Discrete time modelling of disease incidence time series by using Markov chain Monte Carlo methods

Summary.  A stochastic discrete time version of the susceptible–infected–recovered model for infectious diseases is developed. Disease is transmitted within and between communities when infected and susceptible individuals interact. Markov chain Monte Carlo methods are used to make inference about these unobserved populations and the unknown parameters of interest. The algorithm is designed specifically for modelling time series of reported measles cases although it can be adapted for other infectious diseases with permanent immunity. The application to observed measles incidence series motivates extensions to incorporate age structure as well as spatial epidemic coupling between communities.     

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.     

On a tobit–Birnbaum–Saunders model with an application to medical data

The tobit model allows a censored response variable to be described by covariates. Its applications cover different areas such as economics, engineering, environment and medicine. A strong assumption of the standard tobit model is that its errors follow a normal distribution. However, not all applications are well modeled by this distribution. Some efforts have relaxed the normality assumption by considering more flexible distributions. Nevertheless, the presence of asymmetry could not be well described by these flexible distributions. A real-world data application of measles vaccine in Haiti is explored, which confirms this asymmetry. We propose a tobit model with errors following a Birnbaum–Saunders (BS) distribution, which is asymmetrical and has shown to be a good alternative for describing medical data. Inference based on the maximum likelihood method and a type of residual are derived for the tobit–BS model. We perform global and local influence diagnostics to assess the sensitivity of the maximum likelihood estimators to atypical cases. A Monte Carlo simulation study is carried out to empirically evaluate the performance of these estimators. We conduct a data analysis for the mentioned application of measles vaccine based on the proposed model with the help of the R software. The results show the good performance of the tobit–BS model.     

Time series modelling of childhood diseases: a dynamical systems approach

A key issue in the dynamical modelling of epidemics is the synthesis of complex mathematical models and data by means of time series analysis. We report such an approach, focusing on the particularly well-documented case of measles. We propose the use of a discrete time epidemic model comprising the infected and susceptible class as state variables. The model uses a discrete time version of the susceptible–exposed–infected–recovered type epidemic models, which can be fitted to observed disease incidence time series. We describe a method for reconstructing the dynamics of the susceptible class, which is an unobserved state variable of the dynamical system. The model provides a remarkable fit to the data on case reports of measles in England and Wales from 1944 to 1964. Morever, its systematic part explains the well-documented predominant biennial cyclic pattern. We study the dynamic behaviour of the time series model and show that episodes of annual cyclicity, which have not previously been explained quantitatively, arise as a response to a quicker replenishment of the susceptible class during the baby boom, around 1947.     

Analysis of Between–Household Heterogeneity in Disease Transmission from Data on Outbreak Sizes

The paper proposes a method of analysis for data on within–household disease transmission, when only outbreak sizes are available. The method assumes between–household heterogeneity of the transmission probabilities. A random effects model in a hierarchical setting is fitted using MCMC and data augmentation techniques. The procedure is illustrated on a measles dataset.     

Bayesian Inference for Contact Networks Given Epidemic Data

Abstract. In this article, we estimate the parameters of a simple random network and a stochastic epidemic on that network using data consisting of recovery times of infected hosts. The SEIR epidemic model we fit has exponentially distributed transmission times with Gamma distributed exposed and infectious periods on a network where every edge exists with the same probability, independent of other edges. We employ a Bayesian framework and Markov chain Monte Carlo (MCMC) integration to make estimates of the joint posterior distribution of the model parameters. We discuss the accuracy of the parameter estimates under various prior assumptions and show that it is possible in many scientifically interesting cases to accurately recover the parameters. We demonstrate our approach by studying a measles outbreak in Hagelloch, Germany, in 1861 consisting of 188 affected individuals. We provide an R package to carry out these analyses, which is available publicly on the Comprehensive R Archive Network.     

Demographic policy in the light of the resolutions of the Twenty-sixth Congress of the Communist Party

The USSR is moving from extensive to intensive type of population reproduction, not because of any governmental measures but as a reaction to objective circumstances. At present there is a reduction in the population cohort of working age. This has an adverse effect on production. And the number of the elderly is increasing; we must involve them more in the production process, in monitoring the service sphere, for instance. The infant mortality rate has declined sharply in the USSR, especially since World War II. The birthrate has also dropped, but it is still higher than in the US, France, or West Germany. Some authorities think that this (the ZPG) is a good idea, but this author thinks it is a bad idea, meaning a drop in society's productive forces. We need an active demographic policy, meaning one which ensures optimal reproduction of the population with an improvement in its health, culture, and living standard. The policy must be differentiated, as conditions vary from one part of the country to another. An example is the 1981 decree on assistance to families with children which provides for payments of 35-50 rubles/month to mothers who must stay home to look after children. The number of children per family to ensure reproduction must be 2.6 on the average. In the Central Asian republics family sizes of 4-5 children are anticipated, but in the RSFSR, Ukraine, Belorussia, and the Baltic republics the anticipated size of families is rather low. Measures must be taken to alter this by providing assistance to families with children.     

