Nonparametric predictive inference for discrete data via Metropolis-adjusted Dirichlet sequences

BackgroundThe Bayesian approach is now widely recognised as a proper framework for analysing risk in health care. However, the traditional text-book Bayesian approach is in many cases difficult to implement, as it is based on abstract concepts and modelling.MethodsThe essential points of the risk analyses conducted according to the predictive Bayesian approach are identification of observable quantities, prediction and uncertainty assessments of these quantities, using all the relevant information. The risk analysis summarizes the knowledge and lack of knowledge concerning critical operations and other activities, and give in this way a basis for making rational decisions.ResultsIt is shown that Bayesian risk analysis can be significantly simplified and made more accessible compared to the traditional text-book Bayesian approach by focusing on predictions of observable quantities and performing uncertainty assessments of these quantities using subjective probabilities.ConclusionThe predictive Bayesian approach provides a framework for ensuring quality of risk analysis. The approach acknowledges that risk cannot be adequately described and evaluated simply by reference to summarising probabilities. Risk is defined by the combination of possible consequences and associated uncertainties.

Pseudoreplication occurs when the number of measured values or data points exceeds the number of genuine replicates, and when the statistical analysis treats all data points as independent and thus fully contributing to the result. By artificially inflating the sample size, pseudoreplication contributes to irreproducibility, and it is a pervasive problem in biological research. In some fields, more than half of published experiments have pseudoreplication – making it one of the biggest threats to inferential validity. Researchers may be reluctant to use appropriate statistical methods if their hypothesis is about the pseudoreplicates and not the genuine replicates; for example, when an intervention is applied to pregnant female rodents (genuine replicates) but the hypothesis is about the effect on the multiple offspring (pseudoreplicates). We propose using a Bayesian predictive approach, which enables researchers to make valid inferences about biological entities of interest, even if they are pseudoreplicates, and show the benefits of this approach using two in vivo data sets.

Clustering is widely used in biomedical research for meaningful subgroup identification. However, most existing clustering algorithms do not account for the statistical uncertainty of the resulting clusters and consequently may generate spurious clusters due to natural sampling variation. To address this problem, the Statistical Significance of Clustering (SigClust) method was developed to evaluate the significance of clusters in high-dimensional data. While SigClust has been successful in assessing clustering significance for continuous data, it is not specifically designed for discrete data, such as count data in genomics. Moreover, SigClust and its variations can suffer from reduced statistical power when applied to non-Gaussian high-dimensional data. To overcome these limitations, we propose SigClust-DEV, a method designed to evaluate the significance of clusters in count data. Through extensive simulations, we compare SigClust-DEV against other existing SigClust approaches across various count distributions and demonstrate its superior performance. Furthermore, we apply our proposed SigClust-DEV to Hydra single-cell RNA sequencing (scRNA) data and electronic health records (EHRs) of cancer patients to identify meaningful latent cell types and patient subgroups, respectively.

We address the problem of the curtailment or continuation of an experiment or trial at some interim point where say N observations are in hand and at least S > N observations had originally been scheduled for a decision. A Bayesian predictive approach is used to determine the probability that if one continued the trial with a further sample of size M where N +M ≥S, one would come to a particular decision regarding a parameter or a future observable. This point of view can also be applied to significance tests if one is willing to admit the calculation as a subjective assessment.

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.

In studies of wild animals, one frequently encounters both count and mark-recapture-recovery data. Here, we consider an integrated Bayesian analysis of ring¿recovery and count data using a state-space model. We then impose a Leslie-matrix-based model on the true population counts describing the natural birth-death and age transition processes. We focus upon the analysis of both count and recovery data collected on British lapwings (Vanellus vanellus) combined with records of the number of frost days each winter. We demonstrate how the combined analysis of these data provides a more robust inferential framework and discuss how the Bayesian approach using MCMC allows us to remove the potentially restrictive normality assumptions commonly assumed for analyses of this sort. It is shown how WinBUGS may be used to perform the Bayesian analysis. WinBUGS code is provided and its performance is critically discussed.

