Bayesian variable selection for latent class models

In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.     

Latent transition regression for mixed outcomes

Health status is a complex outcome, often characterized by multiple measures. When assessing changes in health status over time, multiple measures are typically collected longitudinally. Analytic challenges posed by these multivariate longitudinal data are further complicated when the outcomes are combinations of continuous, categorical, and count data. To address these challenges, we propose a fully Bayesian latent transition regression approach for jointly analyzing a mixture of longitudinal outcomes from any distribution. Health status is assumed to be a categorical latent variable, and the multiple outcomes are treated as surrogate measures of the latent health state, observed with error. Using this approach, both baseline latent health state prevalences and the probabilities of transitioning between the health states over time are modeled as functions of covariates. The observed outcomes are related to the latent health states through regression models that include subject-specific effects to account for residual correlation among repeated measures over time, and covariate effects to account for differential measurement of the latent health states. We illustrate our approach with data from a longitudinal study of back pain.     

A Bayesian approach for subgroup analysis

Several penalization approaches have been developed to identify homogeneous subgroups based on a regression model with subject-specific intercepts in subgroup analysis. These methods often apply concave penalty functions to pairwise comparisons of the intercepts, such that the subjects with similar intercept values are assigned to the same group, which is very similar to the procedure of the penalization approaches for variable selection. Since the Bayesian methods are commonly used in variable selection, it is worth considering the corresponding approaches to subgroup analysis in the Bayesian framework. In this paper, a Bayesian hierarchical model with appropriate prior structures is developed for the pairwise differences of intercepts based on a regression model with subject-specific intercepts, which can automatically detect and identify homogeneous subgroups. A Gibbs sampling algorithm is also provided to select the hyperparameter and estimate the intercepts and coefficients of the covariates simultaneously, which is computationally efficient for pairwise comparisons compared to the time-consuming procedures for parameter estimation of the penalization methods (e.g., alternating direction method of multiplier) in the case of large sample sizes. The effectiveness and usefulness of the proposed Bayesian method are evaluated through simulation studies and analysis of a Cleveland Heart Disease Dataset.     

What Are the Major Determinants in the Success of Smoking Cessation: Results from the Health Examinees Study

Understanding mechanisms underlying smoking-related factors should be prioritized in establishing smoking prevention and cessation policy. The aim of this study was to identify factors significantly associated with smoking initiation and/or smoking cessation as well as the most important determinants of successful smoking cessation in a developed non-Western setting. Based on multiple logistic regression models, the odds ratios (ORs) for smoking initiation and cessation were estimated among males (N = 24,490) who had participated in the Health Examinees (HEXA) study. The Cox proportional hazards regression model was used to assess the association between selected predictors of smoking cessation and the likelihood of reaching this goal. Finally, Kaplan–Meier curves were constructed to illustrate the distribution of time from age at smoking initiation to age at smoking cessation. We found that the ORs for successfully quitting smoking increased with age, married status, educational achievement, having a non-manual job, drinking cessation and disease morbidity. Those exposed to secondhand smoking showed less likelihood of quitting smoking. A continual decrease in the ORs for successfully quitting smoking was observed according to increased smoking duration, smoking dose per day and lifetime tobacco exposure (p _trend <0.001). Among the selected predictors, lifetime tobacco exposure, educational attainment, alcohol drinking status and birth cohort were the major determinants in the success of smoking cessation. Our findings suggest that lifetime tobacco exposure, educational attainment, alcohol drinking status and birth cohort can determine success in smoking cessation. Public interventions promoting a smoke-free environment are needed to reinforce discouraging the initiation of, reducing, and quitting cigarette smoking.     

Prediction of individual long-term outcomes in smoking cessation trials using frailty models

In smoking cessation clinical trials, subjects commonly receive treatment and report daily cigarette consumption over a period of several weeks. Although the outcome at the end of this period is an important indicator of treatment success, substantial uncertainty remains on how an individual's smoking behavior will evolve over time. Therefore it is of interest to predict long-term smoking cessation success based on short-term clinical observations. We develop a Bayesian method for prediction, based on a cure-mixture frailty model we proposed earlier, that describes the process of transition between abstinence and smoking. Specifically we propose a two-stage prediction algorithm that first uses importance sampling to generate subject-specific frailties from their posterior distributions conditional on the observed data, then samples predicted future smoking behavior trajectories from the estimated model parameters and sampled frailties. We apply the method to data from two randomized smoking cessation trials comparing bupropion to placebo. Comparisons of actual smoking status at one year with predictions from our model and from a variety of empirical methods suggest that our method gives excellent predictions.     

