Regression Diagnostics of the Semiparametric Proportional Rate Model for Irregularly Spaced Repeated Measurements

Counting process techniques have been successfully introduced to semiparametric inference of repeated measurements. Cheng and Wei (2000 Cheng , S. C. , Wei , L. J. ( 2000 ). Inference for a semiparametric model with panel data . Biometrika 87 : 89 – 97 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed a simple inference procedure for the semiparametric proportional rate model, which reduces to relative risk regression models for binary data. While the baseline mean functions are completely unspecified, it still requires several assumptions for valid inference. In this article, a goodness-of-fit test for it is proposed based on cumulative residuals. Theoretical justification is provided and an illustration with a dataset from a clinical trial is given. Results of simulation studies to evaluate finite sample performance are also provided.     

Estimation of treatment effects based on possibly misspecified Cox regression

In randomized clinical trials, a treatment effect on a time-to-event endpoint is often estimated by the Cox proportional hazards model. The maximum partial likelihood estimator does not make sense if the proportional hazard assumption is violated. Xu and O'Quigley (Biostatistics 1:423-439, 2000) proposed an estimating equation, which provides an interpretable estimator for the treatment effect under model misspecification. Namely it provides a consistent estimator for the log-hazard ratio among the treatment groups if the model is correctly specified, and it is interpreted as an average log-hazard ratio over time even if misspecified. However, the method requires the assumption that censoring is independent of treatment group, which is more restricted than that for the maximum partial likelihood estimator and is often violated in practice. In this paper, we propose an alternative estimating equation. Our method provides an estimator of the same property as that of Xu and O'Quigley under the usual assumption for the maximum partial likelihood estimation. We show that our estimator is consistent and asymptotically normal, and derive a consistent estimator of the asymptotic variance. If the proportional hazards assumption holds, the efficiency of the estimator can be improved by applying the covariate adjustment method based on the semiparametric theory proposed by Lu and Tsiatis (Biometrika 95:679-694, 2008).     

Tracing wealth,cooperation and trust: A comparison of two great plains communities

This research examines the relationships between wealth, cooperation, and trust. Utilizing implications from the social capital literature and democratic theory, we found that trust directly affects patterns of socio-economic interactions, especially shopping. We also found that commuting was widespread and it created a rural sprawl deficit that affected trust. Specifically, the results indicated that trust of others in the community (generalized to a certain degree) tended to encourage people to shop more in town, thus contributing to the development of the community, even when controlling for commuting. Findings from this study suggest that further community level research will yield more specifics about how trust (and social capital) works to increase wealth in a community.     

A Bayesian hierarchical mixture model for platelet-derived growth factor receptor phosphorylation to improve estimation of progression-free survival in prostate cancer

Summary.  Advances in understanding the biological underpinnings of many cancers have led increasingly to the use of molecularly targeted anticancer therapies. Because the platelet-derived growth factor receptor (PDGFR) has been implicated in the progression of prostate cancer bone metastases, it is of great interest to examine possible relationships between PDGFR inhibition and therapeutic outcomes. We analyse the association between change in activated PDGFR (phosphorylated PDGFR) and progression-free survival time based on large within-patient samples of cell-specific phosphorylated PDGFR values taken before and after treatment from each of 88 prostate cancer patients. To utilize these paired samples as covariate data in a regression model for progression-free survival time, and be cause the phosphorylated PDGFR distributions are bimodal, we first employ a Bayesian hierarchical mixture model to obtain a deconvolution of the pretreatment and post-treatment within-patient phosphorylated PDGFR distributions. We evaluate fits of the mixture model and a non-mixture model that ignores the bimodality by using a supnorm metric to compare the empirical distribution of each phosphorylated PDGFR data set with the corresponding fitted distribution under each model. Our results show that first using the mixture model to account for the bimodality of the within-patient phosphorylated PDGFR distributions, and then using the posterior within-patient component mean changes in phosphorylated PDGFR so obtained as covariates in the regression model for progression-free survival time, provides an improved estimation.     