Microorganisms play critical roles in human health and disease. They live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical covariates, such as treatment effects, joint (multivariate) statistical models are preferred. Multivariate models allow one to estimate and exploit complex interdependencies among multiple taxa, yielding more powerful tests of exposure or treatment effects than application of taxon-specific univariate analyses. Analysis of microbial count data also requires special attention because data commonly exhibit zero inflation, i.e., more zeros than expected from a standard count distribution. To meet these needs, we developed a Bayesian variable selection model for multivariate count data with excess zeros that incorporates information on the covariance structure of the outcomes (counts for multiple taxa), while estimating associations with the mean levels of these outcomes. Though there has been much work on zero-inflated models for longitudinal data, little attention has been given to high-dimensional multivariate zero-inflated data modeled via a general correlation structure. Through simulation, we compared performance of the proposed method to that of existing univariate approaches, for both the binary ("excess zero") and count parts of the model. When outcomes were correlated the proposed variable selection method maintained type I error while boosting the ability to identify true associations in the binary component of the model. For the count part of the model, in some scenarios the univariate method had higher power than the multivariate approach. This higher power was at a cost of a highly inflated false discovery rate not observed with the proposed multivariate method. We applied the approach to oral microbiome data from the Pediatric HIV/AIDS Cohort Oral Health Study and identified five (of 44) species associated with HIV infection.

On modeling claim frequency data in general insurance with extra zeros

This chapter describes a methodology of constructing probability distributions on the nonnegative integers (aka counting distributions). Counting distributions have historic roots as they have been studied since the beginning of Probability Theory. The reason is their statistical importance and applicability in almost all societal and scientific areas. The methodology is based on considering natural exponential families of probability distributions. These families are uniquely determined by their variance functions. Then, counting distributions can be constructed from variance functions that show some regularity conditions. The counting distributions in this chapter are constructed from polynomial variance functions with degree at most three and from two generalizations of these. The usability of these new counting distributions is exhibited by various applications of data fitting, mortality projection, and insurance risk modeling.

Lately, bivariate zero-inflated (BZI) regression models have been used in many instances in the medical sciences to model excess zeros. Examples include the BZI Poisson (BZIP), BZI negative binomial (BZINB) models, etc. Such formulations vary in the basic modeling aspect and use the EM algorithm (Dempster, Laird and Rubin, 1977) for parameter estimation. A different modeling formulation in the Bayesian context is given by Dagne (2004). We extend the modeling to a more general setting for multivariate ZIP models for count data with excess zeros as proposed by Li, Lu, Park, Kim, Brinkley and Peterson (1999), focusing on a particular bivariate regression formulation. For the basic formulation in the case of bivariate data, we assume that Xi are (latent) independent Poisson random variables with parameters λ i, i = 0, 1, 2. A bi-variate count vector (Y1, Y2) response follows a mixture of four distributions; p0 stands for the mixing probability of a point mass distribution at (0, 0); p1, the mixing probability that Y2 = 0, while Y1 = X0 + X1; p2, the mixing probability that Y1 = 0 while Y2 = X0 + X2; and finally (1 - p0 - p1 - p2), the mixing probability that Yi = Xi + X0, i = 1, 2. The choice of the parameters {pi, λ i, i = 0, 1, 2} ensures that the marginal distributions of Yi are zero inflated Poisson (λ 0 + λ i). All the parameters thus introduced are allowed to depend on co-variates through canonical link generalized linear models (McCullagh and Nelder, 1989). This flexibility allows for a range of real-life applications, especially in the medical and biological fields, where the counts are bivariate in nature (with strong association between the processes) and where there are excess of zeros in one or both processes. Our contribution in this paper is to employ a fully Bayesian approach consolidating the work of Dagne (2004) and Li et al. (1999) generalizing the modeling and sampling-based methods described by Ghosh, Mukhopadhyay and Lu (2006) to estimate the parameters and obtain posterior credible intervals both in the case where co-variates are not available as well as in the case where they are. In this context, we provide explicit data augmentation techniques that lend themselves to easier implementation of the Gibbs sampler by giving rise to well-known and closed-form posterior distributions in the bivariate ZIP case. We then use simulations to explore the effectiveness of this estimation using the Bayesian BZIP procedure, comparing the performance to the Bayesian and classical ZIP approaches. Finally, we demonstrate the methodology based on bivariate plant count data with excess zeros that was collected on plots in the Phoenix metropolitan area and compare the results with independent ZIP regression models fitted to both processes.

In this simulation study, we compared the performance of a hierarchical Bayesian approach for estimating salmon escapement from count data with that of separate maximum likelihood estimation of each year's escapement. We simulated several contrasting counting schedules resulting in data sets that differed in information content. In particular, we were interested in the ability of the Bayesian approach to estimate escapement and timing in years where few or no counts are made after the peak of escapement. We found that the Bayesian hierarchical approach was much better able to estimate escapement and escapement timing in these situations. Separate estimates for such years could be wildly inaccurate. However, even a single postpeak count could dramatically improve the estimability of escapement parameters.

