Semiparametric bayes' proportional odds models for current status data with underreporting

Current status data are a type of interval-censored event time data in which all the individuals are either left or right censored. For example, our motivation is drawn from a cross-sectional study, which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman. We propose a semiparametric Bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure. The proposed approach has the advantage of being straightforward to implement using a simple and efficient Gibbs sampler, whereas alternative semiparametric Bayes' event time models encounter problems for current status data. The model is generalized to allow systematic underreporting in a subset of the data, and the methods are applied to an epidemiologic study of uterine fibroids.     

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.     

Tests of proportional hazards and proportional odds models for grouped survival data

In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small-sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi-squared distribution. Real examples illustrate the proposed tests.     

Statistical Methods for Ordered Categorical Data Based on a Constrained Odds Model

The proportional odds model provides a powerful tool for analysing ordered categorical data and setting sample size, although for many clinical trials its validity is questionable. The purpose of this paper is to present a new class of constrained odds models which includes the proportional odds model. The efficient score and Fisher's information are derived from the profile likelihood for the constrained odds model. These results are new even for the special case of proportional odds where the resulting statistics define the Mann‐Whitney test. A strategy is described involving selecting one of these models in advance, requiring assumptions as strong as those underlying proportional odds, but allowing a choice of such models. The accuracy of the new procedure and its power are evaluated.     

A hierarchical Bayesian model for combining multiple 2 x 2 tables using conditional likelihoods

This paper introduces a hierarchical Bayesian model for combining multiple 2 x 2 tables that allows the flexibility of different odds ratio estimates for different tables and at the same time allows the tables to borrow information from each other. The proposed model, however, is different from a full Bayesian model in that the nuisance parameters are eliminated by conditioning instead of integration. The motivation is a more robust model and a faster and more stable Gibbs algorithm. We work out a Gibbs scheme using the adaptive rejection sampling for log concave density and an algorithm for the mean and variance of the noncentral hypergeometric distribution. The model is applied to a multicenter ulcer clinical trial.     

Missing Exposure Data in Stereotype Regression Model: Application to Matched Case–Control Study with Disease Subclassification

Summary With advances in modern medicine and clinical diagnosis, case–control data with characterization of finer subtypes of cases are often available. In matched case–control studies, missingness in exposure values often leads to deletion of entire stratum, and thus entails a significant loss in information. When subtypes of cases are treated as categorical outcomes, the data are further stratified and deletion of observations becomes even more expensive in terms of precision of the category‐specific odds‐ratio parameters, especially using the multinomial logit model. The stereotype regression model for categorical responses lies intermediate between the proportional odds and the multinomial or baseline category logit model. The use of this class of models has been limited as the structure of the model implies certain inferential challenges with nonidentifiability and nonlinearity in the parameters. We illustrate how to handle missing data in matched case–control studies with finer disease subclassification within the cases under a stereotype regression model. We present both Monte Carlo based full Bayesian approach and expectation/conditional maximization algorithm for the estimation of model parameters in the presence of a completely general missingness mechanism. We illustrate our methods by using data from an ongoing matched case–control study of colorectal cancer. Simulation results are presented under various missing data mechanisms and departures from modeling assumptions.     

Mixture Hazard Models for Lifetime Data

We propose a general family of mixture hazard models to analyze lifetime data associated with bathtub and multimodal hazard functions. With this model we have a great flexibility for fitting lifetime data. Its version with covariates has the proportional hazard and the accelerated failure time models as special cases. A Bayesian analysis is presented for the model using informative priors, using sampling‐based approaches to perform the Bayesian computations. A real example with a medical data illustrates the methodology.     

Multi-stage transitional models with random effects and their application to the Einstein aging study

Longitudinal studies of aging often gather repeated observations of cognitive status to describe the development of dementia and to assess the influence of risk factors. Clinical progression to dementia is often conceptualized by a multi-stage model of several transitions that synthesizes time-varying effects. In this study, we assess the influence of risk factors on the transitions among three cognitive status: cognitive stability (normal cognition for age), memory impairment, and clinical dementia. We have developed a shared random effects model that not only links the propensity of transitions and to the probability of informative missingness due to death, but also incorporates heterogeneous transition between subjects. We evaluate four approaches using generalized logit and four using proportional odds models to the first-order Markov transition probabilities as a function of covariates. Random effects were incorporated into these models to account for within-subject correlations. Data from the Einstein Aging Study are used to evaluate the goodness-of-fit of these models using the Akaike information criterion. The best fitting model for each type (generalized logit and proportional odds) is recommended and their results are discussed in more details.     

