leveraging prognostic baseline variables to gain precision in randomized trials we focus on estimating the average treatment effect in a randomized trial if baseline variables are correlated with the outcome then appropriately adjusting for these variables can improve precision an example is the analysis of covariance ancova estimator which applies when the outcome is continuous the quantity of interest is the difference in mean outcomes comparing treatment versus control and a linear model with only main effects is used ancova is guaranteed to be at least as precise as the standard unadjusted estimator asymptotically under no parametric model assumptions and also is locally semiparametric efficient recently several estimators have been developed that extend these desirable properties to more general settings that allow any real valued outcome e g binary or count contrasts other than the difference in mean outcomes such as the relative risk and estimators based on a large class of generalized linear models including logistic regression to the best of our knowledge we give the first simulation study in the context of randomized trials that compares these estimators furthermore our simulations are not based on parametric models instead our simulations are based on resampling data from completed randomized trials in stroke and hiv in order to assess estimator performance in realistic scenarios we provide practical guidance on when these estimators are likely to provide substantial precision gains and describe a quick assessment method that allows clinical investigators to determine whether these estimators could be useful in their specific trial contexts

discrimination and classification overview publisher summary this chapter discusses discrimination and classification the problem of discrimination and classification is mainly concerned with differentiating between g g 2 mutually exclusive populations and with classifying subjects or objects on the basis of multivariate observation the emphasis of the problem is on deriving a rule that can be used to optimally classify a new subject it is an important problem in statistics and applied mathematics as its applications are found in many diverse areas in practice the distributions are rarely known and if the form of the distributions are known or assumed the parameters are seldom known thus the problem for practical applications is to develop a sample based rule for discrimination and classification the earliest and most well known method is based on the linear discriminant function due to fisher

designs for generalized linear models with random block effects via information matrix approximations summary the selection of optimal designs for generalized linear mixed models is complicated by the fact thatthefisherinformationmatrix onwhichmostoptimalitycriteriadepend iscomputationally expensive to evaluate we provide two novel approximations that reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes or monte carlo approximations thereof an asymptotic approximation that is accurate when there is strong dependence between observations in the same block and an approximation via kriging interpolators for logistic random intercept models we show how interpolation can be especially effective for finding pseudo bayesian designs that incorporate uncertainty in the values of the model parameters the new results are used to evaluate the efficiency for estimating conditional models of optimal designs from closed form approximations to the information matrix derived from marginal models correcting for the marginal attenuation of parameters in binary response models yields much improved designs typically with very high efficiencies however in some experiments exhibiting strong dependence designs for marginal models may still be inefficient forconditionalmodelling ourasymptoticresultsprovidesometheoreticalinsightsintowhysuch inefficiencies occur

a note on the existence of the posterior distribution for a class of mixed models for binomial responses summary necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses the implications of our results are illustrated through an example

sample size considerations and predictive performance of multinomial logistic prediction models multinomial logistic regression mlr has been advocated for developing clinical prediction models that distinguish between three or more unordered outcomes we present a full factorial simulation study to examine the predictive performance of mlr models in relation to the relative size of outcome categories number of predictors and the number of events per variable it is shown that mlr estimated by maximum likelihood yields overfitted prediction models in small to medium sized data in most cases the calibration and overall predictive performance of the multinomial prediction model is improved by using penalized mlr our simulation study also highlights the importance of events per variable in the multinomial context as well as the total sample size as expected our study demonstrates the need for optimism correction of the predictive performance measures when developing the multinomial logistic prediction model we recommend the use of penalized mlr when prediction models are developed in small data sets or in medium sized data sets with a small total sample size ie when the sizes of the outcome categories are balanced finally we present a case study in which we illustrate the development and validation of penalized and unpenalized multinomial prediction models for predicting malignancy of ovarian cancer

confidence intervals for multinomial logistic regression in sparse data logistic regression is one of the most widely used regression models in practice but alternatives to conventional maximum likelihood estimation methods may be more appropriate for small or sparse samples modification of the logistic regression score function to remove first order bias is equivalent to penalizing the likelihood by the jeffreys prior and yields penalized maximum likelihood estimates ples that always exist even in samples in which maximum likelihood estimates mles are infinite ples are an attractive alternative in small to moderate sized samples and are preferred to exact conditional mles when there are continuous covariates we present methods to construct confidence intervals ci in the penalized multinomial logistic regression model and compare ci coverage and length for the ple based methods to that of conventional mle based methods in trinomial logistic regressions with both binary and continuous covariates based on simulation studies in sparse data sets we recommend profile cis over asymptotic wald type intervals for the ples in all cases furthermore when finite sample bias and data separation are likely to occur we prefer ple profile cis over mle methods

