Type I error rates from likelihood‐based repeated measures analyses of incomplete longitudinal data

The last observation carried forward (LOCF) approach is commonly utilized to handle missing values in the primary analysis of clinical trials. However, recent evidence suggests that likelihood‐based analyses developed under the missing at random (MAR) framework are sensible alternatives. The objective of this study was to assess the Type I error rates from a likelihood‐based MAR approach – mixed‐model repeated measures (MMRM) – compared with LOCF when estimating treatment contrasts for mean change from baseline to endpoint (Δ). Data emulating neuropsychiatric clinical trials were simulated in a 4 × 4 factorial arrangement of scenarios, using four patterns of mean changes over time and four strategies for deleting data to generate subject dropout via an MAR mechanism. In data with no dropout, estimates of Δ and SE_Δ from MMRM and LOCF were identical. In data with dropout, the Type I error rates (averaged across all scenarios) for MMRM and LOCF were 5.49% and 16.76%, respectively. In 11 of the 16 scenarios, the Type I error rate from MMRM was at least 1.00% closer to the expected rate of 5.00% than the corresponding rate from LOCF. In no scenario did LOCF yield a Type I error rate that was at least 1.00% closer to the expected rate than the corresponding rate from MMRM. The average estimate of SE_Δ from MMRM was greater in data with dropout than in complete data, whereas the average estimate of SE_Δ from LOCF was smaller in data with dropout than in complete data, suggesting that standard errors from MMRM better reflected the uncertainty in the data. The results from this investigation support those from previous studies, which found that MMRM provided reasonable control of Type I error even in the presence of MNAR missingness. No universally best approach to analysis of longitudinal data exists. However, likelihood‐based MAR approaches have been shown to perform well in a variety of situations and are a sensible alternative to the LOCF approach. MNAR methods can be used within a sensitivity analysis framework to test the potential presence and impact of MNAR data, thereby assessing robustness of results from an MAR method. Copyright © 2004 John Wiley & Sons, Ltd.     

Statistik für bivariate gemischte Poisson–Prozesse am Beispiel der Kraftfahrthaftpflichtversicherung

Zusammenfassung: In diesem Artikel wird der Weg von einem univariaten gemischten Poisson–Prozess, der in vielen Bereichen zum Z?hlen von Ereignissen benutzt wird, zu einem bivariaten gemischten Poisson–Prozess aufgezeigt. Dazu werden einige Eigenschaften des bivariaten Prozesses angegeben. Im zweiten Teil der Arbeit wird gezeigt, wie mit Hilfe dieses Prozesses der übergang von einem herk?mmlichen Bonus–Malus–System in der Kraftfahrthaftpflichtversicherung zu einem Bonus–Malus–System mit Berücksichtigung der Schadenart beschritten werden kann. Dazu wird zuerst eine Modellprüfung der gegebenen Daten vorgenommen und sodann werden für verschiedene mischende Verteilungen die Verteilungsparameter gesch?tzt und Nettopr?mien angegeben sowie die Prognosegenauigkeit getestet.

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Summary: In this paper we show that the model of the bivariate mixed Poisson process arises in a natural way from the univariate mixed Poisson process, which is used in several areas for counting certain events. Furthermore we state some properties of the bivariate process. In the second part of the paper we illustrate how by means of the bivariate mixed Poisson process a bonus–malus system handling different types of accidents can be derived from the classical bonus–malus system in third–party liability insurance. To this end we first check the model on the given data and then estimate distribution parameters and compute net premiums for different mixing distributions as well as test the prediction probabilities.

* Vortrag am Dresdner Forum zur Versicherungsmathematik: Tarifierung in Erst- und Rückversicherung am 25. Juni 2004. Für die Unterstützung zu dieser Arbeit m?chte der Autor Lothar Partzsch, Klaus D. Schmidt (beide Dresden) und Friedemann Spies (München) recht herzlich danken.     