Embracing asymmetry in nature: How to account for skewness in ecological data

Asymmetric regression is an alternative to conventional linear regression that allows us to model the relationship between predictor variables and the response variable while accommodating skewness. Advantages of asymmetric regression include incorporating realistic ecological patterns observed in data, robustness to model misspecification and less sensitivity to outliers. Bayesian asymmetric regression relies on asymmetric distributions such as the asymmetric Laplace (ALD) or asymmetric normal (AND) in place of the normal distribution used in classic linear regression models. Asymmetric regression concepts can be used for process and parameter components of hierarchical Bayesian models and have a wide range of applications in data analyses. In particular, asymmetric regression allows us to fit more realistic statistical models to skewed data and pairs well with Bayesian inference. We first describe asymmetric regression using the ALD and AND. Second, we show how the ALD and AND can be used for Bayesian quantile and expectile regression for continuous response data. Third, we consider an extension to generalize Bayesian asymmetric regression to survey data consisting of counts of objects. Fourth, we describe a regression model using the ALD, and show that it can be applied to add needed flexibility, resulting in better predictive models compared to Poisson or negative binomial regression. We demonstrate concepts by analyzing a data set consisting of counts of Henslow’s sparrows following prescribed fire and provide annotated computer code to facilitate implementation. Our results suggest Bayesian asymmetric regression is an essential component of a scientist’s statistical toolbox.     

Joint Models of Longitudinal Data and Recurrent Events with Informative Terminal Event

This article presents semiparametric joint models to analyze longitudinal data with recurrent events (e.g. multiple tumors, repeated hospital admissions) and a terminal event such as death. A broad class of transformation models for the cumulative intensity of the recurrent events and the cumulative hazard of the terminal event is considered, which includes the proportional hazards model and the proportional odds model as special cases. We propose to estimate all the parameters using the nonparametric maximum likelihood estimators (NPMLE). We provide the simple and efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we evaluate the performance of the method through extensive simulation studies and a real-data application.     

Boosting method for nonlinear transformation models with censored survival data

We propose a general class of nonlinear transformation models for analyzing censored survival data, of which the nonlinear proportional hazards and proportional odds models are special cases. A cubic smoothing spline-based component-wise boosting algorithm is derived to estimate covariate effects nonparametrically using the gradient of the marginal likelihood, that is computed using importance sampling. The proposed method can be applied to survival data with high-dimensional covariates, including the case when the sample size is smaller than the number of predictors. Empirical performance of the proposed method is evaluated via simulations and analysis of a microarray survival data.     

Applications of proportional odds ordinal logistic regression models and continuation ratio models in examining the association of physical inactivity with erectile dysfunction among type 2 diabetic patients

[Purpose]Many studies have observed a high prevalence of erectile dysfunction among individuals performing physical activity in less leisure-time. However, this relationship in patients with type 2 diabetic patients is not well studied. In exposure outcome studies with ordinal outcome variables, investigators often try to make the outcome variable dichotomous and lose information by collapsing categories. Several statistical models have been developed to make full use of all information in ordinal response data, but they have not been widely used in public health research. In this paper, we discuss the application of two statistical models to determine the association of physical inactivity with erectile dysfunction among patients with type 2 diabetes.[Methods]A total of 204 married men aged 20-60 years with a diagnosis of type 2 diabetes at the outpatient unit of the Department of Endocrinology at PSG hospitals during the months of May and June 2019 were studied. We examined the association between physical inactivity and erectile dysfunction using proportional odds ordinal logistic regression models and continuation ratio models.[Results]The proportional odds model revealed that patients with diabetes who perform leisure time physical activity for over 40 minutes per day have reduced odds of erectile dysfunction (odds ratio=0.38) across the severity categories of erectile dysfunction after adjusting for age and duration of diabetes.[Conclusion]The present study suggests that physical inactivity has a negative impact on erectile function. We observed that the simple logistic regression model had only 75% efficiency compared to the proportional odds model used here; hence, more valid estimates were obtained here.     

Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables

This article investigates the performance, in a frequentist sense, of Bayesian confidence intervals (CIs) for the difference of proportions, relative risk, and odds ratio in 2 x 2 contingency tables. We consider beta priors, logit-normal priors, and related correlated priors for the two binomial parameters. The goal was to analyze whether certain settings for prior parameters tend to provide good coverage performance regardless of the true association parameter values. For the relative risk and odds ratio, we recommend tail intervals over highest posterior density (HPD) intervals, for invariance reasons. To protect against potentially very poor coverage probabilities when the effect is large, it is best to use a diffuse prior, and we recommend the Jeffreys prior. Otherwise, with relatively small samples, Bayesian CIs using more informative (even uniform) priors tend to have poorer performance than the frequentist CIs based on inverting score tests, which perform uniformly quite well for these parameters.     

