Bayesian joint modeling of correlated counts data with application to adverse birth outcomes

In disease mapping, health outcomes measured at the same spatial locations may be correlated, so one can consider joint modeling the multivariate health outcomes accounting for their dependence. The general approaches often used for joint modeling include shared component models and multivariate models. An alternative way to model the association between two health outcomes, when one outcome can naturally serve as a covariate of the other, is to use ecological regression model. For example, in our application, preterm birth (PTB) can be treated as a predictor for low birth weight (LBW) and vice versa. Therefore, we proposed to blend the ideas from joint modeling and ecological regression methods to jointly model the relative risks for LBW and PTBs over the health districts in Saskatchewan, Canada, in 2000–2010. This approach is helpful when proxy of areal-level contextual factors can be derived based on the outcomes themselves when direct information on risk factors are not readily available. Our results indicate that the proposed approach improves the model fit when compared with the conventional joint modeling methods. Further, we showed that when no strong spatial autocorrelation is present, joint outcome modeling using only independent error terms can still provide a better model fit when compared with the separate modeling.     

Spatio-temporal modeling of infectious disease dynamics

A stochastic model, which is well suited to capture space–time dependence of an infectious disease, was employed in this study to describe the underlying spatial and temporal pattern of measles in Barisal Division, Bangladesh. The model has two components: an endemic component and an epidemic component; weights are used in the epidemic component for better accounting of the disease spread into different geographical regions. We illustrate our findings using a data set of monthly measles counts in the six districts of Barisal, from January 2000 to August 2009, collected from the Expanded Program on Immunization, Bangladesh. The negative binomial model with both the seasonal and autoregressive components was found to be suitable for capturing space–time dependence of measles in Barisal. Analyses were done using general optimization routines, which provided the maximum likelihood estimates with the corresponding standard errors.     

Hierarchical Bayes estimation of mortality rates for disease mapping

Mapping of incidence rates or mortality rates (relative risks) from diseases like cancer and leukemia is of primary importance in an epidemiological study. The usual procedure is to map the standardized mortality ratio (SMR) across different geographical regions. Direct use of SMR may not be worthwhile, particularly for small places, as it does not take into account the high variability for different population sizes over different regions and the spatial patterns of the regions under study. In this paper a hierarchical Bayes approach is presented in smoothing the relative risks and providing the measures of uncertainty associated with these estimates of relative risks.     

A comparison of univariate and multivariate multilevel models for repeated measures of use of antenatal care in Uttar Pradesh

Summary.  We compare two different multilevel modelling approaches to the analysis of repeated measures data to assess the effect of mother level characteristics on women's use of prenatal care services in Uttar Pradesh, India. We apply univariate multilevel models to our data and find that the model assumptions are severely violated and the parameter estimates are not stable, particularly for the mother level random effect. To overcome this we apply a multivariate multilevel model. The correlation structure shows that, once the decision has been made regarding use of antenatal care by the mother for her first observed birth in the data, she does not tend to change this decision for higher order births.     

Seasonal patterns of fertility measures: theory and data

The distribution of births by month exhibits a seasonal pattern in most populations. The monthly marital fertility rate for an area of Bangladesh provides a good example of the seasonal periodicity. Seasonal patterns of measures of reproduction in a population of married women are considered. Equations are developed that predict the seasonal patterns of these alternative measures under the assumption that the fertility rate (R) follows a trigonometric curve. This is followed by an empirical analysis of the measures in a Bangladesh population that has a pronounced seasonal fertility. The investigation is intended both to validate the theoretical framework developed in the 1st part of the paper as well as to determine whether seasonal variation in actual populations is sufficiently large to affect the alternative measures significantly. 4 measures are considered: pregnancy prevalence (PP)--the proportion of married women who are pregnant at the survey date; mean open birth interval (MOI)--the time from the last live birth to the date of the survey for parous women and from the time of marriage to the date of the survey for nulliparous women; mean closed interval-birth (MCIB)--the mean interval between the last 2 live births for married women who have a birth in the period immediately preceding the survey date; and mean closed interval-woman (MCIW)--the mean interval between the last 2 live births for women who have had at least 2 children by the time of the survey. It is assumed that the seasonal pattern of the fertility rate of a population follows a cosine curve and that there is no trend in annual fertility from year to year. The lag and relative variability of the other measures are considered in comparison with the fertility rate curve. The predictions from this theoretical effort, when compared with observed patterns and trigonometric regression results for each measure in data from Bangladesh, are shown to be quite accurate. The figure and regression results show that R, PP, and MOI have definite seasonal periodicity, but MCIB and MCIW do not display any seasonal patterns. If there is a secular trend in fertility in addition to seasonality, these relationships between the seasonal patterns of the measures may no longer hold. There is a disadvantage to using closed interval measures, for they are unable to detect effects of limiting of childbearing in a population since they are based only on information from women who have births.     

