regression models for relative survival four approaches to estimating a regression model for relative survival using the method of maximum likelihood are described and compared the underlying model is an additive hazards model where the total hazard is written as the sum of the known baseline hazard and the excess hazard associated with a diagnosis of cancer the excess hazards are assumed to be constant within pre specified bands of follow up the likelihood can be maximized directly or in the framework of generalized linear models minor differences exist due to for example the way the data are presented individual aggregated or grouped and in some assumptions e g distributional assumptions the four approaches are applied to two real data sets and produce very similar estimates even when the assumption of proportional excess hazards is violated the choice of approach to use in practice can therefore be guided by ease of use and availability of software we recommend using a generalized linear model with a poisson error structure based on collapsed data using exact survival times the model can be estimated in any software package that estimates glms with user defined link functions including sas stata s plus and r and utilizes the theory of generalized linear models for assessing goodness of fit and studying regression diagnostics

selection of important variables and determination of functional form for continuous predictors in multivariable model building in developing regression models data analysts are often faced with many predictor variables that may influence an outcome variable after more than half a century of research the best way of selecting a multivariable model is still unresolved it is generally agreed that subject matter knowledge when available should guide model building however such knowledge is often limited and data dependent model building is required we limit the scope of the modelling exercise to selecting important predictors and choosing interpretable and transportable functions for continuous predictors assuming linear functions stepwise selection and all subset strategies are discussed the key tuning parameters are the nominal p value for testing a variable for inclusion and the penalty for model complexity respectively we argue that stepwise procedures perform better than a literature based assessment would suggest concerning selection of functional form for continuous predictors the principal competitors are fractional polynomial functions and various types of spline techniques we note that a rigorous selection strategy known as multivariable fractional polynomials mfp has been developed no spline based procedure for simultaneously selecting variables and functional forms has found wide acceptance results of fp and spline modelling are compared in two data sets it is shown that spline modelling while extremely flexible can generate fitted curves with uninterpretable wiggles particularly when automatic methods for choosing the smoothness are employed we give general recommendations to practitioners for carrying out variable and function selection while acknowledging that further research is needed we argue why mfp is our preferred approach for multivariable model building with continuous covariates

layoffs and duration dependence in a model of turnover abstract a semi markov model of turnover resulting from optimizing behavior on the part of workers is developed duration dependence in the transition out of employment is modelled as resulting from a layoff probability which decreases with tenure some preliminary results based on dime data are presented these indicate that a declining hazard rate in the transition out of employment is a significant feature of the data

assessment of stratum covariate interactions in cox s proportional hazards regression model we assess stratum e g treatment interactions with covariates and with the baseline hazard function in the proportional hazards ph regression model for lifetime data we consider models incorporating stratum interactions both with and without stratification of the risk sets in the likelihood function and describe likelihood ratio statistics for tests of the presence of these interactions we also present step down methods for building reduced models which include stratum specific parameters corresponding to covariates which interact with treatment we apply ph models with such interactions to a clinical trial of des in the treatment of prostate cancer to determine optimal treatment conditional on each patient s covariates

information measures for generalized gamma family the objective of this paper is to integrate the generalized gamma gg distribution into the information theoretic literature we study information properties of the gg distribution and provide an assortment of information measures for the gg family which includes the exponential gamma weibull and generalized normal distributions as its subfamilies the measures include entropy representations of the log likelihood ratio aic and bic discriminating information between gg and its subfamilies a minimum discriminating information function power transformation information and a maximum entropy index of fit to histogram we provide the full parametric bayesian inference for the discrimination information measures we also provide bayesian inference for the fit of gg model to histogram using a semi parametric bayesian procedure referred to as the maximum entropy dirichlet med the gg information measures are computed for duration of unemployment and duration of ceo tenure

integral deligne cohomology for real varieties we develop an integral version of deligne cohomology for smooth proper real varieties for this purpose the role played by singular cohomology in the complex case has to be replaced by the ordinary bigraded gal mathbb c mathbb r equivariant cohomology of lewis et al bull am math soc n s 4 2 208 212 1981 the equivariant counterpart of singular cohomology the theory is aimed at giving more precise information about the 2 primary components of regulators we establish basic properties and give a geometric interpretation for the groups in dimension 2 in weights 1 and 2

varying coefficient models we explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables general algorithms are presented for estimating the models flexibly and some examples are given this class of models ties together generalized additive models and dynamic generalized linear models into one common framework when applied to the proportional hazards model for survival data this approach provides a new way of modelling departures from the proportional hazards assumption

variable selection and model choice in geoadditive regression models model choice and variable selection are issues of major concern in practical regression analyses we propose a boosting procedure that facilitates both tasks in a class of complex geoadditive regression models comprising spatial effects nonparametric effects of continuous covariates interaction surfaces random effects and varying coefficient terms the major modelling component are penalized splines and their bivariate tensor product extensions all smooth model terms are represented as the sum of a parametric component and a remaining smooth component with one degree of freedom to obtain a fair comparison between all model terms a generic representation of the geoadditive model allows to devise a general boosting algorithm that implements automatic model choice and variable selection we demonstrate the versatility of our approach with two examples a geoadditive poisson regression model for species counts in habitat suitability analyses and a geoadditive logit model for the analysis of forest health

empirical study of the dependence of the results of multivariable flexible survival analyses on model selection strategy flexible survival models which avoid assumptions about hazards proportionality ph or linearity of continuous covariates effects bring the issues of model selection to a new level of complexity each candidate covariate requires inter dependent decisions regarding i its inclusion in the model and representation of its effects on the log hazard as ii either constant over time or time dependent td and for continuous covariates iii either loglinear or non loglinear nl moreover optimal decisions for one covariate depend on the decisions regarding others thus some efficient model building strategy is necessary we carried out an empirical study of the impact of the model selection strategy on the estimates obtained in flexible multivariable survival analyses of prognostic factors for mortality in 273 gastric cancer patients we used 10 different strategies to select alternative multivariable parametric as well as spline based models allowing flexible modeling of non parametric td and or nl effects we employed 5 fold cross validation to compare the predictive ability of alternative models all flexible models indicated significant non linearity and changes over time in the effect of age at diagnosis conventional parametric models suggested the lack of period effect whereas more flexible strategies indicated a significant nl effect cross validation confirmed that flexible models predicted better mortality the resulting differences in the final model selected by various strategies had also impact on the risk prediction for individual subjects overall our analyses underline a the importance of accounting for significant non parametric effects of covariates and b the need for developing accurate model selection strategies for flexible survival analyses copyright 2008 john wiley sons ltd

information indices unification and applications the unified framework of information theoretic statistics was established by kullback 1959 since then numerous information indices have been developed in various contexts this paper represents many of these indices in a unified context the unification thread is the discrimination information function information indices are all logarithmic measures of discrepancy between two probability distributions first we present a summary of informational aspects of the basic information functions a unification of various information theoretic modeling approaches and some explication in terms of traditional measures we then tabulate a unified representation of assortments of information indices developed in the literature for maximum entropy modeling covariate information and influence diagnostics the subjects of these indices include parametric model fitting nonparametric entropy estimation categorical data analysis the linear and exponential family regression and time series the coverage however is not exhaustive the tabulation includes sampling theory and bayesian indices but the focus is on interpretation as descriptive measures and inferential properties are noted tangentially finally applications of some information indices are illustrated through modeling duration data for sprint s churned customer and choice of long distance provider

model building in nonproportional hazard regression recent developments of statistical methods allow for a very flexible modeling of covariates affecting survival times via the hazard rate including also the inspection of possible time dependent associations despite their immediate appeal in terms of flexibility these models typically introduce additional difficulties when a subset of covariates and the corresponding modeling alternatives have to be chosen that is for building the most suitable model for given data this is particularly true when potentially time varying associations are given we propose to conduct a piecewise exponential representation of the original survival data to link hazard regression with estimation schemes based on of the poisson likelihood to make recent advances for model building in exponential family regression accessible also in the nonproportional hazard regression context a two stage stepwise selection approach an approach based on doubly penalized likelihood and a componentwise functional gradient descent approach are adapted to the piecewise exponential regression problem these three techniques were compared via an intensive simulation study an application to prognosis after discharge for patients who suffered a myocardial infarction supplements the simulation to demonstrate the pros and cons of the approaches in real data analyses

equivariant cohomology and sheaves abstract ro g graded equivariant cohomology was originally defined by using equivariant spectra in this paper we construct a sheaf version of ro g graded equivariant cohomology theory by introducing a complex of presheaves we obtain an isomorphism theorem of two different cohomology theories we further apply the results to the study of real algebraic varieties

topological hypercovers and 1 realizations we show that if u is a hypercover of a topological space x then the natural map hocolim u x is a weak equivalence this fact is used to construct topological realization functors for the 1 homotopy theory of schemes over real and complex fields in an appendix we also prove a theorem about computing homotopy colimits of spaces that are not cofibrant

diagnostic measures for model criticism abstract we discuss the problem of model criticism with emphasis on developing summary diagnostic measures we approach model criticism by identifying possible troublesome features of the currently entertained model embedding the model in an elaborated model and measuring the value of elaborating this requires three elements a model elaboration a prior distribution and a utility function each triplet generates a different diagnostic measure we focus primarily on the measure given by a kullback leibler divergence between the marginal prior and posterior distributions on the elaboration parameter we also develop a linearized version of this diagnostic and use it to show that our procedure is related to other tools commonly used for model diagnostics such as bayes factors and the score function one attraction of this approach is that it allows model criticism to be performed jointly with parameter inference and prediction also this diagnostic approach aims at maintaining an exploratory nature t

algebraic cycles on real varieties and z 2 equivariant homotopy theory in this paper the spaces of algebraic cycles on a real projective variety x are studied as z 2 spaces under the action of the galois group gal c r in particular the equivariant homotopy type of the group of algebraic p cycles zp pc is computed a version of lawson homology for real varieties is proposed the real lawson homology groups are computed for a class of real varieties

the lasso method for variable selection in the cox model summary i propose a new method for variable selection and shrinkage in cox s proportional hazards model my proposal minimizes the log partial likelihood subject to the sum of the absolute values of the parameters being bounded by a constant because of the nature of this constraint it shrinks coe cients and produces some coe cients that are exactly zero as a result it reduces the estimation variance while providing an interpretable final model the method is a variation of the lasso proposal of tibshirani designed for the linear regression context simulations indicate that the lasso can be more accurate than stepwise selection in this setting

formulas for renyi information and related measures for univariate distributions in a recent paper song j stat plan infer 93 2001 51 considered renyi information of order and established its connection to the loglikelihood from this relation an intrinsic distribution measure was proposed and analytic expressions of this measure and renyi information were derived for some standard continuous distributions in this paper we derive analytical formulas for renyi and shannon entropies as well as for song s measure for 26 flexible families of univariate continuous distributions we believe that the results presented here will serve as an important reference for scientists and engineers in many areas

approximate bayesian inference with the weighted likelihood bootstrap we introduce the weighted likelihood bootstrap wlb as a way to simulate approximately from a posterior distribution this method is often easy to implement requiring only an algorithm for calculating the maximum likelihood estimator such as iteratively reweighted least squares in the generic weighting scheme the wlb is first order correct under quite general conditions inaccuracies can be removed by using the wlb as a source of samples in the sampling importance resampling sir algorithm which also allows incorporation of particular prior information the sir adjusted wlb can be a competitive alternative to other integration methods in certain models asymptotic expansions elucidate the second order properties of the wlb which is a generalization of rubin s bayesian bootstrap the calculation of approximate bayes factors for model comparison is also considered we note that given a sample simulated from the posterior distribution the required marginal likelihood may be simulation consistently estimated by the harmonic mean of the associated likelihood values a modification of this estimator that avoids instability is also noted these methods provide simple ways of calculating approximate bayes factors and posterior model probabilities for a very wide class of models

generalized additive modeling with implicit variable selection by likelihood based boosting the use of generalized additive models in statistical data analysis suffers from the restriction to few explanatory variables and the problems of selection of smoothing parameters generalized additive model boosting circumvents these problems by means of stagewise fitting of weak learners a fitting procedure is derived which works for all simple exponential family distributions including binomial poisson and normal response variables the procedure combines the selection of variables and the determination of the appropriate amount of smoothing penalized regression splines and the newly introduced penalized stumps are considered as weak learners estimates of standard deviations and stopping criteria which are notorious problems in iterative procedures are based on an approximate hat matrix the method is shown to be a strong competitor to common procedures for the fitting of generalized additive models in particular in high dimensional settings with many nuisance predictor variables it performs very well

accelerated failure time regression models with a regression model of surviving fraction an application to the analysis of permanent employment in japan abstract accelerated failure time regression models with an additional regression model for the surviving fraction are proposed for the analysis of events that may never occur regardless of censoring for some people in the population risk set the models attempt to estimate simultaneously the effects of covariates on the acceleration deceleration of the timing of a given event and the surviving fraction that is the proportion of the population for which the event never occurs the extended family of the generalized gamma distribution is used for the accelerated failure time regression model the logistic function is used for the regression model of the surviving fraction the models are applied to the data of interfirm job mobility in japan to assess variability in permanent employment among white collar and blue collar employees in firms of different sizes independent from their variability in the timing of interfirm job separations

information theoretic framework for process control abstract this paper proposes a general framework for constructing control charts based on information theory the potential applications include developing information charts for monitoring moments and distributions of a process variable and process attributes in information theoretic process control itpc process moments are mapped to process distributions at in control and monitoring states and then to a control function via constrained maximization of entropy and minimization of kullback leibler function cross entropy variants of information charts can be developed without using distributional assumptions and based on a single criterion function the information discrepancy between two distributions an example of an information chart information mean variance chart imv chart for monitoring process mean and variance is developed the imv chart combines the standard x chart and s 2 chart and provides an information theoretic explication of the traditional procedures based on a run length study it is found that the imv chart singly possesses certain advantages over the standard two chart implementation of x chart and s 2 chart multivariate extension monitoring counts and proportions and monitoring distributional changes are briefly discussed

structured fusion lasso penalized multi state models multi state models generalize survival or duration time analysis to the estimation of transition specific hazard rate functions for multiple transitions when each of the transition specific risk functions is parametrized with several distinct covariate effect coefficients this leads to a model of potentially high dimension to decrease the parameter space dimensionality and to work out a clear image of the underlying multi state model structure one can either aim at setting some coefficients to zero or to make coefficients for the same covariate but two different transitions equal the first issue can be approached by penalizing the absolute values of the covariate coefficients as in lasso regularization if instead absolute differences between coefficients of the same covariate on different transitions are penalized this leads to sparse competing risk relations within a multi state model that is equality of covariate effect coefficients in this paper a new estimation approach providing sparse multi state modelling by the aforementioned principles is established based on the estimation of multi state models and a simultaneous penalization of the l1 norm of covariate coefficients and their differences in a structured way the new multi state modelling approach is illustrated on peritoneal dialysis study data and implemented in the r package penmsm copyright 2016 john wiley sons ltd

information distinguishability with application to analysis of failure data abstract in maximum entropy me modeling the information discrepancy between two distributions is measured in terms of their entropy difference in discrimination information statistics the information discrepancy between two distributions is measured in terms of the kullback leibler function i e relative entropy or cross entropy this article presents an equivalence between kullback leibler functions and entropy differences involving an me distribution based on this equivalence the concept of information discrimination id distinguishability is introduced as a unifying framework for the two methods of measuring information discrepancy between distributions applications of id distinguishability as diagnostics for examining robustness of parametric procedures and sensitivity of nonparametric statistics across parametric families of distributions is proposed the equivalence result facilitates estimation of kullback leibler functions in terms of entropy estimates application of the id distinguish