shape analysis for the anisotropic corpuscle problem the problem of inferring the shape distribution of anisotropically oriented spheroidal particles from their elliptical traces in planar samples is addressed by generalizing a size shape independence condition suggested by wicksell in his original discussion of the corpuscle problem shape statistics are introduced through which the eccentricities of the sampled ellipses may be related to some suitably defined moments of the underlying particle shape distribution taking account of particle orientation practical methods which employ bootstrap resampling of shape statistics are developed with reference to data from a recent neurological study

mmc techniques for limited dependent variables models implementation by the branch and bound algorithm we propose a finite sample approach to some of the most common limited dependent variables models the method rests on the maximized monte carlo mmc test technique proposed by dufour 1998 monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics journal of econometrics this issue we provide a general way for implementing tests and confidence regions we show that the decision rule associated with a mmc test may be written as a mixed integer programming problem the branch and bound algorithm yields a global maximum in finite time an appropriate choice of the statistic yields a consistent test while fulfilling the level constraint for any sample size the technique is illustrated with numerical data for the logit model c 2005 elsevier b v all rights reserved

a note on a albert and j a anderson s conditions for the existence of maximum likelihood estimates in logistic regression models summary this note expands the paper by albert anderson 1984 on the existence and uniqueness of maximum likelihood estimates in logistic regression models their three possible mutually exclusive data pattems i overlap ii complete separation and iii quasiseparation are considered the maximum likelihood estimate exists only in i modifications of the statement and proofs of albert anderson s results are given for ii and iii the identifiability for a more general model arising in the study of iii is discussed together with the maximization of the corresponding likelihood a linear program is presented which determines whether data is of type i ii or iii and in the case of iii identifies albert anderson s minimal set qm

stable reduction of curves and tame ramification we study stable reduction of curves in the case where a tamely ramified base extension is sufficient if x is a smooth curve defined over the fraction field of a strictly henselian discrete valuation ring there is a criterion due to saito that describes precisely in terms of the geometry of the minimal model with strict normal crossings of x when a tamely ramified extension suffices in order for x to obtain stable reduction for such curves we construct an explicit extension that realizes the stable reduction and we furthermore show that this extension is minimal we also obtain a new proof of saito s criterion avoiding the use of l adic cohomology and vanishing cycles

bias correction of bounded location error in binary data binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology many spatially referenced binary data sets suffer from location error which occurs when the recorded location of an observation differs from its true location when location error occurs values of the covariates associated with the true spatial locations of the observations cannot be obtained we show how a change of support cos can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons the cos accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression using a simulation experiment we compare binary regression models with a cos to naive approaches that ignore location error we illustrate the flexibility of the cos by modeling individual level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable but that the cos can be used to eliminate bias while preserving model choice

a dose finding approach based on shrunken predictive probability for combinations of two agents in phase i trials we develop a novel dose finding method for two agent combination phase i trials on the basis of the shrunken predictive probability of toxicity in this method a shrinkage logistic regression model that allows distinct shrinkage multipliers for the coefficients of the main effects of two agents and their interaction on the probability of toxicity constructs the toxicity outcome we also propose dose escalation de escalation decision rules on the basis of the shrunken predictive probability of toxicity simulation studies under various patterns of monotonic dose response relationships for combinations of two agents demonstrated that the proposed method performed no worse than the existing two dose finding methods we selected copyright 2013 john wiley sons ltd

extending the c statistic to nominal polytomous outcomes the polytomous discrimination index diagnostic problems in medicine are sometimes polytomous meaning that the outcome has more than two distinct categories for example ovarian tumors can be benign borderline primary invasive or metastatic extending the main measure of binary discrimination the c statistic or area under the roc curve to nominal polytomous settings is not straightforward this paper reviews existing measures and presents the polytomous discrimination index pdi as an alternative the pdi assesses all sets of k cases consisting of one case from each outcome category for each category i i 1 k it is assessed whether the risk of category i is highest for the case from category i a score of 1 k is given per category for which this holds yielding a set score between 0 and 1 to indicate the level of discrimination the pdi is the average set score and is interpreted as the probability to correctly identify a case from a randomly selected category within a set of k cases this probability can be split up by outcome category yielding k category specific values that result in the pdi when averaged we demonstrate the measures on two diagnostic problems residual mass histology after chemotherapy for testicular cancer diagnosis of ovarian tumors we compare the behavior of the measures on theoretical data showing that pdi is more strongly influenced by simultaneous discrimination between all categories than by partial discrimination between pairs of categories in conclusion the pdi is attractive because it better matches the requirements of a measure to summarize polytomous discrimination copyright 2012 john wiley sons ltd