Hierarchical space-time modelling of epidemic dynamics: an application to measles outbreaks

How infectious diseases spread in space and time is an important question that has received considerable theoretical attention. There are, however, few empirical studies to support theoretical approaches, because data is scarce. In this paper we propose to model the epidemic spread of measles in the London boroughs between 1960 and 1970 by an extension of the Kriged Kalman filter (Mardia et al. , 1998) to count data. Results show the flexibility of our approach in describing complex spatio-temporal dynamics.     

Threshold autoregression analysis for finite-range time series of counts with an application on measles data

This article studies the threshold autoregression analysis for the self-exciting threshold binomial autoregressive processes. Parameters' point estimation and interval estimation problems are considered via the empirical likelihood method. A new algorithm to estimate the threshold value of the threshold model is also given. Simulation study is conducted for the evaluation of the developed approach. An application on measles data is provided to show the applicability of the method.     

Sequential case series analysis for pharmacovigilance

Summary.  The self-controlled case series method is used to evaluate drug safety, particularly the safety of paediatric vaccines with respect to rare adverse reactions. We propose a group sequential version of the method for prospective surveillance of drug safety. We focus on the surveillance of new vaccines. We develop methods that are based on the sequential probability ratio test applied at predetermined surveillance intervals, using both simple and composite alternative hypotheses. We investigate the properties of the methods analytically in a simple setting and by simulations in more realistic scenarios. The methods are applied to data on influenza vaccine and Bell's palsy, and to data on measles, mumps and rubella vaccine and bleeding disorders.     

A random effects model for diseases with heterogeneous rates of infection

One form of data collected in the study of infectious diseases is on the transmission of a disease within households. We consider a model which allows the rate of disease transmission to vary between households. A Bayesian hierarchical approach to fitting the model is proposed and is implemented by the Metropolis–Hastings algorithm, a standard Markov chain Monte Carlo (MCMC) method. Results are presented for both simulated epidemic chain data and the Providence measles data, illustrating the potential that MCMC methods have to dealing with heterogeneity in infectious disease transmission.     

FAMILY BUILDING DIFFERENCES BETWEEN SAME SEX AND MIXED SEX FAMILIES IN AUSTRALIA

From this investigation it seems that an aversion among some couples to a same sex family has some relevance in family building. However, although there are significant differences in the proportions of same sex and mixed sex families having an additional child, the overall effect on average family size of the (apparent) attempt to achieve a child of each sex appears to be slight—an increase of less than 3% in the case of the Melbourne data. Despite the evidence that a significantly greater proportion of women with same sex families have another child, relatively few women admit that the sex structure of the children was the main factor in such a decision. Another insight into the relationship between sex structure and family building was that the desire for a child of each sex may have a negative effect on fertility in that couples who have already achieved such a configuration may decide not to have an additional child that they had originally planned to have. Obviously, it is difficult to separate attitudes to the importance of having both sons and daughters from rationalisations associated with the sex structure of the respondent's own family. Nevertheless the desire for children of each sex seems to be related to traditional attitudes to woman's role, Southern European background, an earlier year of birth, and a lower level of education. However, at the same time women in these categories, particularly the last, seem to be relatively less likely to exhibit behaviour indicative of a controlled response to the sex structure of the family; thus among such groups the probability of same sex families having another child is found to be relatively similar to the proportion of mixed sex families having another child. In other words, they are less likely than other women, who care less about having both sons and daughters, to stop at two (or three) children when at least one son and one daughter have been attained. What of the future relationship between proportions of same sex and mixed sex families having another child? Although it would seem that the combined effect of better educational opportunities and less traditional attitudes of each new generation would further reduce the importance attached to having both sons and daughters, at the same time one would expect an increase in a couple's ability to stop family building when two or three children of the desired sex structure had been achieved. Another factor is that possibly an increasing preference for smaller families will outweigh the wish to have a third (or fourth) child to achieve one child of each sex or for any other reason.     

A parametric method for census based estimation of child mortality

"A parametric method for estimating child mortality from reports concerning children ever born and surviving children is presented. In contrast with previously proposed methods, it facilitates use of single-year age reports by mothers on the survival of their children. In addition, the new method makes it possible to incorporate a priori knowledge of child mortality and fertility in the estimation process. The new method is illustrated by means of an application to data from the 1976 Western Samoa census."     