Estimating percentile-specific treatment effects in counterfactual models: a case-study of micronutrient supplementation, birth weight and infant mortality

Summary.  Clinical trials of micronutrient supplementation are aimed at reducing the risk of infant mortality by increasing birth weight. Because infant mortality is greatest among the low birth weight (LBW) infants (2500 g or under), an effective intervention increases the birth weight among the smallest babies. The paper defines population and counterfactual parameters for estimating the treatment effects on birth weight and on survival as functions of the percentiles of the birth weight distribution. We use a Bayesian approach with data augmentation to approximate the posterior distributions of the parameters, taking into account uncertainty that is associated with the imputation of the counterfactuals. This approach is particularly suitable for exploring the sensitivity of the results to unverifiable modelling assumptions and other prior beliefs. We estimate that the average causal effect of the treatment on birth weight is 72 g (95% posterior regions 33–110 g) and that this causal effect is largest among the LBW infants. Posterior inferences about average causal effects of the treatment on birth weight are robust to modelling assumptions. However, inferences about causal effects for babies at the tails of the birth weight distribution can be highly sensitive to the unverifiable assumption about the correl-ation between the observed and the counterfactuals birth weights. Among the LBW infants who have a large causal effect of the treatment on birth weight, we estimate that a baby receiving the treatment has 5% less chance of death than if the same baby had received the control. Among the LBW infants, we found weak evidence supporting an additional beneficial effect of the treatment on mortality independent of birth weight.     

区域差异导致经济块状发展的空间机理研究

 本文运用空间计量经济学模型以及修正绝对β收敛回归模型,对中国2003—2007年省域经济发展的集聚性与差异性进行研究发现：中国31个省域之间存在着较强的空间集聚和空间依赖性,虽受到地域限制,但集聚辐射区域有逐步扩大的趋势;固定资产投入、人均实际工资以及城镇化率对于区域经济集聚的发展起到稳健的推动作用,FDI对集聚区域发展的促进作用也越加显著,但是财政投入却在一定层度上遏制了块状经济的发展。另外,修正和传统收敛模型均显示,2003-2007年我国经济整体发展呈现明显的不收敛特性。     

图解Bootstrap方法用于空间相关性Moran检验的有效性

因为区域间经济收敛、外商直接投资和知识溢出等领域的空间经济计量研究依赖于空间关系的存在,所以进行空间相关性Moran’s I检验是关键。然而,已有空间相关性Moran’s I检验理论受到众多假设条件限制。利用＂名义水平—实际水平＂图和＂名义水平—功效＂图,解析非对称Wild Bootstrap方法用于空间相关性Moran’s I检验的有限样本性质,发现即使模型不满足经典的分布假设条件,与渐近检验相比,Bootstrap方法也能够有效地检验研究对象间的空间相关性。     

A close look at the spatial structure implied by the CAR and SAR models

Modeling spatial interactions that arise in spatially referenced data is commonly done by incorporating the spatial dependence into the covariance structure either explicitly or implicitly via an autoregressive model. In the case of lattice (regional summary) data, two common autoregressive models used are the conditional autoregressive model (CAR) and the simultaneously autoregressive model (SAR). Both of these models produce spatial dependence in the covariance structure as a function of a neighbor matrix W and often a fixed unknown spatial correlation parameter. This paper examines in detail the correlation structures implied by these models as applied to an irregular lattice in an attempt to demonstrate their many counterintuitive or impractical results. A data example is used for illustration where US statewide average SAT verbal scores are modeled and examined for spatial structure using different spatial models.     

中国人口因素对寿险需求影响的实证分析

应用双对数线性回归模型、岭回归模型对中国寿险需求进行实证分析。着重分析了人口因素对寿险需求的影响，在分析中引入了虚拟变量，并对多重共线性问题利用岭回归加以改善。研究表明：人口的城乡结构对中国寿险需求起着决定性的作用；城镇居民年人均可支配收入与寿险需求有显著的正相关性；少儿负担系数及银行实际利率与寿险需求有显著的负相关关系；受教育程度对寿险需求有显著的正面作用；而老年负担系数显示了对寿险需求正面的但不十分显著的影响。     

An investigation of the spatial correlations for relative purchasing power in Baden–Württemberg