Hierarchical models for the probabilities of conception

In the last thirty years, there has been considerable interest in finding better models to fit data for probabilities of conception. An important early model was proposed by Barrett and Marshall (1969) and extended by Schwartz, MacDonald and Heuchel (1980). Recently, researchers have further extended these models by adding covariates. However, the increasingly complicated models are challenging to analyze with frequentist methods such as the EM algorithm. Bayesian models are more feasible, and the computation can be done via Markov chain Monte Carlo (MCMC). We consider a Bayesian model with an effect for protected intercourse to analyze data from the California Women's Reproductive Health Study and assess the effects of water contaminants and hormones. There are two main contributions in the paper. (1) For protected intercourse, we propose modeling the ratios of daily conception probabilities with protected intercourse to corresponding daily conception probabilities with unprotected intercourse. Due to the small sample size of our data set, we assume the ratios are the same for each day but unknown. (2) We consider Bayesian analysis under a unimodality assumption where the probabilities of conception increase before ovulation and decrease after ovulation. Gibbs sampling is used for finding the Bayesian estimates. There is some evidence that the two covariates affect fecundability.     

Monitoring futility and efficacy in phase II trials with Bayesian posterior distributions—A calibration approach

A multistage single arm phase II trial with binary endpoint is considered. Bayesian posterior probabilities are used to monitor futility in interim analyses and efficacy in the final analysis. For a beta‐binomial model, decision rules based on Bayesian posterior probabilities are converted to “traditional” decision rules in terms of number of responders among patients observed so far. Analytical derivations are given for the probability of stopping for futility and for the probability to declare efficacy. A workflow is presented on how to select the parameters specifying the Bayesian design, and the operating characteristics of the design are investigated. It is outlined how the presented approach can be transferred to statistical models other than the beta‐binomial model.     

Active life expectancy from annual follow-up data with missing responses

Active life expectancy (ALE) at a given age is defined as the expected remaining years free of disability. In this study, three categories of health status are defined according to the ability to perform activities of daily living independently. Several studies have used increment-decrement life tables to estimate ALE, without error analysis, from only a baseline and one follow-up interview. The present work conducts an individual-level covariate analysis using a three-state Markov chain model for multiple follow-up data. Using a logistic link, the model estimates single-year transition probabilities among states of health, accounting for missing interviews. This approach has the advantages of smoothing subsequent estimates and increased power by using all follow-ups. We compute ALE and total life expectancy from these estimated single-year transition probabilities. Variance estimates are computed using the delta method. Data from the Iowa Established Population for the Epidemiologic Study of the Elderly are used to test the effects of smoking on ALE on all 5-year age groups past 65 years, controlling for sex and education.     

Cessation experiences and quitting perspectives of Jordanian cancer patients who smoke

ObjectivesTo describe quitting experiences of cancer patients in a Cancer Center in Jordan; to study patients’ perceptions regarding the process of smoking cessation; and to provide insights about patients in this difficult setting in order to inform oncology practitioners with regards to how improve perceptions and skills related to quitting.MethodsAn Arabic cross-sectional questionnaire was developed to evaluate smoking and quitting behaviors in the context of cancer. The tool used as its framework the Theoretical Domains Framework to capture quitting perceptions of cancer patients who smoke, as well as social, environmental, and system-level factors that influence quitting. Eligible patients who were treated at the Center (both in-patient and out-patient settings) and who were current smokers or who smoked up to the time of cancer diagnosis were eligible. Patients were interviewed between July, 2018 and January 2020 using two versions of the questionnaire: an ‘ex-smokers’ version, and a ‘current smokers’ version.ResultsOnly a third of subjects (104/350) had been smoke-free for at least 30 days. Both smokers and ex-smokers generally felt that quitting was important, but mean importance and confidence scores (out of 10) were significantly lower in current smokers (8.2 versus 9.1, p-value=0.002; 6.4 versus 8.7, p-value=0.000). Roughly 31% of subjects believed smoking harms were exaggerated and that smoking was not an addiction. About 62% of subjects agreed quitting required skills, and 78.5% felt the steps to quit were clear, but across several listed strategies for quitting, use of these was limited (even in ex-smokers). Among current smokers, roughly a third exhibited forms of cessation fatigue.ConclusionJordanian cancer patients who smoke present with limited knowledge about the quitting process. Even when some success is observed, low rates of utilization of specific quitting strategies were observed, highlighting the need for better counseling about quitting.     

