). Our heuristic algorithm bypasses the need for phylogenetic reconstruction, thereby supporting the quick analysis of large genetic data sets. Moreover, this fully automated procedure relies on data-driven gaps in sorted pairwise distances to infer clusters, thus no user-specified threshold values are required. The clustering results obtained by the Gap Procedure on both real and simulated data, closely agree with those found using the threshold approach, while only requiring a fraction of the time to complete the analysis. CONCLUSIONS: Apart from the dramatic gains in computational time, the Gap Procedure is highly effective in finding distinct groups of genetically similar sequences and obviates the need for subjective user-specified values. The clusters of genetically similar sequences returned by this procedure can be used to detect patterns in HIV-1 transmission and thereby aid in the prevention, treatment and containment of the disease.

On Bayesian estimation of marginal structural models.

The purpose of inverse probability of treatment (IPT) weighting in estimation of marginal treatment effects is to construct a pseudo-population without imbalances in measured covariates, thus removing the effects of confounding and informative censoring when performing inference. In this article, we formalize the notion of such a pseudo-population as a data generating mechanism with particular characteristics, and show that this leads to a natural Bayesian interpretation of IPT weighted estimation. Using this interpretation, we are able to propose the first fully Bayesian procedure for estimating parameters of marginal structural models using an IPT weighting. Our approach suggests that the weights should be derived from the posterior predictive treatment assignment and censoring probabilities, answering the question of whether and how the uncertainty in the estimation of the weights should be incorporated in Bayesian inference of marginal treatment effects. The proposed approach is compared to existing methods in simulated data, and applied to an analysis of the Canadian Co-infection Cohort.

Predictive Bayesian inference and dynamic treatment regimes.

While optimal dynamic treatment regimes (DTRs) can be estimated without specification of a predictive model, a model-based approach, combined with dynamic programming and Monte Carlo integration, enables direct probabilistic comparisons between the outcomes under the optimal DTR and alternative (dynamic or static) treatment regimes. The Bayesian predictive approach also circumvents problems related to frequentist estimators under the nonregular estimation problem. However, the model-based approach is susceptible to misspecification, in particular of the "null-paradox" type, which is due to the model parameters not having a direct causal interpretation in the presence of latent individual-level characteristics. Because it is reasonable to insist on correct inferences under the null of no difference between the alternative treatment regimes, we discuss how to achieve this through a "null-robust" reparametrization of the problem in a longitudinal setting. Since we argue that causal inference can be entirely understood as posterior predictive inference in a hypothetical population without covariate imbalances, we also discuss how controlling for confounding through inverse probability of treatment weighting can be justified and incorporated in the Bayesian setting.