Semiparametric Bayesian estimation of quantile function for breast cancer survival data with cured fraction

Existing cure‐rate survival models are generally not convenient for modeling and estimating the survival quantiles of a patient with specified covariate values. This paper proposes a novel class of cure‐rate model, the transform‐both‐sides cure‐rate model (TBSCRM), that can be used to make inferences about both the cure‐rate and the survival quantiles. We develop the Bayesian inference about the covariate effects on the cure‐rate as well as on the survival quantiles via Markov Chain Monte Carlo (MCMC) tools. We also show that the TBSCRM‐based Bayesian method outperforms existing cure‐rate models based methods in our simulation studies and in application to the breast cancer survival data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) database.     

Bayesian cure rate frailty models with application to a root canal therapy study

Due to natural or artificial clustering, multivariate survival data often arise in biomedical studies, for example, a dental study involving multiple teeth from each subject. A certain proportion of subjects in the population who are not expected to experience the event of interest are considered to be "cured" or insusceptible. To model correlated or clustered failure time data incorporating a surviving fraction, we propose two forms of cure rate frailty models. One model naturally introduces frailty based on biological considerations while the other is motivated from the Cox proportional hazards frailty model. We formulate the likelihood functions based on piecewise constant hazards and derive the full conditional distributions for Gibbs sampling in the Bayesian paradigm. As opposed to the Cox frailty model, the proposed methods demonstrate great potential in modeling multivariate survival data with a cure fraction. We illustrate the cure rate frailty models with a root canal therapy data set.     

A Bayesian Semiparametric Survival Model with Longitudinal Markers

Summary We consider inference for data from a clinical trial of treatments for metastatic prostate cancer. Patients joined the trial with diverse prior treatment histories. The resulting heterogeneous patient population gives rise to challenging statistical inference problems when trying to predict time to progression on different treatment arms. Inference is further complicated by the need to include a longitudinal marker as a covariate. To address these challenges, we develop a semiparametric model for joint inference of longitudinal data and an event time. The proposed approach includes the possibility of cure for some patients. The event time distribution is based on a nonparametric Pólya tree prior. For the longitudinal data we assume a mixed effects model. Incorporating a regression on covariates in a nonparametric event time model in general, and for a Pólya tree model in particular, is a challenging problem. We exploit the fact that the covariate itself is a random variable. We achieve an implementation of the desired regression by factoring the joint model for the event time and the longitudinal outcome into a marginal model for the event time and a regression of the longitudinal outcomes on the event time, i.e., we implicitly model the desired regression by modeling the reverse conditional distribution.     

Modeling disease incidence data with spatial and spatio temporal dirichlet process mixtures

Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet process prior. The Dirichlet process is centered around a multivariate normal distribution. This latter distribution arises from a log-Gaussian process model that provides a latent incidence rate surface, followed by block averaging to the areal units determined by the regions in the study. With regard to the resulting posterior predictive inference, the modeling approach is shown to be equivalent to an approach based on block averaging of a spatial Dirichlet process to obtain a prior probability model for the finite dimensional distribution of the spatial random effects. We introduce a dynamic formulation for the spatial random effects to extend the model to spatio-temporal settings. Posterior inference is implemented through Gibbs sampling. We illustrate the methodology with simulated data as well as with a data set on lung cancer incidences for all 88 counties in the state of Ohio over an observation period of 21 years.     

Maximum likelihood estimation in random effects cure rate models with nonignorable missing covariates

We introduce a method of parameter estimation for a random effects cure rate model. We also propose a methodology that allows us to account for nonignorable missing covariates in this class of models. The proposed method corrects for possible bias introduced by complete case analysis when missing data are not missing completely at random and is motivated by data from a pair of melanoma studies conducted by the Eastern Cooperative Oncology Group in which clustering by cohort or time of study entry was suspected. In addition, these models allow estimation of cure rates, which is desirable when we do not wish to assume that all subjects remain at risk of death or relapse from disease after sufficient follow-up. We develop an EM algorithm for the model and provide an efficient Gibbs sampling scheme for carrying out the E-step of the algorithm.     