To compare the clinical efficacy and prognosis differences between conservative treatment and surgical treatment in patients with non-serious neurologically intact pyogenic spondylitis (Nsi-Nsni-PS), and to provide theoretical reference for the clinical treatment of Nsi-Nsni-PS patients. A retrospective analysis was conducted on 112 cases of Nsi-Nsni-PS patients treated in our hospital from June 2016 to June 2021. According to different treatment methods, they were divided into conservative treatment group (53 cases) and surgical treatment group (59 cases). The general data, laboratory tests, imaging examinations, length of hospital stay, duration of antibiotic use, VAS for pain before and after treatment, ODI, local kyphotic angle correction of diseased vertebrae, and recurrence rate were collected and analyzed in both groups. SPSS 26.0 statistical software was used for analysis. Measurement data were expressed as mean ± standard deviation, and independent sample t-test or rank sum test was used for comparison between groups, while variance analysis was used for intra-group comparison. Count data were expressed as number (%) and compared between groups using chi-square test or Fisher's exact test. Mann-Whitney U test was used to evaluate the changes in local kyphotic angle between the two groups. A p value < 0.05 was considered statistically significant. There were no significant differences in general data and imaging characteristics between the two groups (P > 0.05); there were no statistically significant differences in the positive culture rate of pathogens, length of hospital stay, duration of antibiotic use, treatment complications, WBC, CRP, ESR levels at admission and discharge, VAS and ODI at admission and last follow-up between the two groups (P > 0.05). The WBC and CRP levels of patients in the conservative group at discharge were lower than those in the surgical group (P < 0.05), and there was no significant difference in the decrease in inflammatory indicators (WBC, CRP, ESR) between the two groups (P > 0.05). By the last follow-up, the neurological function of patients in both groups had significantly improved compared to admission (P < 0.05), with 12 out of 15 ASIA grade D patients in the conservative group recovering to grade E, and 21 out of 25 grade D patients in the surgical group recovering to grade E, with no worsening of neurological function in either group. The differences in VAS and ODI scores at the last follow-up compared to before treatment were statistically significant in both groups (P < 0.05), and all patients regained normal activity. Compared with before treatment, the correction degree of local kyphotic angle in the surgical group at the last follow-up was 0.93 ± 4.94°, slightly higher than that in the conservative group (-0.83 ± 3.37°), and the difference was statistically significant(P < 0.05). During our follow-up, we found that both conservative and surgical treatments achieved satisfactory clinical outcomes in patients with Nsi-Nsni-PS. Compared to conservative treatment, surgical intervention did not demonstrate significant advantages in reducing hospitalization time and antibiotic usage duration, increasing pathogen culture positivity rate, lowering treatment complications, or controlling recurrence. However, surgical intervention showed superiority in correcting the local kyphotic angle of spinal lesions, albeit with relatively increased surgical trauma, risks, and treatment costs. At the last follow-up, the surgical group did not exhibit better long-term efficacy. Therefore, when formulating clinical treatment strategies for patients with Nsi-Nsni-PS, it may be preferable to prioritize conservative treatment, supplemented by the use of sensitive or empiric antibiotics for infection management, to improve patient prognosis.

In many clinical trials, the primary endpoint is time to an event of interest, for example, time to cardiac attack or tumor progression, and the statistical power of these trials is primarily driven by the number of events observed during the trials. In such trials, the number of events observed is impacted not only by the number of subjects enrolled but also by other factors including the event rate and the follow-up duration. Consequently, it is important for investigators to be able to monitor and predict accurately patient accrual and event times so as to predict the times of interim and final analyses and enable efficient allocation of research resources, which have long been recognized as important aspects of trial design and conduct. The existing methods for prediction of event times all assume that patient accrual follows a Poisson process with a constant Poisson rate over time; however, it is fairly common in real-life clinical trials that the Poisson rate changes over time. In this paper, we propose a Bayesian joint modeling approach for monitoring and prediction of accrual and event times in clinical trials. We employ a nonhomogeneous Poisson process to model patient accrual and a parametric or nonparametric model for the event and loss to follow-up processes. Compared to existing methods, our proposed methods are more flexible and robust in that we model accrual and event/loss-to-follow-up times jointly and allow the underlying accrual rates to change over time. We evaluate the performance of the proposed methods through simulation studies and illustrate the methods using data from a real oncology trial.

Bayesian inference-based deep learning approach for performance prediction and uncertainty quantification of solar photovoltaic-driven heat pump systems

Erratum to: A data-adaptive Bayesian regression approach for polygenic risk prediction.