Principal component regression analysis applied in structure-activity relationships. 2. flexible opioids with unusually high safety margin

Multicollinearities among chemical regressor variables in structure-activity relationships can be avoided using the principal component regression analysis. An example adapted from drug design (conformationally flexible opioids) shows the working technique.     

When is Piece-Wise Regression Really Necessary?

Results are obtained showing that when a response surface can be modelled as a single function, then a single regressor is more efficient and less biased than a segmented regression. However, if the surface is segmented, a segmented regressor is less biased than a single regressor. Areas of application are indicated.     

Modifying the Schwarz Bayesian information criterion to locate multiple interacting quantitative trait loci

The problem of locating multiple interacting quantitative trait loci (QTL) can be addressed as a multiple regression problem, with marker genotypes being the regressor variables. An important and difficult part in fitting such a regression model is the estimation of the QTL number and respective interactions. Among the many model selection criteria that can be used to estimate the number of regressor variables, none are used to estimate the number of interactions. Our simulations demonstrate that epistatic terms appearing in a model without the related main effects cause the standard model selection criteria to have a strong tendency to overestimate the number of interactions, and so the QTL number. With this as our motivation we investigate the behavior of the Schwarz Bayesian information criterion (BIC) by explaining the phenomenon of the overestimation and proposing a novel modification of BIC that allows the detection of main effects and pairwise interactions in a backcross population. Results of an extensive simulation study demonstrate that our modified version of BIC performs very well in practice. Our methodology can be extended to general populations and higher-order interactions.     

A pseudo-bayesian shrinkage approach to regression with missing covariates

Summary We consider the linear regression of outcome Y on regressors W and Z with some values of W missing, when our main interest is the effect of Z on Y, controlling for W. Three common approaches to regression with missing covariates are (i) complete‐case analysis (CC), which discards the incomplete cases, and (ii) ignorable likelihood methods, which base inference on the likelihood based on the observed data, assuming the missing data are missing at random ( Rubin, 1976b ), and (iii) nonignorable modeling, which posits a joint distribution of the variables and missing data indicators. Another simple practical approach that has not received much theoretical attention is to drop the regressor variables containing missing values from the regression modeling (DV, for drop variables). DV does not lead to bias when either (i) the regression coefficient of W is zero or (ii) W and Z are uncorrelated. We propose a pseudo‐Bayesian approach for regression with missing covariates that compromises between the CC and DV estimates, exploiting information in the incomplete cases when the data support DV assumptions. We illustrate favorable properties of the method by simulation, and apply the proposed method to a liver cancer study. Extension of the method to more than one missing covariate is also discussed.     

Small Sample Properties of the Likelihood Estimator in Proportional Hazard Regression Models with Omitted Variables

The paper deals with the effects of incorrectly omitted regressor variables in a parametric proportional hazard regression model. By studying conditions for equality between the estimators of correct and incorrect models it is demonstrated analytically that such cases are not to be expected in practise. A small sample Monte Carlo experiment indicates severe negative effects on the retained parameters both in terms of bias and mean square error.     

Physical characteristics that predict functional performance in Division I college football players

Strength and conditioning professionals who work with collegiate football players focus much of their time and effort on developing programs to enhance athletic performance. Although there has been much speculation, there is little scientific evidence to suggest which combination of physical characteristics best predicts athletic performance in this population. The purpose of this investigation was to examine the relationship among 6 physical characteristics and 3 functional measures in college football players. Data were gathered on 46 NCAA Division I college football players. The 3 response variables were 36.6-m sprint, 18.3-m shuttle run, and vertical jump. The 6 regressor variables were height, weight, percentage of body fat, hamstring length, bench press, and hang clean. A stepwise multiple regression analysis was performed to screen for variables that predict physical performance. Regression analysis revealed clear prediction models for the 36.6-m sprint and 18.3-m shuttle run. The results of this investigation will help strength and conditioning specialists better understand the variables that predict athletic performance in Division I college football players.     