The relative purchasing power—i.e., the purchasing power per inhabitant—is one of the key characteristics for businesses deciding on site selection. Apart from that it also plays a major role in regional planning, pricing policy and market research. In this study we investigate the spatial correlations for relative purchasing power of the townships in Baden–Württemberg. In particular, changes in relative purchasing power are analysed for three different time intervals, 1987–1993, 1993–1998 and 1998–2004, by means of distance-dependent characteristics like the mark–correlation function, the Simpson indices α(r) and β(r) and by tests on random labelling. It is shown that there are positive correlations for small distances between different townships but that these positive correlations become weaker over the years until they are almost nonexistent (in the sense that hypotheses of random labelling are no longer rejected). A conclusion from this loss of spatial correlations with time is that the relative purchasing power might become more and more purely random. This means that the relative purchasing power in a township is less and less influenced by the relative purchasing power of townships nearby. We further analysed these changes in the Bodensee–Oberschwaben and Stuttgart regions to compare the development of the relative purchasing power in both urban and rural environments. This analysis was done in close cooperation with W. Brachat–Schwarz and W. Walla of the Statistical Office of Baden–Württemberg. S.E. is supported by a grant of the graduate college 1100 at Ulm University.     

劳动力流动对中国地区经济差距影响的空间计量经济模型分析

学术界对劳动力流动对地区经济发展产生的影响有两种不同观点：一种观点认为劳动力流动能够缩小地区差距;另一种观点则认为劳动力流动会扩大地区发展差距。考虑各地区经济发展的空间依赖性,通过构建空间计量经济模型,并利用中国各省区经济的面板数据进行研究与实证分析。结果表明：劳动力流动对中国不同地区经济发展的作用方向和强度表现不同,对地区差距的影响是劳动力流入与劳动力流出综合作用产生的结果。     

Spatial model fitting for large datasets with applications to climate and microarray problems

Many problems in the environmental and biological sciences involve the analysis of large quantities of data. Further, the data in these problems are often subject to various types of structure and, in particular, spatial dependence. Traditional model fitting often fails due to the size of the datasets since it is difficult to not only specify but also to compute with the full covariance matrix describing the spatial dependence. We propose a very general type of mixed model that has a random spatial component. Recognizing that spatial covariance matrices often exhibit a large number of zero or near-zero entries, covariance tapering is used to force near-zero entries to zero. Then, taking advantage of the sparse nature of such tapered covariance matrices, backfitting is used to estimate the fixed and random model parameters. The novelty of the paper is the combination of the two techniques, tapering and backfitting, to model and analyze spatial datasets several orders of magnitude larger than those datasets typically analyzed with conventional approaches. Results will be demonstrated with two datasets. The first consists of regional climate model output that is based on an experiment with two regional and two driver models arranged in a two-by-two layout. The second is microarray data used to build a profile of differentially expressed genes relating to cerebral vascular malformations, an important cause of hemorrhagic stroke and seizures.     

Modeling low birth weights using threshold regression: results for U. S. birth data

Babies born live under 2,500 g or with a gestational age under 37 weeks are often inadequately developed and have elevated risks of infant mortality, congenital malformations, mental retardation, and other physical and neurological impairments. In this paper, we model birth weight as a first hitting time (FHT) of a birthing boundary in a Wiener process representing fetal development. We associate the parameters of the process and boundary with covariates describing maternal characteristics and the birthing environment using a relatively new regression methodology called threshold regression. Two FHT models for birth weight are developed. One is a mixture model and the other a competing risks model. These models are tested in a case demonstration using a 4%-systematic sample of the more than four million live births in the United States in 2002. An extensive data set for these births was provided by the National Center for Health Statistics. The focus of this paper is on the conceptual framework, models and methodology. A full empirical study is deferred to a later occasion.     

Fiscal decentralization,financial efficiency and upgrading the industrial structure: an empirical analysis of a spatial heterogeneity model

From the perspective of spatial heterogeneity and using data from 281 prefecture-level cities in China over the 2003–2012 period, we empirically test the interactions and differences in the spatial effects through which fiscal decentralization and financial efficiency influence the upgrading of regional industrial structure. The results indicate that regional differences in fiscal decentralization and financial efficiency lead to significant spatial heterogeneity in upgrading the industrial structure. The interaction mechanism between fiscal decentralization and financial efficiency plays a positive role in promoting the upgrading of the regional industrial structure, which is subject to organic integration between fiscal systems and financial development. Moreover, there is significant spatial dependence in the effects of fiscal decentralization and financial efficiency on upgrading the regional industrial structure, the ‘high-lying-land’ effects and the ‘low-lying-land’ effects coexist in the spatial pattern.     

