Estimation in regression models for longitudinal binary data with outcome-dependent follow-up

In many observational studies, individuals are measured repeatedly over time, although not necessarily at a set of pre-specified occasions. Instead, individuals may be measured at irregular intervals, with those having a history of poorer health outcomes being measured with somewhat greater frequency and regularity. In this paper, we consider likelihood-based estimation of the regression parameters in marginal models for longitudinal binary data when the follow-up times are not fixed by design, but can depend on previous outcomes. In particular, we consider assumptions regarding the follow-up time process that result in the likelihood function separating into two components: one for the follow-up time process, the other for the outcome measurement process. The practical implication of this separation is that the follow-up time process can be ignored when making likelihood-based inferences about the marginal regression model parameters. That is, maximum likelihood (ML) estimation of the regression parameters relating the probability of success at a given time to covariates does not require that a model for the distribution of follow-up times be specified. However, to obtain consistent parameter estimates, the multinomial distribution for the vector of repeated binary outcomes must be correctly specified. In general, ML estimation requires specification of all higher-order moments and the likelihood for a marginal model can be intractable except in cases where the number of repeated measurements is relatively small. To circumvent these difficulties, we propose a pseudolikelihood for estimation of the marginal model parameters. The pseudolikelihood uses a linear approximation for the conditional distribution of the response at any occasion, given the history of previous responses. The appeal of this approximation is that the conditional distributions are functions of the first two moments of the binary responses only. When the follow-up times depend only on the previous outcome, the pseudolikelihood requires correct specification of the conditional distribution of the current outcome given the outcome at the previous occasion only. Results from a simulation study and a study of asymptotic bias are presented. Finally, we illustrate the main results using data from a longitudinal observational study that explored the cardiotoxic effects of doxorubicin chemotherapy for the treatment of acute lymphoblastic leukemia in children.     

A generalized mover-stayer model for panel data

A generalized mover-stayer model is described for conditionally Markov processes under panel observation. Marginally the model represents a mixture of nested continuous-time Markov processes in which sub-models are defined by constraining some transition intensities to zero between two or more states of a full model. A Fisher scoring algorithm is described which facilitates maximum likelihood estimation based only on the first derivatives of the transition probability matrices. The model is fit to data from a smoking prevention study and is shown to provide a significant improvement in fit over a time-homogeneous Markov model. Extensions are developed which facilitate examination of covariate effects on both the transition intensities and the mover-stayer probabilities.     

Linear Logistic Latent Class Analysis

In the present paper the linear logistic extension of latent class analysis is described. Thereby it is assumed that the item latent probabilities as well as the class sizes can be attributed to some explanatory variables. The basic equations of the model state the decomposition of the log-odds of the item latent probabilities and of the class sizes into weighted sums of basic parameters representing the effects of the predictor variables. Further, the maximum likelihood equations for these effect parameters and statistical tests for goodness-of-fit are given. Finally, an example illustrates the practical application of the model and the interpretation of the model parameters.     

Flexible generalized t-link models for binary response data

A critical issue in modelling binary response data is the choiceof the links. We introduce a new link based on the generalizedt-distribution. There are two parameters in the generalizedt-link: one parameter purely controls the heaviness of the tailsof the link and the second parameter controls the scale of thelink. Two major advantages are offered by the generalized t-links.First, a symmetric generalized t-link with an unknown shapeparameter is much more identifiable than a Student t-link withunknown degrees of freedom and a known scale parameter. Secondly,skewed generalized t-links with both unknown shape and scaleparameters provide much more flexible and improved skewed linkregression models than the existing skewed links. Various theoreticalproperties and attractive features of the proposed links areexamined and explored in detail. An efficient Markov chain MonteCarlo algorithm is developed for sampling from the posteriordistribution. The deviance information criterion measure isused for guiding the choice of links. The proposed methodologyis motivated and illustrated by prostate cancer data.     

基于贝叶斯网潜类模型的高维SNPs分析

采用贝叶斯(Bayesian)网的潜类模型对GAW17高维SNPs数据进行分析,为复杂性状疾病遗传以及基因定位等方面的研究提供新的方法支持。本研究从GAW17提供的包含697个个体22条常染色体的上万个SNP中,随机挑选出1号染色体上12个基因的29个SNPs作为研究对象。按照累计信息贡献率达到95%的原则,应用贝叶斯网潜变量模型选出C1S11408,C1S3201,C1S1786等15个与X0互信息量大的SNPs位点来对研究人群进行分类与解释。结果表明697个个体总的被分为2个潜在类别,各类别的概率分别为0.68和0.32。对两类人群的疾病分布状况进行分析,结果表明二者不一致,第二个类别人群患病率(38.64%)明显高于第一个类别人群(25.99%)(χ2=11.46,P=0.001)。由此可见,两类人群疾病患病率的差别正是由选出的15个SNPs造成的,从而有理由认为这些SNPs为可疑致病位点,为进一步的研究提供明确的思路。