cross validated spline methods for the estimation of three dimensional tumor size distributions from observations on two dimensional cross sections abstract we study the problem of estimating the distribution of the three dimensional radiuses of a collection of spheres given measurements of the two dimensional radiuses of a sample of planar cross sections this problem arises in the estimation of the tumor size distribution of spherical microtumors induced in mouse livers following injection of a carcinogen we first convert this problem to a form suitable for the application of cross validated spline methods for the solution of ill posed integral equations given noisy data then we develop special numerical techniques that will allow the spline methods to be accurately applied to integral equations like those associated with the present problem we apply the resulting method to some mouse liver data the subject mouse liver has been completely dissected allowing a rare comparison of the estimate with the truth the statistical properties of the estimate are explored via monte carlo methods the interplay between statistical and numerical analyti

vanishing cycles and geometry of curves over a discrete valuation ring 0 introduction geometry of curves over a discrete valuation ring is reflected in the action of the monodromy on the f adic cohomology groups the stable reduction theorem d m gives an equivalent geometrical condition for the action of the inertia group to be unipotent in the global situation where global means that the curve in consideration is proper in this paper we will generalize it in two directions one is to the local situation with the isolated singularity the other is to consider the geometrical condition for the action of the wild ramification group to be trivial we will also give a purely cohomological proof without using picard schemes of the stable reduction theorem and a new proof of the formula of deligne la theorem 5 1 1 based only on the stable reduction theorem here we only treat a strictly local discrete valuation ring with algebraically closed residue field however the results apply to any discrete valuation ring with perfect residue field since they are etale local we introduce some notations and terminologies

psychometric latent response models in this paper some psychometric models will be presented that belong to the larger class oflatent response models lrms first lrms are introduced by means of an application in the field ofcomponential item response theory embretson 1980 1984 second a general definition of lrms not specific for the psychometric subclass is given third some more psychometric lrms and examples of how they can be applied are presented fourth a method for obtaining maximum likelihood ml and some maximum a posteriori map estimates of the parameters of lrms is presented this method is then applied to theconjunctive rasch model fifth and last an application of the conjunctive rasch model is presented this model was applied to responses to typical verbal ability items open synonym items

a note on a general definition of the coefficient of determination summary a generalization of the coefficient of determination r2 to general regression models is discussed a modification of an earlier definition to allow for discrete models is proposed

information recovery in a study with surrogate endpoints recently there has been a lot of interest in statistical methods for analyzing data with surrogate endpoints in this article we consider parameter estimation from a model that relates a variable y to a set of covariates x in the presence of a surrogate s we assume that the data are made up of two random samples from the population a validation set where y x s are observed on every subject and a nonvalidation set where only x s are measured we show how information from the nonvalidation set can be incorporated to improve upon estimation of a parameter using the validation data only the method we suggest does not require knowledge on the joint distribution between y s given x it is based on a two sample empirical likelihood that simultaneously combines the estimating equations from the validation set and the nonvalidation set the proposed nonparametric likelihood formulation brings a few attractive features to the inference in first the maximum empirical likelihood estimate is m

material identification of real impact sounds effects of size variation in steel glass wood and plexiglass plates identification of the material of struck objects of variable size was investigated previous studies on this issue assumed recognition to be based on acoustical measures of damping this assumption was tested comparing the power of a damping measure in explaining identification data with that of several other acoustical descriptors listeners performance was perfect with respect to gross material categories steel glass and wood plexiglass comprising materials of vastly different mechanical properties impaired performance was observed for materials within the same gross category identification being based on the size of the objects alone the damping descriptor accounted for the identification of the gross categories however other descriptors such as signal duration explained the results equally well materials within the same gross category were identified mainly on the basis of signal frequency overall poor support for the relevance of damping to material perception was found an analysis of the acoustical support for perfect material identification was carried out sufficient acoustical information for perfect performance was found thus procedural biases for the origin of the effects of size could be discarded pointing toward their cognitive rather than methodological nature identification performance was explained in terms of the regularities of the everyday acoustical environment