Exploring the drivers of wildlife population dynamics from insufficient data by Bayesian model averaging

A long-standing interest in ecology and wildlife management is to find drivers of wildlife population dynamics because it is crucial for implementing the effective wildlife management. Recent studies have demonstrated the usefulness of state-space modeling for this purpose, but we often confront the lack of the necessary time-series data. This is particularly common in wildlife management because of limited funds or early stage of data collection. In this study, we proposed a Bayesian model averaging technique in a state-space modeling framework for identifying the drivers of wildlife population dynamics from limited data. To exemplify the utility of Bayesian model averaging for wildlife management, we illustrate here the population dynamics of wild boars Sus scrofa in Chiba prefecture, central Japan. Despite the fact that our data are limited in both temporal and spatial resolution, Bayesian model averaging revealed the potential influence of bamboo forests and abandoned agricultural fields on wild boar population dynamics, and largely enhanced model predictability compared to the full model. Although Bayesian model averaging is not commonly used in ecology and wildlife management, our case study demonstrated that it may help to find influential drivers of wildlife population dynamics and develop a better management plan even from limited time-series data.     

Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates

We present Bayesian hierarchical spatial models for spatially correlated small-area health service outcome and utilization rates, with a particular emphasis on the estimation of both measured and unmeasured or unknown covariate effects. This Bayesian hierarchical model framework enables simultaneous modeling of fixed covariate effects and random residual effects. The random effects are modeled via Bayesian prior specifications reflecting spatial heterogeneity globally and relative homogeneity among neighboring areas. The model inference is implemented using Markov chain Monte Carlo methods. Specifically, a hybrid Markov chain Monte Carlo algorithm (Neal, 1995, Bayesian Learning for Neural Networks; Gustafson, MacNab, and Wen, 2003, Statistics and Computing, to appear) is used for posterior sampling of the random effects. To illustrate relevant problems, methods, and techniques, we present an analysis of regional variation in intraventricular hemorrhage incidence rates among neonatal intensive care unit patients across Canada.     

Bayesian Semiparametric Models for Survival Data with a Cure Fraction

We propose methods for Bayesian inference for a new class of semiparametric survival models with a cure fraction. Specifically, we propose a semiparametric cure rate model with a smoothing parameter that controls the degree of parametricity in the right tail of the survival distribution. We show that such a parameter is crucial for these kinds of models and can have an impact on the posterior estimates. Several novel properties of the proposed model are derived. In addition, we propose a class of improper noninformative priors based on this model and examine the properties of the implied posterior. Also, a class of informative priors based on historical data is proposed and its theoretical properties are investigated. A case study involving a melanoma clinical trial is discussed in detail to demonstrate the proposed methodology.     

Bayesian Inference for Smoking Cessation with a Latent Cure State

Summary .  We present a Bayesian approach to modeling dynamic smoking addiction behavior processes when cure is not directly observed due to censoring. Subject-specific probabilities model the stochastic transitions among three behavioral states: smoking, transient quitting, and permanent quitting (absorbent state). A multivariate normal distribution for random effects is used to account for the potential correlation among the subject-specific transition probabilities. Inference is conducted using a Bayesian framework via Markov chain Monte Carlo simulation. This framework provides various measures of subject-specific predictions, which are useful for policy-making, intervention development, and evaluation. Simulations are used to validate our Bayesian methodology and assess its frequentist properties. Our methods are motivated by, and applied to, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large (29,133 individuals) longitudinal cohort study of smokers from Finland.     

A Bayesian approach for the analysis of panel-count data with dependent termination

We consider modeling and Bayesian analysis for panel-count data when the termination time for each subject may depend on its history of the recurrent events. We propose a fully specified semiparametric model for the joint distribution of the recurrent events and the termination time. For this model, we provide a natural motivation, derive several novel properties, and develop a Bayesian analysis based on a Markov chain Monte Carlo algorithm. Comparisons are made to other existing models and methods for panel-count data. We demonstrate the usefulness of our new models and methodologies through the reanalysis of a data set from a clinical trial.     

Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.     

Bayesian Calibration of a Stochastic Kinetic Computer Model Using Multiple Data Sources

Summary .  In this article, we describe a Bayesian approach to the calibration of a stochastic computer model of chemical kinetics. As with many applications in the biological sciences, the data available to calibrate the model come from different sources. Furthermore, these data appear to provide somewhat conflicting information about the model parameters. We describe a modeling framework that allows us to synthesize this conflicting information and arrive at a consensus inference. In particular, we show how random effects can be incorporated into the model to account for between-individual heterogeneity that may be the source of the apparent conflict.     