Bayesian inferences on umbrella orderings

In regression applications with categorical predictors, interest often focuses on comparing the null hypothesis of homogeneity to an ordered alternative. This article proposes a Bayesian approach for addressing this problem in the setting of normal linear and probit regression models. The regression coefficients are assigned a conditionally conjugate prior density consisting of mixtures of point masses at 0 and truncated normal densities, with a (possibly unknown) changepoint parameter included to accommodate umbrella ordering. Two strategies of prior elicitation are considered: (1) a Bayesian Bonferroni approach in which the probability of the global null hypothesis is specified and local hypotheses are considered independent; and (2) an approach which treats these probabilities as random. A single Gibbs sampling chain can be used to obtain posterior probabilities for the different hypotheses and to estimate regression coefficients and predictive quantities either by model averaging or under the preferred hypothesis. The methods are applied to data from a carcinogenesis study.     

Smoking among shift workers: More than a confounding factor

In studies on the cardiovascular disease risk among shift workers, smoking is considered to be a confounding factor. In a study of 239 shift and 157 daytime workers, it was found that shift work was prospectively related to increased cigarette consumption, indicating that smoking might be in the causative pathway; however, the number of study subjects was too low to warrant sound conclusions. Therefore, data from the Maastricht Cohort study were used to investigate the longitudinal relation between smoking and shift work in a much larger population. In this study, a total of 12,140 employees were followed for two years by means of self-administered questionnaires. The authors compared workers who normally worked during daytime hours only (74%) with those who worked other than day shifts (26%). Logistic regression analyses were performed, adjusting for demographic factors of age, gender, and educational level to evaluate the risk of starting to smoke (n=25) in the group of non-smoking workers and the risk of quitting (n=318) in the group of smoking workers. Logistic regression analysis showed a significant association between shift work and taking up smoking during the two-year follow-up (odds ratio: 1.46, p=0.03). The risk to stop smoking was somewhat lower in shift workers (odds ratio: 0.91) but not statistically significant (p=0.5). To conclude, this study showed that, independent of educational level, shift workers are more prone to start smoking. This finding might have important implications for studies on the health effects of shift workers and for possible interventions aimed at the reduction of the excess health risk among shift workers.     

Constraining prior probabilities of phylogenetic trees

Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means of the Principal Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form.     

Socioeconomic and Geographic Patterning of Smoking Behaviour in Canada: A Cross-Sectional Multilevel Analysis

Objective

To describe the socioeconomic and geographic distribution of smoking behaviour in Canada among 19,383 individuals (51% women) aged 15–85 years.

Methods

Current smoking and quitting were modeled using standard and multilevel logistic regression. Markers of socioeconomic status (SES) were education and occupation. Geography was defined by Canadian Provinces.

Results

The adjusted prevalence of current smoking was 20.2% (95% confidence interval [CI]: 18.8–21.7) and 63.7% (95% CI: 61.1–66.3) of ever smokers had quit. Current smoking decreased and quitting increased with increasing SES. The adjusted prevalence of current smoking was 32.8% (95% CI: 28.4–37.5) among the least educated compared to 11.0% (95% CI: 8.9–13.4) for the highest educated. Among the least educated, 53.0% (95% CI: 46.8–59.2) had quit, rising to 68.7% (95% CI: 62.7–74.1) for the most educated. There was substantial variation in current smoking and quitting at the provincial level; current smoking varied from 17.9% in British Columbia to 26.1% in Nova Scotia, and quitting varied from 57.4% in Nova Scotia to 67.8% in Prince Edward Island. Nationally, increasing education and occupation level were inversely associated with current smoking (odds ratio [OR] 0.64, 95% CI: 0.60–0.68 for education; OR 0.82, 95% CI: 0.77–0.87 for occupation) and positively associated with quitting (OR 1.27, 95% CI: 1.16–1.40 for education; OR 1.20, 95% CI: 1.12–1.27 for occupation). These associations were consistent in direction across provinces although with some variability in magnitude.

Conclusion

Our findings indicate that socioeconomic inequalities in smoking have persisted in Canada; current smoking was less likely and quitting was more likely among the better off groups and in certain provinces. Current prevention and cessation policies have not been successful in improving the situation for all areas and groups. Future efforts to reduce smoking uptake and increase cessation in Canada will need consideration of socioeconomic and geographic factors to be successful.     

Model misspecification and probabilistic tests of topology: evidence from empirical data sets

Probabilistic tests of topology offer a powerful means of evaluating competing phylogenetic hypotheses. The performance of the nonparametric Shimodaira-Hasegawa (SH) test, the parametric Swofford-Olsen-Waddell-Hillis (SOWH) test, and Bayesian posterior probabilities were explored for five data sets for which all the phylogenetic relationships are known with a very high degree of certainty. These results are consistent with previous simulation studies that have indicated a tendency for the SOWH test to be prone to generating Type 1 errors because of model misspecification coupled with branch length heterogeneity. These results also suggest that the SOWH test may accord overconfidence in the true topology when the null hypothesis is in fact correct. In contrast, the SH test was observed to be much more conservative, even under high substitution rates and branch length heterogeneity. For some of those data sets where the SOWH test proved misleading, the Bayesian posterior probabilities were also misleading. The results of all tests were strongly influenced by the exact substitution model assumptions. Simple models, especially those that assume rate homogeneity among sites, had a higher Type 1 error rate and were more likely to generate misleading posterior probabilities. For some of these data sets, the commonly used substitution models appear to be inadequate for estimating appropriate levels of uncertainty with the SOWH test and Bayesian methods. Reasons for the differences in statistical power between the two maximum likelihood tests are discussed and are contrasted with the Bayesian approach.     

Smoking among Shift Workers: More Than a Confounding Factor

In studies on the cardiovascular disease risk among shift workers, smoking is considered to be a confounding factor. In a study of 239 shift and 157 daytime workers, it was found that shift work was prospectively related to increased cigarette consumption, indicating that smoking might be in the causative pathway; however, the number of study subjects was too low to warrant sound conclusions. Therefore, data from the Maastricht Cohort study were used to investigate the longitudinal relation between smoking and shift work in a much larger population. In this study, a total of 12,140 employees were followed for two years by means of self‐administered questionnaires. The authors compared workers who normally worked during daytime hours only (74%) with those who worked other than day shifts (26%). Logistic regression analyses were performed, adjusting for demographic factors of age, gender, and educational level to evaluate the risk of starting to smoke (n=25) in the group of non‐smoking workers and the risk of quitting (n=318) in the group of smoking workers. Logistic regression analysis showed a significant association between shift work and taking up smoking during the two‐year follow‐up (odds ratio: 1.46, p=0.03). The risk to stop smoking was somewhat lower in shift workers (odds ratio: 0.91) but not statistically significant (p=0.5). To conclude, this study showed that, independent of educational level, shift workers are more prone to start smoking. This finding might have important implications for studies on the health effects of shift workers and for possible interventions aimed at the reduction of the excess health risk among shift workers.     

Bayesian Mapping of Lichens Growing on Trees

Suitability of trees as hosts for epiphytic lichens are studied in a forest stand of size 25 ha. Suitability is measured as occupation probabilites which are modelled using hierarchical Bayesian approach. These probabilities are useful for an ecologist. They give smoothed spatial distribution map of suitability for each of the species and can be used in detecting high‐ and low‐probability areas. In addition, suitability is explained by tree‐level covariates. Spatial dependence, which is due to unobserved spatially structured covariates, is modelled through an unobserved Markov random field. Markov chain Monte Carlo method has been applied in Bayesian computation. The extensive spatial data consist of the occurrences of eight lichen species and one bryophyte on all of the 1253 potential host trees. In addition, coordinates of the trees and several tree characteristics have been recorded. The data have been analysed for four most abundant species: Lobaria pulmonaria, Nephroma bellum, Nephroma parile and Peltigera praetextata. The tree level parameters, subject to estimation, consist of the occurrence probabilities for each tree and for each lichen species. Model validation is discussed in detail and, in addition to Bayesian validation tools, the autologistic model and case‐control design based on logistic regression have been suggested for validation of covariate effects. As a result we present suitability maps for the four lichen species. We observed, that among the observed tree covariates, the diameter at breast height (DBH) correlates with lichen occurrence. Our modelling approach has close connections to disease mapping in spatial epidemiology.     

Estimating Survival for Elusive Juvenile Pond-Breeding Salamanders

Juvenile vital rates have important effects on population dynamics for many species, but this demographic is often difficult to locate and track. As such, we frequently lack reliable estimates of juvenile survival, which are necessary for accurately assessing population stability and potential management approaches to conserve biodiversity. We estimated survival rates for elusive juveniles of 3 species, the ringed salamander (Ambystoma annulatum), spotted salamander (A. maculatum), and small-mouthed salamander (A. texanum), using 2 approaches. First, we conducted an 11-month (2016–2017) mark-recapture study within semi-natural enclosures and used Bayesian Cormack-Jolly-Seber models to estimate survival and recapture probabilities. Second, we inferred the expected annual juvenile survival rate given published vital rates for pre-metamorphic and adult ambystomatids assuming stable population growth. For all 3 species, juvenile survival probabilities were constant across recapture occasions, whereas recapture probability estimates were time-dependent. Further, survival and recapture probabilities among study species were similar. Post-study sampling revealed that the initial study period median estimate of annual survival probability (0.39) underestimated the number of salamanders known alive at 11 months. We therefore appended approximately 1 year of opportunistic data, which produced a median annual survival probability of 0.50, encompassing salamanders that we knew to have been alive. Calculation from literature values suggested a mean annual terrestrial juvenile ambystomatid survival probability of 0.49. Similar results among our approaches indicated that juvenile survival estimates for the study species were robust and likely comparable to rates in nature. These estimates can now be confidently applied to research, monitoring, and management efforts for the study species and ecologically similar taxa. Our findings indicated that similarly robust vital rate estimates for subsets of ecologically and phylogenetically similar species can provide reasonable surrogate demographic information that can be used to reveal key factors influencing population viability for data-deficient species. © 2020 The Wildlife Society.     

ednaoccupancy: An r package for multiscale occupancy modelling of environmental DNA data

In this article, we describe ednaoccupancy , an r package for fitting Bayesian, multiscale occupancy models. These models are appropriate for occupancy surveys that include three nested levels of sampling: primary sample units within a study area, secondary sample units collected from each primary unit and replicates of each secondary sample unit. This design is commonly used in occupancy surveys of environmental DNA (eDNA). ednaoccupancy allows users to specify and fit multiscale occupancy models with or without covariates, to estimate posterior summaries of occurrence and detection probabilities, and to compare different models using Bayesian model‐selection criteria. We illustrate these features by analysing two published data sets: eDNA surveys of a fungal pathogen of amphibians and eDNA surveys of an endangered fish species.     

On the influence of prior information evaluated by fully Bayesian criteria in a personalized whole-brain model of epilepsy spread

Individualized anatomical information has been used as prior knowledge in Bayesian inference paradigms of whole-brain network models. However, the actual sensitivity to such personalized information in priors is still unknown. In this study, we introduce the use of fully Bayesian information criteria and leave-one-out cross-validation technique on the subject-specific information to assess different epileptogenicity hypotheses regarding the location of pathological brain areas based on a priori knowledge from dynamical system properties. The Bayesian Virtual Epileptic Patient (BVEP) model, which relies on the fusion of structural data of individuals, a generative model of epileptiform discharges, and a self-tuning Monte Carlo sampling algorithm, is used to infer the spatial map of epileptogenicity across different brain areas. Our results indicate that measuring the out-of-sample prediction accuracy of the BVEP model with informative priors enables reliable and efficient evaluation of potential hypotheses regarding the degree of epileptogenicity across different brain regions. In contrast, while using uninformative priors, the information criteria are unable to provide strong evidence about the epileptogenicity of brain areas. We also show that the fully Bayesian criteria correctly assess different hypotheses about both structural and functional components of whole-brain models that differ across individuals. The fully Bayesian information-theory based approach used in this study suggests a patient-specific strategy for epileptogenicity hypothesis testing in generative brain network models of epilepsy to improve surgical outcomes.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.