Local polynomial estimation of Poisson intensities in the presence of reporting delays

Summary.  The system for monitoring suicides in Hong Kong has considerable delays in reporting as the cause of death needs to be determined by a coroner's investigation. However, timely estimates of suicide rates are desirable to assist in the formulation of public health policies. This motivated us to develop a non-parametric procedure to estimate the intensity function of a Poisson process in the presence of reporting delays. We give closed form estimators of the Poisson intensity and the delay distribution, conduct simulation studies to evaluate the method proposed and derive their asymptotic properties. The method proposed is applied to estimate the intensity of suicide in Hong Kong.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

设计素描的四种基本功

设计素描作为学习设计的一门基础课程,通过观察方法、思维方式、表现形式、立体观念和细节刻画四个方面的介绍说明设计素描对于学习产品设计的重要性.     

一类变系数高阶线性齐次微分方程解的探求(英文)

本文对系数全为多项式和广义多项式的n阶线性齐次微分方程引入特征方程的概念。给出了具有指数型解的充要条件，推广了经典的常系数线性方程和著名的Euler方程的的解法，为求解变系数线性微分方程提供了有效的方法。     

Generalized Leverage and its Applications

The generalized leverage of an estimator is defined in regression models as a measure of the importance of individual observations. We derive a simple but powerful result, developing an explicit expression for leverage in a general M -estimation problem, of which the maximum likelihood problems are special cases. A variety of applications are considered, most notably to the exponential family non-linear models. The relationship between leverage and local influence is also discussed. Numerical examples are given to illustrate our results     

Three pseudo-paradoxes in ‘quantum’ decision theory: Apparent effects of observation on probability and utility

In quantum domains, the measurement (or observation) of one of a pair of complementary variables introduces an unavoidable uncertainty in the value of that variable's complement. Such uncertainties are negligible in Newtonian worlds, where observations can be made without appreciably disturbing the observed system. Hence, one would not expect that an observation of a non-quantum probabilistic outcome could affect a probability distribution over subsequently possible states, in a way that would conflict with classical probability calculations. This paper examines three problems in which observations appear to affect the probabilities and expected utilities of subsequent outcomes, in ways which may appear paradoxical. Deeper analysis of these problems reveals that the anomalies arise, not from paradox, but rather from faulty inferences drawn from the observations themselves. Thus the notion of quantum decision theory is disparaged.     

学校本位教学视导模式的实证研究——以兰州市E中学为例

本研究目的在于通过对兰州市E中学施行的学校本位教学视导模式的深入观察,全方位了解学校本位教学视导模式的具体运作方式。以兰州市一所薄弱学校为研究场域,通过课堂观察的方式,全面了解学校为提高办学质量所开展的“学案分组教学法”,及进行学校本位化视导模式的具体运作状态。在兰州市E中学开展学校本位教学视导模式的过程中,学校校长与某大学教育学院课程与教学领域的教授专家参与视导过程。主要采取校长主导,专家参与的合作视导方式,对兰州市E中学初中二年级屈老师数学课进行为期一周的教学观察与记录。实施以学校为本位的合作视导方式,目的在于发现兰州市E中学进行“学案分组教学法”中的具体教学问题,通过大学与中学的合作,开展学校本位视导模式,有效促进教师的专业发展与增强教学有效性,提高学校办学质量。     

新型农业经营主体的经营绩效与差异分析——基于农村固定观察点的数据调查

新型农业经营主体的经营绩效关系到其可持续发展。采用农村固定观察点对我国各省区新型农业经营主体的调查数据,运用随机前沿分析法,对不同类型的经营主体的经营绩效进行分析,并进一步分析新型农业经营主体的差异性。结果表明：相比小农户而言,新型农业经营主体的经营绩效相对较高,但是其平均绩效还有很大的改善空间;新型农业经营主体面临融资难和人才缺乏的问题,且该问题在农民专业合作社中最为突出;我国家庭农场的经营绩效在三种新型农业经营主体中是最高的,其次是农业（龙头）企业,最后是农民专业合作社。对此,提出应完善土地“三权分置”机制,实现新型农业经营主体的规模化生产,进一步解决其融资难和人才缺乏的问题,加大政策扶持力度等建议。