Marker pair selection for mapping quantitative trait loci

Mapping of quantitative trait loci (QTL) for backcross and F(2) populations may be set up as a multiple linear regression problem, where marker types are the regressor variables. It has been shown previously that flanking markers absorb all information on isolated QTL. Therefore, selection of pairs of markers flanking QTL is useful as a direct approach to QTL detection. Alternatively, selected pairs of flanking markers can be used as cofactors in composite interval mapping (CIM). Overfitting is a serious problem, especially if the number of regressor variables is large. We suggest a procedure denoted as marker pair selection (MPS) that uses model selection criteria for multiple linear regression. Markers enter the model in pairs, which reduces the number of models to be considered, thus alleviating the problem of overfitting and increasing the chances of detecting QTL. MPS entails an exhaustive search per chromosome to maximize the chance of finding the best-fitting models. A simulation study is conducted to study the merits of different model selection criteria for MPS. On the basis of our results, we recommend the Schwarz Bayesian criterion (SBC) for use in practice.     

Defining the heterogeneity of anti-tumor antibody responses.

Studies were undertaken to analyze the humoral in vivo and in vitro antibody response of BALB/c mice to a syngeneic MSV-induced tumor cell line. With a sensitive radioimmunoassay, sera obtained from individual progressor and regressor mice were shown to vary greatly in total tumor-specific antibody concentration as well as immunoglobulin class distribution of the antibody, but no significant difference existed between the groups of progressor and regressor mice as a whole. In addition, serum antibodies from all animals were shown to have extensive cross-reactivity against a variety of cell lines chosen to share one or more antigens with the cell line used for immunization. Conversely, when in vitro fragment cultures of splenic tissue from progressor and regressor mice were stimulated with tumor-related antigen, differences in responsiveness among normal, progressor, and regressor mice were observed. In addition, antibodies derived from fragment cultures displayed several different cross-reactivity patterns all of which were more restricted in specificity than serum antibodies.     

Tumor immunity generated in the course of regression of v-src-induced sarcomas.

Previous studies have indicated that the regression versus progression of v-src-DNA-induced sarcomas is dependent on chicken line. As a first step in analyzing the role of tumor immunity as a determinant of this line dependence, experiments were undertaken to ascertain whether an antisarcoma immune response is generated in the course of sarcoma growth in TK chickens, a regressor line. To assay for this response, test TK chickens in which v-src-induced wing web sarcomas had regressed, as well as control TK chickens that had not been exposed to v-src, were challenged in protocols known to yield v-src-dependent sarcoma formation and monitored for challenge sarcoma growth. Compared with the control chickens, the test chickens showed a significant resistance to the sarcomagenic challenge. These results raise the possibility that the antisarcoma response that is inducible in regressor lines, as demonstrated here in terms of a protective effect against a subsequent sarcomagenic challenge, may also underlie the regression of v-src-induced primary sarcomas.     

The effect of environmental factors on estimated viable and total populations of planktonic bacteria in lakes and experimental enclosures

SUMMARY. The difference between the results of viable and total counting procedures for bacteria are exemplified by vertical profiles from a deep and a shallow lake and from seasonal changes in the epilimnion and hypolimnion of a shallow eutrophic lake. The viable count was, on average, 0.25% of the total count, the greatest difference being noted in the anoxic hypolimnion, probably due to the inadequacy of the viable counting procedure for the isolation of bacteria from such samples. There was a general trend for the more nutrient-rich waters to support larger bacterial populations but such observations did not provide any further information on the factors responsible for the population changes observed. Seasonal fluctuations in the counts are studied and the qualitative and quantitative changes resulting from artificial enclosure of water are discussed. Not all the temporal changes could be explained and short-term changes resulting from nutrient additions to the experimental enclosures were not always reproducible. Horizontal variability was examined, found to be significant and could play an important role where water movement and turbulence is considerable. Results from six sites sampled between 1969 and 1974, representing total and viable bacterial population estimates and a total of eighteen independent or regressor variables were then subjected to principal components analysis. Results taken from the whole water column showed the overwhelming effect of the process of stratification on the bacterial population accounting for 30%-60% of its variability. Secondary components representing algal productivity could account for 10% to 20% of the variability. Many of the chosen regressor variables were acting as measures of the same phenomenon without providing significant information on what affected the bacterial population. To overcome this problem results from the hypolimnion and epilimnion were analysed separately. The analysis demonstrated the importance of seasonal changes in nutrient concentrations in the epilimnion and the development of anoxic conditions in the hypolimnion. Algal biomass, phosphate concentration and the interaction of pH and ammonia appeared to be important. It was concluded that most of the variability in the bacterial population estimates could have been explained by five of the regressor variables and that the factors most likely to provide more information would include some measure of predation and lake retention time.     