blocked designs for experiments with correlated non normal response many experiments measure a response that cannot be adequately described by a linear model with normally distributed errors and are often run in blocks of homogeneous experimental units we develop the first general methods of obtaining efficient blocked designs for experiments with an exponential family response described by a marginal model fitted via generalized estimating equations this methodology is appropriate when the blocking factor is a nuisance variable as often occurs in industrial experiments a d optimality criterion is developed for finding designs robust to the values of the marginal model parameters and applied using two strategies unrestricted algorithmic search and blocking of an optimal design for the corresponding generalized linear model glm designs from each strategy are critically compared and shown to be more efficient than use of a random allocation to blocks of the points from an optimal glm design the designs are compared for a range of values of the intra block working c

the kernel method for unfolding sphere size distributions abstract suppose spherical particles are embedded in an opaque matrix sphere radii are independent random variables with unknown density f we wish to estimate f from the circular profiles of the spheres intersecting a plane section through the material a recent proposal by c c taylor j microscopy132 57 1983 is to estimate f by stereologically unfolding a kernel estimator derived from the observed profiles we give some theoretical results for the bias and variance of this estimator and draw some sharp contrasts with ordinary density estimation the unfolding causes the estimator to converge at a surprisingly slow rate but it is also shown that this slow convergence is intrinsic to the problem and is not a deficiency of taylor s method the arguments are extended to cover also some other cases of stereological unfolding where a theoretical closed form solution exists

partial separation in logistic discrimination summary the problem of maximum likelihood estimates in logistic discrimination is receiving growing attention in the literature the existence is known to be highly dependent on the data configuration observed here we focus on the practically important case where the group samples form a set of clusters that are completely separated from each other which we call partial separation the classical fisher iris data set is a good example of the problem discussed a non existence theorem is proven and a general algorithm is developed to help to distinguish separation from multicollinearity given divergence in maximum likelihood estimation

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

multiple imputation of industry and occupation codes in census public use samples using bayesian logistic regression abstract we describe methods used to create a new census data base that can be used to study comparability of industry and occupation classification systems this project represents the most extensive application of multiple imputation to date and the modeling effort was considerable as well hundreds of logistic regressions were estimated one goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project to multiply impute 1980 census comparable codes for industries and occupations in two 1970 census public use samples logistic regression models were estimated with flattening constants for many of the regression models considered the data were too sparse to support conventional maximum likelihood analysis so some alternative had to be employed these methods solve existence and

diagnostic and sampling models in screening summary screening methods are developed which raise the proportion of successes in the retained population to a predetermined level specification regions for the screening variables are derived within both the diagnostic and sampling paradigms dawid 1976 logistic and normal models are used for the two frameworks and the results are illustrated by an example of screening for malnourishment

a general strategy for analyzing data from split plot and multistratum experimental designs increasingly industrial experiments use multistratum designs such as split plot and strip plot designs often these experiments span more than one processing stage the challenge is to identify an appropriate multistratum design along with an appropriate statistical model in this article we introduce hasse diagrams in the response surface context as a tool to visualize the unit structure of the experimental design the randomization and sampling approaches used the stratum in which each experimental factor is applied and the degrees of freedom available in each stratum to estimate main effects interactions and variance components we illustrate their use on several responses measured in a large study of the adhesion properties of coatings to polypropylene we discuss quantitative binary and ordered categorical responses for designs ranging from a simple split plot to a strip plot that involves repeated measurements of the response the datasets discussed in this article are available online a

on the degrees of freedom of the lasso we study the effective degrees of freedom of the lasso in the framework of stein s unbiased risk estimation sure we show that the number of nonzero coefficients is an unbiased estimate forthe degrees of freedom of the lasso a conclusion that requires no special assumption on the predictors in addition the unbiased estimator is shown to be asymptotically consistent with these results on hand various model selection criteria cp aic and bic are available which along with the lars algorithm provide a principled and efficient approach to obtaining the optimal lasso fit with the computational effort of a single ordinary least squares fit

binary time series modeling with application to adhesion frequency experiments repeated adhesion frequency assay is the only published method for measuring the kinetic rates of cell adhesion cell adhesion plays an important role in many physiological and pathological processes traditional analysis of adhesion frequency experiments assumes that the adhesion test cycles are independent bernoulli trials this assumption often can be violated in practice motivated by the analysis of repeated adhesion tests a binary time series model incorporating random effects is developed a goodness of fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects the asymptotic distribution of the goodness of fit statistic is derived and its finite sample performance is examined through a simulation study application of the proposed methodology to real data from a t cell experiment reveals some interesting information including the dependency between repeated adhesion tests