additive and multiplicative covariate regression models for relative survival incorporating fractional polynomials for time dependent effects relative survival is used to estimate patient survival excluding causes of death not related to the disease of interest rather than using cause of death information from death certificates which is often poorly recorded relative survival compares the observed survival to that expected in a matched group from the general population models for relative survival can be expressed on the hazard mortality rate scale as the sum of two components where the total mortality rate is the sum of the underlying baseline mortality rate and the excess mortality rate due to the disease of interest previous models for relative survival have assumed that covariate effects act multiplicatively and have thus provided relative effects of differences between groups using excess mortality rate ratios in this paper we consider i the use of an additive covariate model which provides estimates of the absolute difference in the excess mortality rate and ii the use of fractional polynomials in relative survival models for the baseline excess mortality rate and time dependent effects the approaches are illustrated using data on 115 331 female breast cancer patients diagnosed between 1 january 1986 and 31 december 1990 the use of additive covariate relative survival models can be useful in situations when the excess mortality rate is zero or slightly less than zero and can provide useful information from a public health perspective the use of fractional polynomials has advantages over the usual piecewise estimation by providing smooth estimates of the baseline excess mortality rate and time dependent effects for both the multiplicative and additive covariate models all models presented in this paper can be estimated within a generalized linear models framework and thus can be implemented using standard software copyright 2005 john wiley sons ltd

quaternionic algebraic cycles and reality in this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real brauer severi varieties under the action of the galois group gal c r appropriate stabilizations of these spaces yield two equivariant spectra the first one classifies dupont seymour s quaternionic k theory and the other one classifies an equivariant cohomology theory 3 which is a natural recipient of characteristic classes kh x 3 x for quaternionic bundles over real spaces x

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

ordering univariate distributions by entropy and variance this paper examines the role of variance and entropy in ordering distributions and random prospects there is no universal relation between entropy and variance orderings of distributions but we place their relationship in the context of a stronger ordering relation known as dispersion ordering further some conditions are identified under which variance and entropy order similarly when continuous variables are transformed we also analyze parametric changes which do not disturb the agreement between these rankings the results are conveniently tabulated in terms of distribution parameters

bigraded equivariant cohomology of real quadrics we give a complete description of the bigraded bredon co homology ring of smooth projective real quadrics with coefficients in the constant mackey functor z these invariants are closely related to the integral motivic cohomology ring which is not known for these va rieties some of the results and techniques introduced can be applied to other geometrically cellular real varieties

thin plate regression splines discuss the production of low rank smoothers for d greater than or equal to 1 dimensional data which can be fitted by regression or penalized regression methods the smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension of the basis used to construct the smoother by making use of lanczos iteration the basis change and truncation are computationally efficient the smoothers allow the use of approximate thin plate spline models with large data sets avoid the problems that are associated with knot placement that usually complicate modelling with regression splines or penalized regression splines provide a sensible way of modelling interaction terms in generalized additive models provide low rank approximations to generalized smoothing spline models appropriate for use with large data sets provide a means for incorporating smooth functions of more than one variable into non linear models and improve the computational efficiency of penalized likelihood models incorporating thin plate splines given that the approach produces spline like models with a sparse basis it also provides a natural way of incorporating unpenalized spline like terms in linear and generalized linear models and these can be treated just like any other model terms from the point of view of model selection inference and diagnostics

simple parametric and nonparametric models for excess and relative mortality this paper studies two classes of hazard rate based models for the mortality in a group of individuals taking normal life expectancy into account in a multiplicative hazard model the estimate for the relative mortality generalises the standardised mortality ratio and the adequacy of a model with constant relative mortality can be tested using a type of total time on test statistic in an additive hazard model continuous time generalisations of a corrected survival curve and a normal survival curve are obtained and the adequacy of a model with constant excess mortality can again be tested using a type of total time on test statistic a model including both the multiplicative hazard model and the additive hazard model is briefly considered the use of the models is illustrated on a set of data concerning survival after operation for malignant melanoma