A note on MAR, identifying restrictions, model comparison, and sensitivity analysis in pattern mixture models with and without covariates for incomplete data

Summary Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions is one approach to mixture model identification ( Little, 1995 , Journal of the American Statistical Association 90 , 1112–1121; Little and Wang, 1996 , Biometrics 52 , 98–111; Thijs et al., 2002 , Biostatistics 3 , 245–265; Kenward, Molenberghs, and Thijs, 2003 , Biometrika 90 , 53–71; Daniels and Hogan, 2008 , in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis) and is a natural starting point for missing not at random sensitivity analysis ( Thijs et al., 2002 , Biostatistics 3 , 245–265; Daniels and Hogan, 2008 , in Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis). However, when the pattern specific models are multivariate normal, identifying restrictions corresponding to missing at random (MAR) may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g., baseline covariates with time‐invariant coefficients). In this article, we explore conditions necessary for identifying restrictions that result in MAR to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. In addition, we propose alternative modeling and sensitivity analysis strategies under a less restrictive assumption for the distribution of the observed response data. We adopt the deviance information criterion for model comparison and perform a simulation study to evaluate the performances of the different modeling approaches. We also apply the methods to a longitudinal clinical trial. Problems caused by baseline covariates with time‐invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.     

Bayesian nonparametric centered random effects models with variable selection

In a linear mixed effects model, it is common practice to assume that the random effects follow a parametric distribution such as a normal distribution with mean zero. However, in the case of variable selection, substantial violation of the normality assumption can potentially impact the subset selection and result in poor interpretation and even incorrect results. In nonparametric random effects models, the random effects generally have a nonzero mean, which causes an identifiability problem for the fixed effects that are paired with the random effects. In this article, we focus on a Bayesian method for variable selection. We characterize the subject‐specific random effects nonparametrically with a Dirichlet process and resolve the bias simultaneously. In particular, we propose flexible modeling of the conditional distribution of the random effects with changes across the predictor space. The approach is implemented using a stochastic search Gibbs sampler to identify subsets of fixed effects and random effects to be included in the model. Simulations are provided to evaluate and compare the performance of our approach to the existing ones. We then apply the new approach to a real data example, cross‐country and interlaboratory rodent uterotrophic bioassay.     

Bayesian back-calculation and nowcasting for line list data during the COVID-19 pandemic

Surveillance is critical to mounting an appropriate and effective response to pandemics. However, aggregated case report data suffers from reporting delays and can lead to misleading inferences. Different from aggregated case report data, line list data is a table contains individual features such as dates of symptom onset and reporting for each reported case and a good source for modeling delays. Current methods for modeling reporting delays are not particularly appropriate for line list data, which typically has missing symptom onset dates that are non-ignorable for modeling reporting delays. In this paper, we develop a Bayesian approach that dynamically integrates imputation and estimation for line list data. Specifically, this Bayesian approach can accurately estimate the epidemic curve and instantaneous reproduction numbers, even with most symptom onset dates missing. The Bayesian approach is also robust to deviations from model assumptions, such as changes in the reporting delay distribution or incorrect specification of the maximum reporting delay. We apply the Bayesian approach to COVID-19 line list data in Massachusetts and find the reproduction number estimates correspond more closely to the control measures than the estimates based on the reported curve.     

Bayesian analysis of mass spectrometry proteomic data using wavelet-based functional mixed models

Summary .   In this article, we apply the recently developed Bayesian wavelet-based functional mixed model methodology to analyze MALDI-TOF mass spectrometry proteomic data. By modeling mass spectra as functions, this approach avoids reliance on peak detection methods. The flexibility of this framework in modeling nonparametric fixed and random effect functions enables it to model the effects of multiple factors simultaneously, allowing one to perform inference on multiple factors of interest using the same model fit, while adjusting for clinical or experimental covariates that may affect both the intensities and locations of peaks in the spectra. For example, this provides a straightforward way to account for systematic block and batch effects that characterize these data. From the model output, we identify spectral regions that are differentially expressed across experimental conditions, in a way that takes both statistical and clinical significance into account and controls the Bayesian false discovery rate to a prespecified level. We apply this method to two cancer studies.     