关于利用伪变量对多点试验进行回归分析的改进

针对文［１］仅考虑了各点回归方程间常数项可能不同，而忽略了其它回归系数也可能不同的情况，本文对伪变量形式进行了修正，通过引入伪变量的相互作用项，使得到的回归模型更合理，可靠性更高．     

Tumor regression induced by intratumor therapy with a disabled infectious single cycle (DISC) herpes simplex virus (HSV) vector, DISC/HSV/murine granulocyte-macrophage colony-stimulating factor, correlates with antigen-specific adaptive immunity

Direct intratumor injection of a disabled infectious single cycle HSV-2 virus encoding the murine GM-CSF gene (DISC/mGM-CSF) into established murine colon carcinoma CT26 tumors induced a significant delay in tumor growth and complete tumor regression in up to 70% of animals. Pre-existing immunity to HSV did not reduce the therapeutic efficacy of DISC/mGM-CSF, and, when administered in combination with syngeneic dendritic cells, further decreased tumor growth and increased the incidence of complete tumor regression. Direct intratumor injection of DISC/mGM-CSF also inhibited the growth of CT26 tumor cells implanted on the contralateral flank or seeded into the lungs following i.v. injection of tumor cells (experimental lung metastasis). Proliferation of splenocytes in response to Con A was impaired in progressor and tumor-bearer, but not regressor, mice. A potent tumor-specific CTL response was generated from splenocytes of all mice with regressing, but not progressing tumors following in vitro peptide stimulation; this response was specific for the gp70 AH-1 peptide SPSYVYHQF and correlated with IFN-gamma, but not IL-4 cytokine production. Depletion of CD8(+) T cells from regressor splenocytes before in vitro stimulation with the relevant peptide abolished their cytolytic activity, while depletion of CD4(+) T cells only partially inhibited CTL generation. Tumor regression induced by DISC/mGM-CSF virus immunotherapy provides a unique model for evaluating the immune mechanism(s) involved in tumor rejection, upon which tumor immunotherapy regimes may be based.     

A Technique for the Analysis of Unbalanced Data

The regression methods with dummy variables have been shown to be effective in preventing confusion in the analysis of linear models. In particular, this model simplifies interpretation of parameters and clarifies hypothesis statements. All existing methods have been shown as special cases of the general linear hypothesis in regression setting. Three regression on dummy variables methods are examined critically to bring out the salient features of each method. The choice of a method should be based on the way definitions of the parameters are desired. The linear models are considered in a regression model setting. This has been done by defining appropriate dummy variables in a regression model which often is desirable, if not mandatory, when dealing with unbalanced data involving two or more factors.     

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.     

The distribution of some freshwater planktonic bacteria in two stratified eutrophic lakes

SUMMARY. Changes in bacterial populations and certain physical and chemical variables in Esthwaite Water between June and September 1975 were studied and compared with results obtained from 1972 to 1974 in the hypolimnia of Blelham Tarn and the Lund tubes. The counts of total bacteria ranged between 1 and 7 × 10⁶ml⁻¹ and were highest in the anoxic hypolimnion. The bacterial genera examined in more detail constituted only a small percentage of this count and included Ochrobium (10⁴ml⁻¹), Naumanniella (10³ml⁻¹), Leptothrix (10²ml⁻¹), Planctomyces (10³ml⁻¹), and Metallogenium (10²ml⁻¹). The iron bacteria appear to grow best in the oxycline where there was not only sufficient oxygen for aerobic growth but also a plentiful supply of reduced iron. Planctomyces numbers increased as the thermocline became depressed in September. The results from Blelham Tarn might be interpreted as further evidence of growth by iron bacteria in the absence of dissolved oxygen, but other explanations are possible. Examination of the results by multiple regression analysis showed that it was possible to explain a significant proportion of the bacterial variation (with the notable exception of the Planctomyces counts) in spite of considerable intercorrelation of the regressor variables.     

Mechanisms of "cytostasis" of tumours in vitro by syngeneic lymphoid cells of tumour bearers.

The cytostasis assay is an in vivo-in vitro radioactive technique which detects antitumour responses of the syngeneic tumour-bearing hosts. Examination and characterization of effector mechanisms at the cellular and humoral levels revealed that the cytostasis assay using Meth A (a 3-methylcholanthrene-induced) tumour was T cell independent. Furthermore, both B cells and macrophages were required. It was concluded that the mechanism involved complement-dependent antibody-mediated lysis of the tumour cells, with B cells producing antibody and macrophages producing the complement components during incubation. However, antibody-dependent cell-mediated cytotoxicity with or without complement could not be completely excluded. Although antibody was detected in vivo, specific antibody against Meth A tumour was produced in vitro by cultured lymphoid cells from the tumour-bearers. Antibody-coated Meth A cells caused regression of some tumours when inoculated into BALB/c mice. When these regressor mice were rechallenged with tumour, they were found to be permanently immune to the tumour. In the light of these findings, the role of antibody in the protection of tumours and its implications are discussed.     

Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora

The richness of Norwegian mountain plants in 75 grid squares is mapped from published distributional data for 109 species. Eleven explanatory variables representing bedrock geology, geography and topography, climate, and history (relative abundance of unglaciated areas) Tor each square are used in multiple regression analysis with associated Monte Carlo permutation tests to find statistically significant predictor variables for species richness. The variance in richness explained by the four major groups or explanatory variables is established by (partial) multiple regression analysis in which the groups of predictors are entered in different orders. The variance in species richness explained by the predictor variables is partitioned into four independent components. A predictive model for species richness using partial least squares regression and all explanatory variables has a coefficient of determination (R²) of 0.79. The statistical results consistently show that species-richness patterns are well explained by modern-day factors such as climate, geology, elevation, and geography without recourse to historical variables. The nunatak hypothesis of plant survival on unglaciated areas within Norway does not explain the observed richness patterns when modern ecological factors are considered first. The nunatak hypothesis thus appears to be redundant, a view supported by recent palaeobotanical. biosystematical, and evolutionary studies.     

Approximate standard errors in semiparametric models

We consider semiparametric models with p regressor terms and q smooth terms. We obtain an explicit expression for the estimate of the regression coefficients given by the back-fitting algorithm. The calculation of the standard errors of these estimates based on this expression is a considerable computational exercise. We present an alternative, approximate method of calculation that is less demanding. With smoothing splines, the method is exact, while with loess, it gives good estimates of standard errors. We assess the adequacy of our approximation and of another approximation with the help of two examples.     

Partial least squares regression as an alternative to current regression methods used in ecology

This paper briefly presents the aims, requirements and results of partial least squares regression analysis (PLSR), and its potential utility in ecological studies. This statistical technique is particularly well suited to analyzing a large array of related predictor variables (i.e. not truly independent), with a sample size not large enough compared to the number of independent variables, and in cases in which an attempt is made to approach complex phenomena or syndromes that must be defined as a combination of several variables obtained independently. A simulation experiment is carried out to compare this technique with multiple regression (MR) and with a combination of principal component analysis and multiple regression (PCA+MR), varying the number of predictor variables and sample sizes. PLSR models explained a similar amount of variance to those results obtained by MR and PCA+MR. However, PLSR was more reliable than other techniques when identifying relevant variables and their magnitudes of influence, especially in cases of small sample size and low tolerance. Finally, we present one example of PLSR to illustrate its application and interpretation in ecology.     

Genetic analysis of a divergent selection for resistance to Rous sarcomas in chickens?. This article is dedicated to the memory of Pierrick Thoraval (1960–2000).

Selection for disease resistance related traits is a tool of choice for evidencing and exploring genetic variability and studying underlying resistance mechanisms. In this framework, chickens originating from a base population, homozygote for the B¹⁹ major histocompatibility complex (MHC) were divergently selected for either progression or regression of tumors induced at 4 weeks of age by a SR-D strain of Rous sarcoma virus (RSV). The first generation of selection was based on a progeny test and subsequent selections were performed on full-sibs. Data of 18 generations including a total of 2010 birds measured were analyzed for the tumor profile index (TPI), a synthetic criterion of resistance derived from recording the volume of the tumors and mortality. Response to selection and heritability of TPI were estimated using a restricted maximum likelihood method with an animal model. Significant progress was shown in both directions: the lines differing significantly for TPI and mortality becoming null in the "regressor" line. Heritability of TPI was estimated as 0.49 ± 0.05 and 0.53 ± 0.06 within the progressor and regressor lines respectively, and 0.46 ± 0.03 when estimated over lines. Preliminary results showed within the progressor line a possible association between one Rfp-Y type and the growth of tumors.