Mantel-Haenszel estimators for irregular sparse K2×J tables

This paper deals with sparse K2×J(J>2)$K2\times J(J>2)$ tables. Projection-method Mantel–Haenszel (MH) estimators of the common odds ratios have been proposed for K2×J$K2\times J$ tables, which include Greenland's generalized MH estimator as a special case. The method projects log-transformed MH estimators for all K2×2$K2\times 2$ subtables, which were called naive MH estimators, onto a linear space spanned by log odds ratios. However, for sparse tables it is often the case that naive MH estimators are unable to be computed. In this paper we introduce alternative naive MH estimators using a graph that represents K2×J$K2\times J$ tables, and apply the projection to these alternative estimators. The idea leads to infinitely many reasonable estimators and we propose a method to choose the optimal one by solving a quadratic optimization problem induced by the graph, where some graph-theoretic arguments play important roles to simplify the optimization problem. An illustration is given using data from a case–control study. A simulation study is also conducted, which indicates that the MH estimator tends to have a smaller mean squared error than the MH estimator previously suggested and the conditional maximum likelihood estimator for sparse tables.     

Preventive replacement policies with products update announcements

Abstract

When we consider the improvement of the functional performances that are released by the new updates of the products, it is an interesting problem to revisit the existing replacement policies. For such a viewpoint, four replacement models with product update announcements, i.e., PUA for abbreviation, are given in this paper: Model 1, the unit is replaced at time T or at PUA over time T. Model 2, the unit is replaced at the Kth failure or at PUA over the Kth failure. By considering both time T and failure K, Models 3 and 4 are obtained based on the approaches of replacement first and last. We obtain the expected cost rates for four models and discuss analytically their optimal replacement policies Further, numerical examples are given when the time for PUA has an exponential distribution.     

Efficient Regularization Parameter Selection Via Information Criteria

In a nonlinear regression model based on a regularization method, selection of appropriate regularization parameters is crucial. Information criteria such as generalized information criterion (GIC) and generalized Bayesian information criterion (GBIC) are useful for selecting the optimal regularization parameters. However, the optimal parameter is often determined by calculating information criterion for all candidate regularization parameters, and so the computational cost is high. One simple method by which to accomplish this is to regard GIC or GBIC as a function of the regularization parameters and to find a value minimizing GIC or GBIC. However, it is unclear how to solve the optimization problem. In the present article, we propose an efficient Newton–Raphson type iterative method for selecting optimal regularization parameters with respect to GIC or GBIC in a nonlinear regression model based on basis expansions. This method reduces the computational time remarkably compared to the grid search and can select more suitable regularization parameters. The effectiveness of the method is illustrated through real data examples.     

Euler characteristic heuristic for approximating the distribution of the largest eigenvalue of an orthogonally invariant random matrix

The Euler characteristic heuristic has been proposed as a method for approximating the upper tail probability of the maximum of a random field with smooth sample path. When the random field is Gaussian, this method is proved to be valid in the sense that the relative approximation error is exponentially smaller. However, very little is known about the validity of the method when the random field is non-Gaussian. In this paper, as a milestone to developing the general theory about the validity of the Euler characteristic heuristic, we examine the Euler characteristic heuristic for approximating the distribution of the largest eigenvalue of an orthogonally invariant non-Gaussian random matrix. In this particular example, if the probability density function of the random matrix converges to zero sufficiently fast at the boundary of its support, the approximation error of the Euler characteristic heuristic is proved to be small and the approximation is valid. Moreover, for several standard orthogonally invariant random matrices, the approximation formula for the distribution of the largest eigenvalue and its asymptotic error are obtained explicitly. Our formulas are practical enough for the purpose of numerical calculations.     

日本横滨大同学校之创立

日本横滨大同学校是康有为、梁启超等维新派和孙中山、陈少白等革命派共同创办的华侨子弟教育机构。以前的研究由于资料不足和革命派与维新派的记载互有出入，所以关于大同学校的创办日期众说纷纭，正确的说法应该是分别从“创立”、“开校”两个不同层面来判断。日本大同学校的创立不仅反映了革命派与维新派的不同教育价值观，也折射出清末政治的潮起潮落。     

《礼纬含文嘉·精魅篇》的辟邪思想与鬼神观

台湾图书馆、浙江省图书馆所藏《礼纬含文嘉》是十分珍贵的包括天文五行占等的占书资料。虽然此书在宋代到清代的各种资料中被提及,但因为传本极少,所以至今一直被学者们所忽略。其所载《精魅篇》实际上是《白泽图》辟邪文化发展史上非常重要的资料之一。本文拟基于已往的成果来探讨《礼纬含文嘉·精魅篇》的辟邪思想与作为其背景的鬼神观,并进一步研究《白泽图》与由此派生的辟邪文物,以及它们在朝鲜与日本的传播。