Non‐random correlation of species dynamics in tropical tree communities

The importance of environmental stochasticity for tropical tree dynamics has been recently stressed by several studies. This has spurred the development of a ‘time‐averaged neutral model’ of community dynamics by Kalyuzhny and colleagues that extends the neutral model by incorporating environmental stochasticity. We here show that this framework can be used to assess the presence of non‐random correlations between species dynamics. Indeed, the time‐averaged neutral model makes the simplifying assumption that species responses to environmental variation are uncorrelated. We therefore propose to use this model as a null hypothesis against which observed community dynamics can be compared. This study makes five contributions. First, we describe a novel time‐averaged neutral model of community dynamics that is close to, but more flexible than the one previously proposed by Kalyuzhny and colleagues. Second, we develop an inference method based on approximate Bayesian computation (ABC) and demonstrate the identifiability of the model parameters from community time series data. Third, we develop a test of the significance of environmental stochasticity, and a method to quantify its contribution to population variance. Fourth, we develop a test of non‐random correlation between species dynamics. Fifth, we apply these developments to three datasets of tropical tree dynamics. We evidence both a strong contribution of environmental stochasticity to population variance in the three datasets, and a non‐random correlation of species dynamics in one of them. We finally discuss the implications of these results for the modelling of tropical tree community dynamics.     

Structure-based phylogeny of polyene macrolide antibiotic glycosyltransferases

Antibiotic glycosyltransferases (AGts) attach unusual deoxy-sugars to aglycons so antibiotics can exert function. It has been reported that polyene macrolide (PEM) AGts have different evolutionary origin when compared with other polyketide AGts, and our previous analysis have suggested that they could be results of horizontal gene transfer (HGT) from eukaryotes. In this paper, we compared the structures of PEM AGts with structures of eukaryotes and other AGts, and then built models of the representative PEM AGts and GT-1 glycosyltransferases. We also constructed the Neighbor-Joining (NJ) trees based on the normalized Root Mean Square (RMS) distance, the Bayesian tree guided by structural alignments, and carried out analysis on several key conserved residues in PEM AGts. The NJ tree showed a close relationship between PEM AGts and eukaryotic glycosyltransferases, and Bayesian tree further supported their affinity with UDP-glucuronosyltransferases (UGTs). Analysis on key conserved residues showed that PEM AGts may have similar interaction mechanism such as in the formation of hydrogen bonds as eukaryotic glycosyltransferases. Using structure-based phylogenetic approaches, this study further supported that PEM AGts were the result of HGT between prokaryotes and eukaryotes.     

The performance of random coefficient regression in accounting for residual confounding

Greenland (2000, Biometrics 56, 915-921) describes the use of random coefficient regression to adjust for residual confounding in a particular setting. We examine this setting further, giving theoretical and empirical results concerning the frequentist and Bayesian performance of random coefficient regression. Particularly, we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding. This devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model. The approach described by Gustafson (2005, Statistical Science 20, 111-140) is used to quantify the performance of a Bayesian estimator arising from a nonidentified model. From both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints. In terms of point-estimator bias this superiority arises when the extent of residual confounding is substantial, but the advantage is much broader in terms of interval estimation. The benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality, for the standard identifying constraints are equivalent to priors that typically correspond much worse.     

Recommendations for estimating mark rate of cetaceans in photo-ID research: A critique of field sampling protocols and variance estimation

Mark rate, or the proportion of the population with unique, identifiable marks, must be determined in order to estimate population size from photographic identification data. In this study we address field sampling protocols and estimation methods for robust estimation of mark rate and its uncertainty in cetacean populations. We present two alternatives for estimating the variance of mark rate: (1) a variance estimator for clusters of unequal sizes (SRCS) and (2) a hierarchical Bayesian model (SRCS-Bayes), and compare them to the simple random sampling (SRS) variance estimator. We tested these variance estimators using a simulation to see how they perform at varying mark rates, number of groups sampled, photos per group, and mean group sizes. The hierarchical Bayesian model outperformed the frequentist variance estimators, with the true mark rate of the population held in its 95% HDI 91.9% of the time (compared with coverage of 79% for the SRS method and 76.3% for the SRCS-Cochran method). The simulation results suggest that, ideally, mark rate and its precision should be quantified using hierarchical Bayesian modeling, and researchers should attempt to sample as many unique groups as possible to improve accuracy and precision.