Bayesian informative dropout model for longitudinal binary data with random effects using conditional and joint modeling approaches

Dropouts are common in longitudinal study. If the dropout probability depends on the missing observations at or after dropout, this type of dropout is called informative (or nonignorable) dropout (ID). Failure to accommodate such dropout mechanism into the model will bias the parameter estimates. We propose a conditional autoregressive model for longitudinal binary data with an ID model such that the probabilities of positive outcomes as well as the drop‐out indicator in each occasion are logit linear in some covariates and outcomes. This model adopting a marginal model for outcomes and a conditional model for dropouts is called a selection model. To allow for the heterogeneity and clustering effects, the outcome model is extended to incorporate mixture and random effects. Lastly, the model is further extended to a novel model that models the outcome and dropout jointly such that their dependency is formulated through an odds ratio function. Parameters are estimated by a Bayesian approach implemented using the user‐friendly Bayesian software WinBUGS. A methadone clinic dataset is analyzed to illustrate the proposed models. Result shows that the treatment time effect is still significant but weaker after allowing for an ID process in the data. Finally the effect of drop‐out on parameter estimates is evaluated through simulation studies.     

Semiparametric transformation models with random effects for joint analysis of recurrent and terminal events

Summary .  We propose a broad class of semiparametric transformation models with random effects for the joint analysis of recurrent events and a terminal event. The transformation models include proportional hazards/intensity and proportional odds models. We estimate the model parameters by the nonparametric maximum likelihood approach. The estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Simple and stable numerical algorithms are provided to calculate the parameter estimators and to estimate their variances. Extensive simulation studies demonstrate that the proposed inference procedures perform well in realistic settings. Applications to two HIV/AIDS studies are presented.     

Phylogeography in continuous space: coupling species distribution models and circuit theory to assess the effect of contiguous migration at different climatic periods on genetic differentiation in Busseola fusca (Lepidoptera: Noctuidae)

Current population genetic models fail to cope with genetic differentiation for species with large, contiguous and heterogeneous distribution. We show that in such a case, genetic differentiation can be predicted at equilibrium by circuit theory, where conductance corresponds to abundance in species distribution models (SDMs). Circuit‐SDM approach was used for the phylogeographic study of the lepidopteran cereal stemborer Busseola fuscaFüller (Noctuidae) across sub‐Saharan Africa. Species abundance was surveyed across its distribution range. SDMs were optimized and selected by cross‐validation. Relationship between observed matrices of genetic differentiation between individuals, and between matrices of resistance distance was assessed through Mantel tests and redundancy discriminant analyses (RDAs). A total of 628 individuals from 130 localities in 17 countries were genotyped at seven microsatellite loci. Six population clusters were found based on a Bayesian analysis. The eastern margin of Dahomey gap between East and West Africa was the main factor of genetic differentiation. The SDM projections at present, last interglacial and last glacial maximum periods were used for the estimation of circuit resistance between locations of genotyped individuals. For all periods of time, when using either all individuals or only East African individuals, partial Mantel r and RDA conditioning on geographic distance were found significant. Under future projections (year 2080), partial r and RDA significance were different. From this study, it is concluded that analytical solutions provided by circuit theory are useful for the evolutionary management of populations and for phylogeographic analysis when coalescence times are not accessible by approximate Bayesian simulations.     

Merits of Modelling Multivariate Survival Data Using Random Effects Proportional Odds Model

Recently, there has been a great deal of interest in the analysis of multivariate survival data. In most epidemiological studies, survival times of the same cluster are related because of some unobserved risk factors such as the environmental or genetic factors. Therefore, modelling of dependence between events of correlated individuals is required to ensure a correct inference on the effects of treatments or covariates on the survival times. In the past decades, extension of proportional hazards model has been widely considered for modelling multivariate survival data by incorporating a random effect which acts multiplicatively on the hazard function. In this article, we consider the proportional odds model, which is an alternative to the proportional hazards model at which the hazard ratio between individuals converges to unity eventually. This is a reasonable property particularly when the treatment effect fades out gradually and the homogeneity of the population increases over time. The objective of this paper is to assess the influence of the random effect on the within‐subject correlation and the population heterogeneity. We are particularly interested in the properties of the proportional odds model with univariate random effect and correlated random effect. The correlations between survival times are derived explicitly for both choices of mixing distributions and are shown to be independent of the covariates. The time path of the odds function among the survivors are also examined to study the effect of the choice of mixing distribution. Modelling multivariate survival data using a univariate mixing distribution may be inadequate as the random effect not only characterises the dependence of the survival times, but also the conditional heterogeneity among the survivors. A robust estimate for the correlation of the logarithm of the survival times within a cluster is obtained disregarding the choice of the mixing distributions. The sensitivity of the estimate of the regression parameter under a misspecification of the mixing distribution is studied through simulation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local average treatment effects estimation via substantive model compatible multiple imputation

