On a generalization of a result of W. G. Cochran

A relationship due to W.G. Cochran showing the effect on leastsquares regression coefficients of marginalizing over or conditioningon an explanatory variable is generalized to quantile regressioncoefficients. The condition under which conditioning does notinduce interaction or effect reversal is shown. Examples aregiven. The discussion is simplest when all variables are continuous;the extension to discrete variables is outlined.     

A general Akaike-type criterion for model selection in robust regression

Akaike's procedure (1970) for selecting a model minimises anestimate of the expected squared error in predicting new, independentobservations. This selection criterion was designed for modelsfitted by least squares. A different model-fitting technique,such as least absolute deviation regression, requires an appropriatemodel selection procedure. This paper presents a general Akaike-typecriterion applicable to a wide variety of loss functions formodel fitting. It requires only that the function be convexwith a unique minimum, and twice differentiable in expectation.Simulations show that the estimators proposed here well approximatetheir respective prediction errors.     

Regression Modeling of a Physiological Parameter Affected by Both Intrinsic and Extrinsic Factors

We discuss regression modeling of a physiological parameter affected by both intrinsic and extrinsic factors. Such parameter commonly exists in our daily life (e.g., the sleeping quality of human beings or other animals). An additive regression model is suggested which consists of two parts. The first part is for explaining the effect of intrinsic factors and the second part is for describing the effect of extrinsic factors. The fitted model is proved to be statistically consistent. Hypothesis tests about the model coefficients are also discussed. Some simulation results are presented and the modeling procedure is applied to a rat sleep data set.     

近五十年北京板栗始花物候对光合有效辐射变化的响应

与全球范围内气候变暖对植物物候影响研究相比,其他气候因素（如光合有效辐射PAR等）对物候影响报道较少,果树花期物候对光合有效辐射变化响应的研究更是未见报道。本研究以1963—2008年间北京板栗始花物候资料及相应的日光合有效辐射数据为基础,利用偏最小二乘回归法确定了PAR影响板栗始花物候的两个关键阶段,进而分析了两阶段内PAR、温度及相对湿度变化对板栗花期的具体影响。结果表明,北京过去50年两相关阶段内PAR呈显著下降趋势,其中9月24日至次年2月5日问PAR下降对板栗花期提前具有促进作用,可解释12％的花期提前趋势;2月6日至次年5月31日间PAR下降促使花期延迟,但未达显著水平（P〉0．1）。板栗花期提前主要与2月6日至次年5月31日间温度升高有关,其间温度变化可解释41％的花期提前趋势;其次是相对湿度,PAR变化对花期影响较小。鉴于PAR、温度及相对湿度间的互作效应,PAR和相对湿度对花期物候的影响可由温度效应加以解释。     

Response of Chestnut Flowering in Beijing to Photosynthetically Active Radiation Variation and Change in Recent Fifty Years

Climate warming has affected plant phenology throughout the world, but few studies have evaluated plant phenology response to other climate factors (eg. photosynthetically active radiation PAR). In particular, the response of fruit flowering to PAR variation has not been explored yet. Long term (1963-2008) of chestnut (Castanea mollissima Blume) first flowering dates from Beijing, China were related with daily PAR for the 12 months, using Partial Least Squares (PLS) regression analysis. Two relevant phases were identified, during which mean PAR, temperature, and relative humidity (RH) were correlated with flowering dates, respectively. PAR during the both relevant periods decreased significantly in Beijing over the past 50 years. Reduced PAR during 24 September 5 February showed an advance impact on chestnut flowering, and could explain 12% of advance trend in flowering timing. Deceased PAR during 6 February 31 May had a delayed effect on tree flowering, but it was not significant enough to reject the null hypothesis of no impact over time. Advanced flowering of chestnut was mainly determined by increasing temperature between 6 February and 31 May which could explain 41% of flowering trend. Relative humidity variation during this period played secondly important role on tree flowering. Considering the interaction among these three climate factors, the impacts of PAR and RH on flowering timing could partially be attributed to the effects of temperature variation.     