空间经济计量滞后模型Bootstrap Moran检验功效的模拟分析

 当误差项不服从独立同分布时,利用Moran’s I统计量的渐近检验,无法有效判断空间经济计量滞后模型2SLS估计残差间存在空间关系与否。本文采用两种基于残差的Bootstrap方法,诊断空间经济计量滞后模型残差中的空间相关关系。大量Monte Carlo模拟结果显示,从功效角度看,无论误差项服从独立同分布与否,与渐近检验相比,Bootstrap Moran检验都具有更好的有限样本性质,能够更有效地进行空间相关性检验。尤其是,在样本量较小和空间衔接密度较高情况下,Bootstrap Moran检验的功效显著大于渐近检验。     

中国人口出生率下降与经济发展

中国人口出生率下降以及人口老龄化引起了人们对计划生育政策调整的激烈讨论。作者根据全国27个地区1980~2011年的面板数据,在横截面存在相关性的情形下,运用面板单位根和协整方法,定量考察了人口出生率、人口死亡率、城镇职工工资水平、农村居民收入水平之间的关系。研究发现：1）尽管我国实行了计划生育政策,但人口出生率与经济发展变量之间仍然存在着长期稳定的关系;2）城市和农村的经济发展对于人口出生率的影响存在显著差异。前者会刺激人口出生率的提高,但后者会降低人口出生率,且影响程度比前者大。3）人口出生率与经济发展变量之间的关系存在明显的地区差异。根据以上结论,作者认为放松计划生育政策不会引起我国人口数量猛增,反而会优化人口结构,提高人口整体素质。     

Testing equality of cause-specific hazard rates corresponding to m competing risks among K groups

In this paper, a class of tests is developed for comparing the cause-specific hazard rates of m competing risks simultaneously in K ( 2) groups. The data available for a unit are the failure time of the unit along with the identifier of the risk claiming the failure. In practice, the failure time data are generally right censored. The tests are based on the difference between the weighted averages of the cause-specific hazard rates corresponding to each risk. No assumption regarding the dependence of the competing risks is made. It is shown that the proposed test statistic has asymptotically chi-squared distribution. The proposed test is shown to be optimal for a specific type of local alternatives. The choice of weight function is also discussed. A simulation study is carried out using multivariate Gumbel distribution to compare the optimal weight function with a proposed weight function which is to be used in practice. Also, the proposed test is applied to real data on the termination of an intrauterine device.An erratum to this article can be found at     

中国雾霾污染的空间关联研究

本文利用非线性Granger因果检验识别了中国279个城市间雾霾污染的空间依赖关系,结合多样化的网络分析方法与滚动窗口技术揭示出雾霾污染空间关联的整体特征与微观模式,进而基于指数随机图模型考察了雾霾污染空间关联的影响因素及作用机制。研究发现：样本城市间普遍存在雾霾污染依赖关系并且这种空间关联的紧密程度逐渐上升,近年来中国大范围雾霾污染的频繁爆发与雾霾污染区域性特征的日趋强化密切相关。除了自然因素之外,人类经济社会活动在雾霾污染空间关联的形成中发挥了重要作用。本文的研究结论对雾霾污染及其区域传输的还原论、自然决定论等观点进行了有力的反驳,有助于确立人在雾霾治理中的主观能动性。     

Max-Linear Competing Factor Models

Models incorporating “latent” variables have been commonplace in financial, social, and behavioral sciences. Factor model, the most popular latent model, explains the continuous observed variables in a smaller set of latent variables (factors) in a matter of linear relationship. However, complex data often simultaneously display asymmetric dependence, asymptotic dependence, and positive (negative) dependence between random variables, which linearity and Gaussian distributions and many other extant distributions are not capable of modeling. This article proposes a nonlinear factor model that can model the above-mentioned variable dependence features but still possesses a simple form of factor structure. The random variables, marginally distributed as unit Fréchet distributions, are decomposed into max linear functions of underlying Fréchet idiosyncratic risks, transformed from Gaussian copula, and independent shared external Fréchet risks. By allowing the random variables to share underlying (latent) pervasive risks with random impact parameters, various dependence structures are created. This innovates a new promising technique to generate families of distributions with simple interpretations. We dive in the multivariate extreme value properties of the proposed model and investigate maximum composite likelihood methods for the impact parameters of the latent risks. The estimates are shown to be consistent. The estimation schemes are illustrated on several sets of simulated data, where comparisons of performance are addressed. We employ a bootstrap method to obtain standard errors in real data analysis. Real application to financial data reveals inherent dependencies that previous work has not disclosed and demonstrates the model’s interpretability to real data. Supplementary materials for this article are available online.