Nonadherence to assigned treatment is common in randomized controlled trials (RCTs). Recently, there has been increased interest in estimating causal effects of treatment received, for example, the so‐called local average treatment effect (LATE). Instrumental variables (IV) methods can be used for identification, with estimation proceeding either via fully parametric mixture models or two‐stage least squares (TSLS). TSLS is popular but can be problematic for binary outcomes where the estimand of interest is a causal odds ratio. Mixture models are rarely used in practice, perhaps because of their perceived complexity and need for specialist software. Here, we propose using multiple imputation (MI) to impute the latent compliance class appearing in the mixture models. Since such models include an interaction term between the latent compliance class and randomized treatment, we use “substantive model compatible” MI (SMC MIC), which can additionally handle missing data in outcomes and other variables in the model, before fitting the mixture models via maximum likelihood to the MI data sets and combining results via Rubin's rules. We use simulations to compare the performance of SMC MIC to existing approaches and also illustrate the methods by reanalyzing an RCT in UK primary health. We show that SMC MIC can be more efficient than full Bayesian estimation when auxiliary variables are incorporated, and is superior to two‐stage methods, especially for binary outcomes.     

Efficient Bayesian analysis of occupancy models with logit link functions

Occupancy models (Ecology, 2002; 83: 2248) were developed to infer the probability that a species under investigation occupies a site. Bayesian analysis of these models can be undertaken using statistical packages such as WinBUGS, OpenBUGS, JAGS, and more recently Stan, however, since these packages were not developed specifically to fit occupancy models, one often experiences long run times when undertaking an analysis. Bayesian spatial single‐season occupancy models can also be fit using the R package stocc. The approach assumes that the detection and occupancy regression effects are modeled using probit link functions. The use of the logistic link function, however, is algebraically more tractable and allows one to easily interpret the coefficient effects of an estimated model by using odds ratios, which is not easily done for a probit link function for models that do not include spatial random effects. We develop a Gibbs sampler to obtain posterior samples from the posterior distribution of the parameters of various occupancy models (nonspatial and spatial) when logit link functions are used to model the regression effects of the detection and occupancy processes. We apply our methods to data extracted from the 2nd Southern African Bird Atlas Project to produce a species distribution map of the Cape weaver (Ploceus capensis) and helmeted guineafowl (Numida meleagris) for South Africa. We found that the Gibbs sampling algorithm developed produces posterior samples that are identical to those obtained when using JAGS and Stan and that in certain cases the posterior chains mix much faster than those obtained when using JAGS, stocc, and Stan. Our algorithms are implemented in the R package, Rcppocc. The software is freely available and stored on GitHub ( https://github.com/AllanClark/Rcppocc ).     

揭示群落结构及其环境响应的联合物种分布模型的研究进展

物种分布模型通常用于基础生态和应用生态研究,用来确定影响生物分布和物种丰富度的因素,量化物种与非生物条件的关系,预测物种对土地利用和气候变化的反应,并确定潜在的保护区.在传统的物种分布模型中,生物的相互作用很少被纳入,而联合物种分布模型(JSDMs)作为近年提出的一种新的可行方法,可以同时考虑环境因素和生物交互作用,因而成为分析生物群落结构和种间相互作用过程的有力工具.JSDMs以物种分布模型(SDMs)为基础,通常采用广义线性回归模型建立物种对环境变量的多变量响应,以随机效应的形式获取物种间的关联,同时结合隐变量模型(LVMs),并基于Laplace近似和马尔科夫蒙脱卡罗模拟的最大似然估计或贝叶斯方法来估算模型参数.本文对JSDMs的产生及理论基础进行归纳总结,重点介绍了不同类型JSDMs的特点及其在现代生态学中的应用,阐述了JSDMs的应用前景、使用过程中存在的问题及发展方向.随着对环境因素与多物种种间关系研究的深入,JSDMs将是今后物种分布模型研究的重点.