Microarray gene expression data with linked survival phenotypes: diffuse large-B-cell lymphoma revisited

Diffuse large-B-cell lymphoma (DLBCL) is an aggressive malignancy of mature B lymphocytes and is the most common type of lymphoma in adults. While treatment advances have been substantial in what was formerly a fatal disease, less than 50% of patients achieve lasting remission. In an effort to predict treatment success and explain disease heterogeneity clinical features have been employed for prognostic purposes, but have yielded only modest predictive performance. This has spawned a series of high-profile microarray-based gene expression studies of DLBCL, in the hope that molecular-level information could be used to refine prognosis. The intent of this paper is to reevaluate these microarray-based prognostic assessments, and extend the statistical methodology that has been used in this context. Methodological challenges arise in using patients' gene expression profiles to predict survival endpoints on account of the large number of genes and their complex interdependence. We initially focus on the Lymphochip data and analysis of Rosenwald et al. (2002). After describing relationships between the analyses performed and gene harvesting (Hastie et al., 2001a), we argue for the utility of penalized approaches, in particular least angle regression-least absolute shrinkage and selection operator (Efron et al., 2004). While these techniques have been extended to the proportional hazards/partial likelihood framework, the resultant algorithms are computationally burdensome. We develop residual-based approximations that eliminate this burden yet perform similarly. Comparisons of predictive accuracy across both methods and studies are effected using time-dependent receiver operating characteristic curves. These indicate that gene expression data, in turn, only delivers modest predictions of posttherapy DLBCL survival. We conclude by outlining possibilities for further work.     

Fitting semiparametric additive hazards models using standard statistical software

The Cox proportional hazards model has become the standard in biomedical studies, particularly for settings in which the estimation covariate effects (as opposed to prediction) is the primary objective. In spite of the obvious flexibility of this approach and its wide applicability, the model is not usually chosen for its fit to the data, but by convention and for reasons of convenience. It is quite possible that the covariates add to, rather than multiply the baseline hazard, making an additive hazards model a more suitable choice. Typically, proportionality is assumed, with the potential for additive covariate effects not evaluated or even seriously considered. Contributing to this phenomenon is the fact that many popular software packages (e.g., SAS, S-PLUS/R) have standard procedures to fit the Cox model (e.g., proc phreg, coxph), but as of yet no analogous procedures to fit its additive analog, the Lin and Ying (1994) semiparametric additive hazards model. In this article, we establish the connections between the Lin and Ying (1994) model and both Cox and least squares regression. We demonstrate how SAS's phreg and reg procedures may be used to fit the additive hazards model, after some straightforward data manipulations. We then apply the additive hazards model to examine the relationship between Model for End-stage Liver Disease (MELD) score and mortality among patients wait-listed for liver transplantation.     

On Choosing Among Several Experimental Treatments and a Control

The two classical selection approaches in comparing experimental treatments with a control are combined to form an integrated approach. In this integrated approach, there is a preference zone (PZ) and an indifference zone (IZ), and the concept of a correct decision (CD) is defined differently in each of these zones. In the PZ, we are required to select the best treatment for a correct decision (CD₁) but in the IZ, we define any selected subset to be correct (CD₂) if it contains the best treatment among all the experimental treatments and the controlled treatment. We propose a single-stage procedure R to achieve the selection goals CD₁ and CD₂ simultaneously with certain probability requirements. It is shown that both the probability of a correct decision under PZ, P(CD₁ | PZ), and the probability of a correct decision under IZ, P(CD₂ | IZ), satisfy some monotonicity properties and the least favorable configuration in PZ and the worst configuration in IZ are derived by these properties. We also derive formulas for the probabilities of correct decision and provide a brief table to illustrate the magnitude of the procedure parameters and the common sample sizes needed for various probability requirements and configurations.     

Discretizing a Normal Prior for Change Point Estimation in Switching Regressions

Bayes decision procedures are considered for change point estimation in the simple bilinear segmented model. A discretized normal prior density is employed as the prior distribution for the change point index. Posterior probability functions are developed for this index under a vague prior formulation on the regression parameters. The procedure is applied to an example involving mercury toxicity data.