Penalized spline joint models for longitudinal and time-to-event data

The joint models for longitudinal data and time-to-event data have recently received numerous attention in clinical and epidemiologic studies. Our interest is in modeling the relationship between event time outcomes and internal time-dependent covariates. In practice, the longitudinal responses often show non linear and fluctuated curves. Therefore, the main aim of this paper is to use penalized splines with a truncated polynomial basis to parameterize the non linear longitudinal process. Then, the linear mixed-effects model is applied to subject-specific curves and to control the smoothing. The association between the dropout process and longitudinal outcomes is modeled through a proportional hazard model. Two types of baseline risk functions are considered, namely a Gompertz distribution and a piecewise constant model. The resulting models are referred to as penalized spline joint models; an extension of the standard joint models. The expectation conditional maximization (ECM) algorithm is applied to estimate the parameters in the proposed models. To validate the proposed algorithm, extensive simulation studies were implemented followed by a case study. In summary, the penalized spline joint models provide a new approach for joint models that have improved the existing standard joint models.     

二美杂会还是洁秽相混？——屈赋“芳泽杂糅”诸句释意简析

对屈原《离骚》等作品中的"芳与泽其杂糅兮"诸句,古今学者的解释存在分歧和矛盾。本文支持王逸以来释"芳与泽"为芳香与润泽的观点,并分析了解"泽"作与"芳"相对的污秽、垢腻之类义项的释意的错误原因,指出其思路与前提本不确当,可以视为读懂古书、解决某些字句训释分歧时应吸取的经验教训。     

Tests and Confidence Intervals for an Extended Variance Component Using the Modified Likelihood Ratio Statistic

Abstract.  The large deviation modified likelihood ratio statistic is studied for testing a variance component equal to a specified value. Formulas are presented in the general balanced case, whereas in the unbalanced case only the one-way random effects model is studied. Simulation studies are presented, showing that the normal approximation to the large deviation modified likelihood ratio statistic gives confidence intervals for variance components with coverage probabilities very close to the nominal confidence coefficient.     

On the analysis of multivariate repeated measures designs

The relationship between the mixed-model analysis and multivariate approach to a repeated measures design with multiple responses is presented. It is shown that by taking the trace of the appropriate submatrix of the hypothesis (error) sums of squares and crossproducts (SSCP) matrix obtained from the multivariate approach, one can get the hypothesis (error) SSCP matrix for the mixed-model analysis. Thus, when analyzing data from a multivariate repeated measures design, it is advantageous to use the multivariate approach because the result of the mixed-model analysis can also be obtained without additional computation.     

Constructing optimal designs for fitting pharmacokinetic models

We consider some computational issues that arise when searching for optimal designs for pharmacokinetic (PK) studies. Special factors that distinguish these are (i) repeated observations are taken from each subject and the observations are usually described by a nonlinear mixed model (NLMM), (ii) design criteria depend on the model fitting procedure, (iii) in addition to providing efficient parameter estimates, the design must also permit model checking, (iv) in practice there are several design constraints, (v) the design criteria are computationally expensive to evaluate and often numerical integration is needed and finally (vi) local optimisation procedures may fail to converge or get trapped at local optima.We review current optimal design algorithms and explore the possibility of using global optimisation procedures. We use these latter procedures to find some optimal designs.For multi-purpose designs we suggest two surrogate design criteria for model checking and illustrate their use.     

The Effect of Drop-Out on the Efficiency of Longitudinal Experiments

It is shown that drop-out often reduces the efficiency of longitudinal experiments considerably. In the framework of linear mixed models, a general, computationally simple method is provided, for designing longitudinal studies when drop-out is to be expected, such that there is little risk of large losses of efficiency due to the missing data. All the results are extensively illustrated using data from a randomized experiment with rats.     

关于孟德斯鸠分权理论的几个问题

近代以前的西方分权理论表现为混合政体理论，其本质是阶级分权，平衡社会各阶级之间的利益。孟德斯鸠对分权理论的贡献是把自由与分权相联系，并具体提出了三权分立的方案。三权分立只是现代国家分权模式的一种，它一般适用于内忧外患较少的国家。要实现真正的三权分立与制衡，局部的权力混合交叉是必要的。议会制国家事实上是议行合一。分权除了防止权力的滥用外，还能提高政府的工作效率。     

高阶混合型周期系统的周期解

应用Ｆｏｕｒｉｅｒ分析的方法，结合一些不等式技巧得到了ｎ阶常系数带有滞后与超前偏差变元的混合型线性周期系统存在周期解的充要条件．     

Feature significance in generalized additive models

This paper develops inference for the significance of features such as peaks and valleys observed in additive modeling through an extension of the SiZer-type methodology of Chaudhuri and Marron (1999) and Godtliebsen et al. (2002, 2004) to the case where the outcome is discrete. We consider the problem of determining the significance of features such as peaks or valleys in observed covariate effects both for the case of additive modeling where the main predictor of interest is univariate as well as the problem of studying the significance of features such as peaks, inclines, ridges and valleys when the main predictor of interest is geographical location. We work with low rank radial spline smoothers to allow to the handling of sparse designs and large sample sizes. Reducing the problem to a Generalised Linear Mixed Model (GLMM) framework enables derivation of simulation-based critical value approximations and guards against the problem of multiple inferences over a range of predictor values. Such a reduction also allows for easy adjustment for confounders including those which have an unknown or complex effect on the outcome. A simulation study indicates that our method has satisfactory power. Finally, we illustrate our methodology on several data sets.     

AN ALGORITHMIC APPROACH TO BAYESIAN LINEAR MODEL CALCULATIONS

A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects.