monotonic single index models to assess drug interactions although single index models have been extensively studied the monotonicity of the link function f in the single index model is rarely studied in many situations it is desirable that f is monotonic which results in a monotonic single index model that can be very useful in economics and biometrics in this article we propose a monotonic single index model in which the link function is constructed using penalized i splines along with constraints on coefficients to achieve monotonicity of the link function f an algorithm to estimate the single index parameters and the link function is developed and the sandwich estimate of the variance of the index parameters is provided we propose to apply this monotonic single index model to estimate the dose response surface and assess drug interactions while considering the variability of the observed data an extensive simulation study was carried out to evaluate the performance of the proposed monotonic single index model a case study is provided to illustrate the application of the proposed model to estimate the dose response surface and assess drug interactions both the simulation and case study show that the proposed monotonic single index model works very well copyright 2016 john wiley sons ltd

some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

experimental design and interaction analysis of combination studies of drugs with log linear dose responses drug combination is a major treatment approach in cancer and antiviral therapies a key issue is to find which combinations are additive synergistic or antagonistic in this paper we develop statistical methods for experimental design and data analysis of combination studies of drugs that have log linear dose response curves this class of dose response includes the hill sigmoid and simple exponential models the experimental design dose finding and sample size determination is derived by means of uniform measures that maximize the minimum power of the f test to detect any departures from additive action and at the same time minimizes the maximum bias due to lack of fit among all potential departures of a given meaningful magnitude furthermore we propose a model free interaction index surface to capture the interaction of two drugs the nonparametric function of the interaction index is estimated using the technique developed in thin plate splines these methods are applicable to both in vivo and in vitro experiments a study of two anticancer drugs suberoylanilide hydroxamic acid vorinostat and etoposide applied sequentially against the cell line hl 60 is given to illustrate the proposed methods of experimental design and interaction analysis

testing and estimating shape constrained nonparametric density and regression in the presence of measurement error in many applications we can expect that or are interested to know if a density function or a regression curve satisfies some specific shape constraints for example when the explanatory variable x represents the value taken by a treatment or dosage the conditional mean of the response y is often anticipated to be a monotone function of x indeed if this regression mean is not monotone in the appropriate direction then the medical or commercial value of the treatment is likely to be significantly curtailed at least for values of x that lie beyond the point at which monotonicity fails in the case of a density common shape constraints include log concavity and unimodality if we can correctly guess the shape of a curve then nonparametric estimators can be improved by taking this information into account addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint and if the conclusion of the test is positive a technique for e

semiparametric nonlinear mixed effects models and their applications nonlinear mixed effects models nlmms and self modeling nonlinear regression semor models are often used to fit repeated measures data they use a common function shared by all subjects to model variation within each subject and some fixed and or random parameters to model variation between subjects the parametric nlmm may be too restrictive and the semiparametric semor model ignores correlations within each subject in this article we propose a class of semiparametric nonlinear mixed effects models snmms that extend nlmms semor models and many other existing models in a natural way a snmm assumes that the mean function depends on some parameters and nonparametric functions the parameters provide an interpretable data summary the nonparametric functions provide flexibility to allow the data to decide some unknown or uncertain components such as the shape of the mean response over time a second stage model with fixed and random effects is used to model the parameters smoothing splines are us

universal presheaves on group geometries and modular representations abstract we extend the ideas of sheaf homology on buildings m a ronan and s d smith j algebra 96 1985 319 346 to more general geometries with transitive automorphism groups the main technical result is the construction of a universal extension of certain partial sheaves this guarantees a rich supply of sheaves on such geometries computation of zero homology then affords representations of the group we consider various applications of the technique for example to modular irreducibles for sporadic simple groups

critical behaviour of directed self avoiding walks a new directed self avoiding walk directed saw is proposed and studied on a square lattice the critical behaviour of such directed saws in two dimensions is established and shown to be of different universality class from that of an ordinary saw

on the estimation of an instantaneous transformation for time series summary we modify ramsay s algorithm for estimating monotonic transformations in regression and extend it to autoregression where strict monotonicity is an essential requirement compared with other methods our method can capture some characteristics that are pertinent to the time series and is much easier to implement an order selection method is introduced and developed some real data sets are analysed

unified approach to testing functional hypotheses in semiparametric contexts abstract we suggest a new method with very wide applicability for testing semiparametric hypotheses about functions such as regression means and probability densities the technique is based on characterising hypotheses in terms of functionals which can be estimated root n consistently and constructing test statistics in terms of estimators of the functionals since the tests are semiparametric it is appropriate to assess them on the basis of their ability to detect departures of size n 1 2 from the null hypothesis we show that they do indeed have this property unlike tests constructed in a nonparametric setting their power does not depend critically on choice of a bandwidth and in particular smoothing parameter selection is not an issue that has to be addressed by users of the tests bootstrap methods are suggested for calibrating the tests in a regression setting applications include tests of specification such as partial linear and index models against nonparametric or semiparametric alternatives and tests of monotonicity concavity separability equality of regression functions and base independence of equivalence scales in a density setting they include tests of radial symmetry and stochastic dominance

estimating smooth monotone functions many situations call for a smooth strictly monotone function f of arbitrary flexibility the family of functions defined by the differential equation d 2 f w df where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions the solution to this equation is f c 0 c 1 d 1 exp d 1 w where c 0 and c 1 are arbitrary constants and d 1 is the partial integration operator a basis for expanding w is suggested that permits explicit integration in the expression of f in fitting data it is also useful to regularize f by penalizing the integral of w 2 since this is a measure of the relative curvature in f applications are discussed to monotone nonparametric regression to the transformation of the dependent variable in non linear regression and to density estimation

bootstrap approximations in model checks for regression abstract let m m be a parametric model for an unknown regression function m for example m may consist of all polynomials or trigonometric polynomials with a given bound on the degree to check the full model m i e to test for h 0 m e m it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals in this article we show that the distribution of this process may be approximated by the wild bootstrap the method is applied to simulated datasets as well as to real data

critical properties of directed self avoiding walks the generating functions and mean displacements of various two dimensional directed self avoiding walk models are calculated exactly by a simple transfer matrix approach asymptotically the authors find r sub n approximately rn2 1 2 approximately n and rperpendicular to n2 1 approximately n1 2 where n is the number of steps in the walk and and perpendicular to refer to projections of the displacement parallel and perpendicular to the preferred axis of the walk respectively some general properties of directed self avoiding walks for arbitrary dimensions are discussed as well

directed self avoiding walks on sierpinski carpets series results using a graph counting technique suitable for self similar fractals we obtain the exact densities of partially pdsaw and fully fdsaw directed self avoiding walks on sierpinski carpets from them we calculate the root mean square transverse and longitudinal displacements of the n step walks up to n 20 for pdsaws and up to n 23 for fdsaws the critical exponents nu perpendicular to found for the pdsaw depend on the fractal dimension as well as on the lacunarity of the lattice the results indicate that pdsaws and fdsaws have different critical behaviour on the same carpet

smooth isotonic additive interaction models with application to computer system architecture design the regression relationship between a predictor vector and a response is assumed to be smooth additive with low order interactions and monotone in some of the predictors we consider two modeling approaches the first approach is to fit an unconstrained additive model first and subsequently impose the isotonic constraint to cause the least perturbation of the fit the second approach optimizes the fitting criterion that includes a roughness penalty over isotonic smoothing splines the advantage of the first approach is its modularity and ease of implementation one can incorporate a variety of smoothing methods as building blocks of the unconstrained model in the article we develop the theory for this approach in particular we show that one can use a combination of off the shelf smoothing fitting and isotonic routines however it is empirically shown that fitting an isotonic smoothing spline model produces superior results over a broad range of target functions the methodology is applied to model

the critical exponents ν ν and ν of directed saw on sierpinski carpets a computer simulation study the critical behaviour of fully directed self avoiding walks dsaw on sierpinski carpets is studied by numerical simulation the authors propose a fractal cell generation method to form an infinite fractal lattice with the structure of a sierpinski carpet the obtained critical exponent is independent of the fractal dimension of a sierpinski carpet df but and are dependent on df the results indicate that dsaw on different sierpinski carpets belong to different universality classes

self modelling with random shift and scale parameters and a free knot spline shape function the shape invariant model is a semi parametric approach to estimating a function relationship from clustered data multiple observations on each of a number of individuals the common response curve shape over individuals is estimated by adjusting for individual scaling differences while pooling shape information in practice the common response curve is restricted to some flexible family of functions this paper introduces the use of a free knot spline shape function and reduces the number of parameters in the shape invariant model by assuming a random distribution on the parameters that control the individual scaling of the shape function new graphical diagnostics are presented parameter identifiability and estimation are discussed and an example is presented

deconvolution of microfluorometric histograms with b splines abstract we consider the problem of estimating a probability density from observations from that density which are further contaminated by random errors we propose a method of estimation using spline functions discuss the numerical implementation of the method and prove its consistency the problem is motivated by the analysis of dna content obtained by microfluorometry and an example of such an analysis is included

smoothing noisy data under monotonicity constraints existence characterization and convergence rates in recent years there has been an increasing interest in the study of interpolation procedures preserving some shape defined in the form of a convex constraint such as monotonicity positivity and convexity in a recent paper the author proved that the convergence rates obtained using interpolatory monotone or positive or convex splines are the same as those obtained in the unconstrained case in this paper we aim to extend those results to the case of constrained smoothing splines we define general constrained smoothing splines and obtain theorems proving their existence uniqueness and a general result concerning their characterization we use this result to characterize the monotone smoothing spline finally we study the convergence rates of this smoothing splines when smoothing data coming from a smooth function plus noise if we calls n c to the smoothing spline and 2 to the variance of the data we prove that e left left f s n lambda c right k 2 right o lambda frac m k m sigma 2 o left frac 1 n lambda frac 2k 1 2m right this result shows that in the case of smoothing splines the attainable convergence rates are the same in the unconstrained and constrained cases

a short note on directed self avoiding walks the critical behaviour of partially directed self avoiding walks saws on a cubic lattice with only one axis directed is studied using exact enumerations the critical exponents nu sub 0 999 or 0 005 nu perpendicular to 0 501 or 0 006 and gamma 1 000 or 0 001 found here further support the universality hypothesis that various partially directed saws belong to the same universality class as fully directed saws and they are also dimension independent for d or 2

estimation in covariance components models abstract estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes the estimation of fixed and random effects when the variances and covariances are known is presented in bayesian terms point estimates of the unknown variances and covariances are computed using the em algorithm for maximum likelihood estimation from incomplete data the techniques are illustrated with data on law schools field mice and professional football teams

1 cohomology of chevalley groups abstract we relate the 1 cohomology of a finite chevalley group to induced modules and finite geometry as a corollary we get the 1 cohomology of most adjoint modules

nonparametric kernel regression subject to monotonicity constraints we suggest a method for monotonizing general kernel type estimators for example local linear estimators and nadaraya watson estimators attributes of our approach include the fact that it produces smooth estimates indeed with the same smoothness as the unconstrained estimate the method is applicable to a particularly wide range of estimator types it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented therefore an experimenter may use his or her favorite kernel estimator and their favorite bandwidth selector to construct the basic nonparametric smoother and then use our technique to render it monotone in a smooth way implementation involves only an off the shelf programming routine the method is based on maximizing fidelity to the conventional empirical approach subject to monotonicity we adjust the unconstrained estimator by tilting the empirical distribution so as to make the least possible change in the sense of a distance measure subject to imposing the constraint of monotonicity

on decomposition of modular representations from cohen macaulay geometries abstract chain spaces for a cohen macaulay complex split into subspaces corresponding to cycles for truncations of the complex precisely when the cycles are non degenerate in the natural bilinear form application to the tits building provides a simple geometric approach to the well known splitting of ind g b 1 for a lie type group g in natural characteristic an application to a sporadic geometry is also indicated

duality for representations of a reductive group over a finite field the purpose of this paper is to construct a duality operation for representations of a reductuve group over a finite field its effect very roughly speaking is to interchange irreducible representations of small degree with ones of large degree for example the unit and steinberg representation at level of characters this operation has been also considered by alvis 11 curtis 2 and kawanaka 4 we shall now fix some notation g will denote a connected reductive group defined over a finite field fq iv s its weyl group and f the set of orbits of the frobenius map on s the subsets of parametrize the classes of parabolic subgroup of g which are defined over fq let 9 be the class corresponding to z c s thus 9 is the class of bore1 subgroups and s g we denote by g the group of f rational points of g and by 9 the set of parabolic subgroups in 9 with are defined over fq similarly if p e 3 we denote by p its group of fq rational points and by u the group of f rational points of its unipotent radical let k be an algebraically closed field of characteristic zero all g modules will be over k let e be a g module for each z c we define

polynomial splines and their tensor products in extended linear modeling 1994 wald memorial lecture analysis of variance type models are considered for a regression function or for the logarithm of a probability function conditional probability function density function conditional density function hazard function conditional hazard function or spectral density function polynomial splines are used to model the main effects and their tensor products are used to model any interaction components that are included in the special context of survival analysis the baseline hazard function is modeled and nonproportionality is allowed in general the theory involves the l 2 rate of convergence for the fitted model and its components the methodology involves least squares and maximum likelihood estimation stepwise addition of basis functions using rao statistics stepwise deletion using wald statistics and model selection using the bayesian information criterion cross validation or an independent test set publicly available software written in c and interfaced to s s plus is used to apply this methodology to real data

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

binomial regression with monotone splines a psychometric application abstract a binomial regression function p x models the probability of rj successes in nj trials as a function of the values of an observed covariate xj and or a latent variable j j 1 j this article explores the use of monotone regression splines to define p and applies them to the representation of test items as functions of examinee ability some illustrative data suggest that the flexibility of monotone splines permits the detection of item characteristics not observable using logistic based or log linear approaches a simulation study indicates that estimates of both item characteristic curves and ability are reasonably precise for numbers of items and examinees typical of large university lectures given a set of such binomial regression functions it can be useful to study the principal components of functional variation the extension of multivariate principal components analysis to permit the analysis of many item characteristic curves is described

monotone smoothing with application to dose response curves and the assessment of synergism a spline based procedure for monotone curve smoothing is proposed and is illustrated by application to dose response curves it is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs

optimal smoothing in single index models single index models generalize linear regression they have applications to a variety of fields such as discrete choice analysis in econometrics and dose response models in biometrics where high dimensional regression models are often employed single index models are similar to the first step of projection pursuit regression a dimension reduction method in both cases the orientation vector can be estimated root n consistently even if the unknown univariate function or nonparametric link function is assumed to come from a large smoothness class however as we show in the present paper the similarities end there in particular the amount of smoothing necessary for root n consistent orientation estimation is very different in the two cases we suggest a simple empirical rule for selecting the bandwidth appropriate to single index models this rule is studied in a small simulation study and an application in binary response models

penalized spline estimation for partially linear single index models single index models are potentially important tools for multivariate nonparametric regression they generalize linear regression by replacing the linear combination 0tx with a nonparametric component 0 0tx where 0 is an unknown univariate link function by reducing the dimensionality from that of a general covariate vector x to a univariate index 0tx single index models avoid the so called curse of dimensionality we propose penalized spline p spline estimation of 0 in partially linear single index models where the mean function has the form 0 0tx 0tz the p spline approach offers a number of advantages over other fitting methods for single index models all parameters in the p spline single index model can be estimated simultaneously by penalized nonlinear least squares as a direct least squares fitting method our approach is rapid and computationally stable standard nonlinear least squares software can be used moreover joint inference for 0 0 and 0 is possible by

a semiparametric approach to analysing dose response data in the analysis of a quantal dose response experiment with grouped data the most commonly used parametric procedure is logistic regression commonly referred to as logit analysis the adequacy of the fit by the logistic regression curve is tested using the chi square lack of fit test if the lack of fit test is not significant then the logistic model is assumed to be adequate and estimation of effective doses and confidence intervals on the effective doses can be made when the tolerance distribution of the dose response data is not known and cannot be assumed by the user one can use non parametric methods such as kernel regression or local linear regression to estimate the dose response curve effective doses and confidence intervals this research proposes another alternative based on semi parametric regression to analysing quantal dose response data called model robust quantal regression mrqr mrqr linearly combines the parametric and non parametric predictions with the use of a mixing parameter mrqr uses logistic regression as the parametric portion of the model and local linear regression as the non parametric portion of the model our research has shown that the mrqr procedure can improve the fit of the dose response curve by producing narrower confidence intervals for predictions while providing improved precision of estimates of the effective doses with respect to either logistic or local linear regression results

on the apparent failure of a flory approximation for directed linear polymers the author discusses the apparent failure of a flory approximation for directed linear polymers commenting on the details implicit in this type of picture the relationship of a standard flory viewpoint to a simplified application of fractal theory is explored and a correspondence is drawn between aspects of both theories

asymptotic properties of penalized spline estimators we study the class of penalized spline estimators which enjoy similarities to both regression splines without penalty and with fewer knots than data points and smoothing splines with knots equal to the data points and a penalty controlling the roughness of the fit depending on the number of knots sample size and penalty we show that the theoretical properties of penalized regression spline estimators are either similar to those of regression splines or to those of smoothing splines with a clear breakpoint distinguishing the cases we prove that using fewer knots results in better asymptotic rates than when using a large number of knots we obtain expressions for bias and variance and asymptotic rates for the number of knots and penalty parameter

utilizing concentration response data from individual components to detect statistically significant departures from additivity in chemical mixtures the classical approach for detecting interactions in a combination of drugs or chemicals is that of the isobologram quantified and generalized by berenbaum 1981 advances il cancer research 35 269 335 in this formulation it is assumed that contours of constant response of the dose response surface are planar if the compounds do not interact building upon this approach this paper develops methodology for detecting and characterizing departures from additivity reflecting the local rather than global nature of departure from additivity this methodology only requires doseresponse data for the individual components and the specific combinations s of interest this is in contrast to the larger experiments required to estimate the multidimensional dose response surface for the combination procedures for incorporating data from multiple control groups are developed for a fixed effects model a random effects model and through use of a generalized estimating equations approach an example is given that illustrates the application of these techniques to the analysis of a mixture of polycyclic aromatic hydrocarbons found in kerosene soot

uniform design theory and application a uniform design ud seeks design points that are uniformly scattered on the domain it has been popular since 1980 a survey of ud is given in the first portion the fundamental idea and construction method are presented and discussed and examples are given for illustration it is shown that ud s have many desirable properties for a wide variety of applications furthermore we use the global optimization algorithm threshold accepting to generate ud s with low discrepancy the relationship between uniformity and orthogonality is investigated it turns out that most ud s obtained here are indeed orthogonal

smoothing under diffeomorphic constraints with homeomorphic splines in this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms this diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate time dependent vector field this solution has a closed form expression which can be computed using classical unconstrained spline smoothing techniques this method does not require the use of quadratic or linear programming under inequality constraints and has therefore a low computational cost in a one dimensional setting incorporating diffeomorphic constraints is equivalent to imposing monotonicity thus as an illustration it is shown that such a monotone spline can be used to make monotone any unconstrained estimator of a regression function and that this monotone smoother inherits the convergence properties of the unconstrained estimator some numerical experiments are proposed to illustrate its finite sample performances and to compare them with another monotone estimator we also provide a two dimensional application on the computation of diffeomorphisms for landmark and image matching

nonparametric estimation of rate equations for nutrient uptake abstract knowledge of the rate of a biological process is important for characterizing the system and is necessary for gaining a deeper understanding of the process consider measurements y made over time on a system following the model y f t e where f is a smooth unknown function and e is measurement error although most statistical methodology has focused on estimating f t or f t in some applications what is of real biological interest is the relationship between f and f one example is the study of nitrogen absorption by plant roots through a solution depletion experiment in this case f t is the nitrate concentration of the solution surrounding the roots at time t and f t is the absorption rate of nitrate by plant roots at time t one is interested in the rate of nitrate absorption as a function of concentration that is one is interested in where f f knowledge of is important in quantifying the ability of a particular plant species to absorb nitrogen and in comparing

an application of a hill based response surface model for a drug combination experiment on lung cancer combination chemotherapy with multiple drugs has been widely applied to cancer treatment owing to enhanced efficacy and reduced drug resistance for drug combination experiment analysis response surface modeling has been commonly adopted in this paper we introduce a hill based global response surface model and provide an application of the model to a 512 run drug combination experiment with three chemicals namely ag490 u0126 and indirubin 3 monoxime i 3 m on lung cancer cells the results demonstrate generally improved goodness of fit of our model from the traditional polynomial model as well as the original hill model on the basis of fixed ratio drug combinations we identify different dose effect patterns between normal and cancer cells on the basis of our model which indicates the potential effectiveness of the drug combination in cancer treatment meanwhile drug interactions are analyzed both qualitatively and quantitatively the distinct interaction patterns between u0126 and i 3 m on two types of cells uncovered by the model could be a further indicator of the efficacy of the drug combination copyright 2014 john wiley sons ltd

inequality constrained multivariate smoothing splines with application to the estimation of posterior probabilities abstract we consider the problem of estimating a smooth function of several variables given discrete scattered noisy observations of its values and given that it satisfies a family of linear inequality constraints constraints such as positivity over some region are included the model is z i f y 1 i yd e i 1 n where the e i s are independent zero mean random variables f is assumed to be smooth with smoothness defined in terms of square integrability of certain derivatives and f is known to satisfy a given set of linear inequality constraints it is proposed that f be estimated as the minimizer in an appropriate function space of subject to f satisfying the constraints if they are a finite family or satisfying a finite approximating set of constraints if they are not a finite family where j m f is the thin plate penalty functional defined by j m f 1 d m m 1 d m f y 11 y d d 2 dy 1 dy d more generally the results apply to the model wh

dose response curve estimation a semiparametric mixture approach summary in the estimation of a dose response curve parametric models are straightforward and efficient but subject to model misspecifications nonparametric methods are robust but less efficient as a compromise we propose a semiparametric approach that combines the advantages of parametric and nonparametric curve estimates in a mixture form our estimator takes a weighted average of the parametric and nonparametric curve estimates in which a higher weight is assigned to the estimate with a better model fit when the parametric model assumption holds the semiparametric curve estimate converges to the parametric estimate and thus achieves high efficiency when the parametric model is misspecified the semiparametric estimate converges to the nonparametric estimate and remains consistent we also consider an adaptive weighting scheme to allow the weight to vary according to the local fit of the models we conduct extensive simulation studies to investigate the performance of the proposed methods and illustrate them with two real examples

on the geometry of the adjoint representation of a chevalley group abstract we prove that the adjoint module of a chevalley group not of type c l has a presentation by long root subalgebras subject to certain relations determined by the minimal parabolic subgroups

a generalized response surface model with varying relative potency for assessing drug interaction when multiple drugs are administered simultaneously investigators are often interested in assessing whether the drug combinations are synergistic additive or antagonistic based on the loewe additivity reference model many existing response surface models require constant relative potency and some of them use a single parameter to capture synergy additivity or antagonism however the assumption of constant relative potency is too restrictive and these models using a single parameter to capture drug interaction are inadequate to describe the phenomenon when synergy additivity and antagonism are interspersed in different regions of drug combinations we propose a generalized response surface model with a function of doses instead of one single parameter to identify and quantify departure from additivity the proposed model can incorporate varying relative potencies among multiple drugs as well examples and simulations are given to demonstrate that the proposed model is effective in capturing different patterns of drug interaction

the monotone smoothing of scatterplots we consider the problem of summarizing a scatterplot with a smooth monotone curve a solution that combines local averaging and isotonic regression is proposed and we demonstrate its use with two examples in the second example the procedure is applied in a regression setting to some data from box and cox 1964 and it is shown how this new procedure generalizes box and cox s well known family of transformations in the same example the bootstrap is applied to obtain a measure of the variability of the procedure

irreducible modules and parabolic subgroups summary it seems desirable from the point of view of finite group theorists to develop further the representation theory of finite chevalley groups in the characteristic of their definition say p by focusing attention on the full array of p local subgroups that is the parabolics rather than the usual single borel or cartan subgroup the following observation may be regarded as a generalization to arbitrary parabolic subgroups of the standard result 3 theorem 39 d for a borel subgroup namely that in an irreducible module the subspace fixed by a maximal unipotent subgroup is 1 dimensional and so affords an irreducible module for a levi complement which is an abelian cartan subgroup it seems natural to state the result first for algebraic groups

spin modules in characteristic 2 abstract some properties of spin modules for orthogonal groups are developed particularly with regard to parabolic subgroups an application is given to a problem in the structure theory of finite simple groups

spline based tests in survival analysis this paper examines a method for testing hypotheses on covariate effects in a proportional hazards model and also on how effects change over time in regression analysis of survival data the technique used is very general and can be applied to testing many other aspects of parametric and semiparametric models the basic idea is to formulate a flexible parametric alternative using fixed knot splines together with a penalty function that penalizes noisy alternatives more than smooth ones to focus the power of the tests toward smooth alternatives the test statistics are the analogs of ordinary likelihood based statistics only computed from a penalized likelihood formed by subtracting the penalty function from the ordinary log likelihood large sample approximations to the distributions are found when the number of knots is held fixed as the sample size increases numerical results suggest these approximations may be adequate with moderate sized samples

size and shape of directed lattice animals uses position space renormalisation and exact enumeration methods to study configurational properties of directed lattice animals clusters of directed bonds in which the tail of a new bond must be added to the head of existing bonds exponents are found for the divergence of correlation lengths parallel and perpendicular to the preferred axis in addition an exponent is found that characterises the singularity of the directed animal generating function and critical points are located

unimodal regression using bernstein schoenberg splines and penalties summary research in the field of nonparametric shape constrained regression has been intensive however only few publications explicitly deal with unimodality although there is need for such methods in applications for example in dose response analysis in this article we propose unimodal spline regression methods that make use of bernstein schoenberg splines and their shape preservation property to achieve unimodal and smooth solutions we use penalized splines and extend the penalized spline approach toward penalizing against general parametric functions instead of using just difference penalties for tuning parameter selection under a unimodality constraint a restricted maximum likelihood and an alternative bayesian approach for unimodal regression are developed we compare the proposed methodologies to other common approaches in a simulation study and apply it to a dose response data set all results suggest that the unimodality constraint or the combination of unimodality and a penalty can substantially improve estimation of the functional relationship