Analysis of familial aggregation in the presence of varying family sizes

Summary.  Family studies are frequently undertaken as the first step in the search for genetic and/or environmental determinants of disease. Significant familial aggregation of disease is suggestive of a genetic aetiology for the disease and may lead to more focused genetic analysis. Of course, it may also be due to shared environmental factors. Many methods have been proposed in the literature for the analysis of family studies. One model that is appealing for the simplicity of its computation and the conditional interpretation of its parameters is the quadratic exponential model. However, a limiting factor in its application is that it is not reproducible , meaning that all families must be of the same size. To increase the applicability of this model, we propose a hybrid approach in which analysis is based on the assumption of the quadratic exponential model for a selected family size and combines a missing data approach for smaller families with a marginalization approach for larger families. We apply our approach to a family study of colorectal cancer that was sponsored by the Cancer Genetics Network of the National Institutes of Health. We investigate the properties of our approach in simulation studies. Our approach applies more generally to clustered binary data.     

论《怀念狼》三段论手法的审美意蕴

“三”是生活中常见的数字。民间叙事文学中“三”的运用形成了循环往复、意蕴丰富的艺术手法。《怀念狼》较为成功地将民间叙事的三段原理创化为审美三段论手法:人物塑造三段论在社会背景下塑造鲜活的人物形象,在人与自然的矛盾冲突中展示复杂的人物性格,挖掘人物悲剧性命运的美学意义;情节演进三段论通过单纯的意象性情节变化强化作品的可读性,探寻人物心路历程,展示广阔的社会生活和时代病症。     

Applications of a simple regression model to acid rain data

This paper addresses two vital and seemingly simple questions concerning wet deposition of sulfates, a major contributor to acid rain. The first is to estimate the annual wet deposition of sulfate at a monitoring site under emissions that existed during the 1980s. This problem is complicated by missing data. The second is to estimate accurately the effect of a change in pollution emissions on concentrations of sulfate in precipitation. This problem is made difficult by the substantial natural variations in sulfate concentrations due to weather variations between years. As a tool for addressing both of these problems, we develop a regression model for the sulfate concentration of precipitation on a particular day as a function of amount of precipitation and time of the year. The model is used as a basis for imputing missing sulfate concentrations to handle the missing-data problem. It is also used to explain some of the variability in annual sulfate concentrations due to meteorology and hence provide more accurate estimates of the effect of changes in emissions.     

Bias correction in logistic regression with missing categorical covariates

Logistic regression plays an important role in many fields. In practice, we often encounter missing covariates in different applied sectors, particularly in biomedical sciences. Ibrahim (1990) proposed a method to handle missing covariates in generalized linear model (GLM) setup. It is well known that logistic regression estimates using small or medium sized missing data are biased. Considering the missing data that are missing at random, in this paper we have reduced the bias by two methods; first we have derived a closed form bias expression using Cox and Snell (1968), and second we have used likelihood based modification similar to Firth (1993). Here we have analytically shown that the Firth type likelihood modification in Ibrahim led to the second order bias reduction. The proposed methods are simple to apply on an existing method, need no analytical work, with the exception of a little change in the optimization function. We have carried out extensive simulation studies comparing the methods, and our simulation results are also supported by a real world data.     

Inference about parameters in Binomial-Poisson distribution with additional incomplete data

ABSTRACT

This article considers the distribution of Binomial-Poisson random vector which has two components and includes two parameters: one is the rate of a Poisson distribution, the other is the proportion in a Binomial distribution. The inference about the two parameters is usually made based on only paired observations. However, the number of paired observations is, in general, not large enough because of either technical difficulty or budget limitation, and so one can not make efficient inferences with only paired data. Instead, it is often much easier and not too costly to have incomplete observation on only one component independently. In this article we will combine both the paired complete data and unpaired incomplete data for estimating the two parameters. The performances of various estimators are compared both analytically and numerically. It is observed that fully using the unpaired incomplete data can always improve the inference, and the improvement is very significant in the case when there are only a few paired complete observations.     

Disaggregating Data Using Related Series

Quarterly real GNP and implicit GNP deflator series are derived for the 1948–1970 period using the related series technique of Chow and Lin. These estimated series are compared with the official, revised series; to official, unrevised series; and to univariate proxies using regression, time series, and spectral methods. The derived series possess autocorrelation and turning point characteristics similar to those of the official, revised series. The derived series also deliver structural equation parameter estimates similar to those based on official, revised data.     

A study of regression calibration in a partially observed stratified Cox model

Regression calibration is a simple method for estimating regression models when covariate data are missing for some study subjects. It consists in replacing an unobserved covariate by an estimator of its conditional expectation given available covariates. Regression calibration has recently been investigated in various regression models such as the linear, generalized linear, and proportional hazards models. The aim of this paper is to investigate the appropriateness of this method for estimating the stratified Cox regression model with missing values of the covariate defining the strata. Despite its practical relevance, this problem has not yet been discussed in the literature. Asymptotic distribution theory is developed for the regression calibration estimator in this setting. A simulation study is also conducted to investigate the properties of this estimator.     

Symmetric pattern models: a latent variable approach to item non-response in attitude scales

This paper proposes a new approach to the treatment of item non-response in attitude scales. It combines the ideas of latent variable identification with the issues of non-response adjustment in sample surveys. The latent variable approach allows missing values to be included in the analysis and, equally importantly, allows information about attitude to be inferred from non-response. We present a symmetric pattern methodology for handling item non-response in attitude scales. The methodology is symmetric in that all the variables are given equivalent status in the analysis (none is designated a 'dependent' variable) and is pattern based in that the pattern of responses and non-responses across individuals is a key element in the analysis. Our approach to the problem is through a latent variable model with two latent dimensions: one to summarize response propensity and the other to summarize attitude, ability or belief. The methodology presented here can handle binary, metric and mixed (binary and metric) manifest items with missing values. Examples using both artificial data sets and two real data sets are used to illustrate the mechanism and the advantages of the methodology proposed.     

Empirical likelihood for the response mean of generalized linear models with missing at random responses

In this article, we present a new empirical likelihood ratio for constructing the confidence interval of the response mean of generalized linear models with missing at random responses. Compared with the existing methods, the proposal can avoid the so-called “curse of dimensionality” problem when the dimension of covariates is high, and is still chi-squared distributed asymptotically, nevertheless. Simulation studies are also provided to illustrate the performance of the developed method.     

Bayesian analysis for partially observed network data,missing ties,attributes and actors

We consider partially observed network data as defined in Handcock and Gile (2010). More specifically we introduce an elaboration of the Bayesian data augmentation scheme of Koskinen et al. (2010) that uses the exchange algorithm (Caimo and Friel, 2011) for inference for the exponential random graph model (ERGM) where tie variables are partly observed. We illustrate the generating of posteriors and unobserved tie-variables with empirical network data where 74% of the tie variables are unobserved under the assumption that some standard assumptions hold true. One of these assumptions is that covariates are fixed and completely observed. A likely scenario is that also covariates might only be partially observed and we propose a further extension of the data augmentation algorithm for missing attributes. We provide an illustrative example of parameter inference with nearly 30% of dyads affected by missing attributes (e.g. homophily effects). The assumption that all actors are known is another assumption that is liable to be violated so that there are “covert actors”. We briefly discuss various aspects of this problem with reference to the Sageman (2004) data set on suspected terrorists. We conclude by identifying some areas in need of further research.