Analysing survey data with incomplete responses by using a method based on empirical likelihood

Summary.  In many surveys, missing response is a common problem. As an example, Zahner, Jacobs, Freeman and Trainor analysed data from a study of child psychopathology in the State of Connecticut, USA. In that study, the response variable, psychopathology, was inferred from questions that were addressed to teachers of the children and was subject to a high level of missingness. However, the missing responses were supplemented by surrogate information that was provided by the parents and/or the primary care providers of the children. In such a situation, it is conceivable that the supplemental information can be used to recover some of the information that has been lost in the cases with missing response. This paper considers a method using empirical likelihood. Empirical likelihood is well known in providing nonparametric inference. But its application has largely been confined to complete-data situations. The method proposed exploits the semiparametric nature of empirical likelihood. The method gives consistent estimates if the cases with non-missing responses form a random sample of the population. In large samples, the method behaves similarly to a regression estimate that is applied to estimating equations. The method is easy to implement with standard statistical packages. In a small sample study, the method was found to give favourable results, when compared with existing methods.     

career story: The importance of being ERNIE

ERNIE is the Electronic Random Number Indicator Equipment that caused huge interest in 1957 when it began selecting prize-winners for the new Premium Bonds, the first government-sponsored gamble in Britain in modern times. Stephanie Shirley was a young statistician working on ERNIE. Today, as Steve Shirley or Dame Stephanie , she is one of the wealthiest women in Britain—not through winning on Premium Bonds herself, but through the pioneering software company she formed which, for the first time, gave female-friendly employment to women programmers (and statisticians) who had children and dependants at home to care for. She is now a major philanthropist and a driving force for research into the social effects of the Internet and into autism. She has given more than £50 million to charities in those fields. Julian Champkin interviews her.     

图书出版流程、知识螺旋与员工创新行为的影响研究——基于国内少儿出版社转企改制的实证调查

立足近两年中国出版行业转企改制后的现状,以图书出版流程四维度为解释变量,知识螺旋为中介变量,构建了影响员工创新行为的结构方程模型,基于中国56家少儿出版社279份问卷调查的样本数据进行实证分析。研究发现:首先,图书流程中的选题策划、技术选择和营销服务分别显著影响员工创新行为,编校质量对员工创新行为的影响作用不显著;其次,选题策划、编校质量和技术选择分别显著影响知识螺旋,营销服务对知识螺旋的影响作用不显著;最后,知识螺旋在选题策划与员工创新行为间具有部分中介效应,知识螺旋在技术选择与员工创新行为间具有部分中介效应,知识螺旋在编校质量与员工创新行为间具有完全中介效应,知识螺旋在营销服务与员工创新行为间的中介效应不显著。     

子女数量对家庭收入的影响

基于2005年全国1%人口抽样调查数据,利用生育偏好和生育政策的城乡差异构造工具变量,实证分析子女数量对家庭收入的影响。结果显示,子女数量的增加显著抑制家庭收入的提升,生育二胎导致家庭收入平均下降20.8%。此外,这种负向影响还表现出显著的城乡差异,农村家庭生育二胎使得家庭收入显著下降8.8%,而城镇家庭收入则下降21.2%。进一步地,区分是否三代同住以及母亲职业类型家庭的异质性分析结果显示,在非三代同住家庭、母亲在机关企事业单位任领导职务或从事专业技术类职业的家庭中,子女数量对家庭收入均具有显著的负向影响。分析结论凸显了宏观层面人口结构调整和居民收入提升以及微观层面生育决策与家庭收入之间的双重权衡。     

Measurement and analysis of demographic processes: the characteristics of generation

Since it would take too long (100 years) to ascertain all demographic data about a given age group, i.e., all those born in a given year, these data are determined hypothetically by measuring the various characteristics of persons of all ages in a given time period (1-2 years). Also needed is an indicator of the population as a whole; cumulative coefficients are used for this purpose. One of these is the overall coefficient of births, meaning the number of children a women would have over her whole period of fertility if she had the precise number of children at each period in her life as other women of that age. An analogous indicator is used for measuring mortality--the average life expectancy of a person at each stage in his life. The crude coefficient of population reproduction represents the number of girls to which each woman will give birth between the ages of 15 and 50. This has to be corrected by the number of those who will not live to reproductive age. The result is the corrected coefficient of reproduction of the female population. This coefficient is often thought to reflect the population's growth prospects; if less than unity, therefore, the population will not reproduce itself. This is an incorrect interpretation. The impact of immigration and emigration on the population must also be incorportated. In addition to the above hypothetical indicators, we must also develop real population indicators. Techniques must also be employed to evaluate the reliability of these demographic indicators.     

Moo-cow! Mummy! More! How do children learn so many words?

Learning the words of your language is a huge challenge for children. In particular, it is a challenge of scale. At least 40,000 words have to be learnt. At 18 months a child's vocabulary starts to explode. How do they do it? Bob McMurray says it is all to down to statistics.