bias reduced and separation proof gee with small or sparse longitudinal binary data generalized estimating equation gee is a popular approach for analyzing correlated binary data however the problems of separation in gee are still unknown the separation created by a covariate often occurs in small correlated binary data and even in large data with rare outcome and or high intra cluster correlation and a number of influential covariates this paper investigated the consequences of separation in gee and addressed them by introducing a penalized gee termed as pgee the pgee is obtained by adding firth type penalty term which was originally proposed for generalized linear model score equation to standard gee and shown to achieve convergence and provide finite estimate of the regression coefficient in the presence of separation which are not often possible in gee further a small sample bias correction to the sandwich covariance estimator of the pgee estimator is suggested simulations also showed that the gee failed to achieve convergence and or provided infinitely large estimate of the regression coefficient in the presence of complete or quasi complete separation whereas the pgee showed significant improvement by achieving convergence and providing finite estimate even in the presence of near to separation the pgee also showed superior properties over the gee furthermore the bias corrected sandwich estimator for the pgee estimator showed substantial improvement over the standard sandwich estimator by reducing bias in estimating type i error rate an illustration using real data also supported the findings of simulation the pgee with bias corrected sandwich covariance estimator is recommended to use for small to moderate size sample n 50 and even can be used for large sample if there is any evidence of separation or near to separation

improved estimation in cumulative link models for the estimation of cumulative link models for ordinal data the bias reducing adjusted score equations of firth in 1993 are obtained whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood estimator their form suggests a parameter dependent adjustment of the multinomial counts which in turn suggests the solution of the adjusted score equations through iterated maximum likelihood fits on adjusted counts greatly facilitating implementation like the maximum likelihood estimator the reduced bias estimator is found to respect the invariance properties that make cumulative link models a good choice for the analysis of categorical data its additional finiteness and optimal frequentist properties along with the adequate behaviour of related asymptotic inferential procedures make the reduced bias estimator attractive as a default choice for practical applications furthermore the estimator proposed enjoys certain shrinkage properties that are defensible from an experimental point of view relating to the nature of ordinal data

probability matrix decomposition models in this paper we consider a class of models for two way matrices with binary entries of 0 and 1 first we considerboolean matrix decomposition conceptualize it as alatent response model lrm and by making use of this conceptualization generalize it to a larger class of matrix decomposition models second probability matrix decomposition pmd models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models third an algorithm for the computation of the maximum likelihood ml and the maximum a posteriori map estimates of the parameters of pmd models is presented this algorithm is an em algorithm and is a special case of a more general algorithm that can be used for the whole class of lrms and fourth as an example a pmd model is applied to data on decision making in psychiatric diagnosis

mixture generalized linear models for multiple interval mapping of quantitative trait loci in experimental crosses summary quantitative trait loci mapping in experimental organisms is of great scientific and economic importance there has been a rapid advancement in statistical methods for quantitative trait loci mapping various methods for normally distributed traits have been well established some of them have also been adapted for other types of traits such as binary count and categorical traits in this article we consider a unified mixture generalized linear model glim for multiple interval mapping in experimental crosses the multiple interval mapping approach was proposed by kao zeng and teasdale 1999 genetics 152 1203 1216 for normally distributed traits however its application to nonnormally distributed traits has been hindered largely by the lack of an efficient computation algorithm and an appropriate mapping procedure in this article an effective expectation maximization algorithm for the computation of the mixture glim and an epistasis effect adjusted multiple interval mapping procedure is developed a real data set radiata pine data is analyzed and the data structure is used in simulation studies to demonstrate the desirable features of the developed method

the efficiency of multinomial logistic regression compared with multiple group discriminant analysis abstract multinomial logistic regression also referred to as polychotomous logistic regression is frequently used for the analysis of categorical response data with continuous or categorical explanatory variables parameter estimates are usually obtained through direct maximum likelihood estimation normal discriminant analysis has been used as an alternative approach to this methodology although it is strictly appropriate only when the usual normal discriminant assumptions concerning the explanatory variables are valid comparative evaluations of the two procedures including the investigation of bias and efficiency in parameter estimation have been almost entirely limited to the case of two response groups for both normal and nonnormal explanatory variables bull and donner 1987 extended the comparison of logistic regression and normal discrimination in the normal case to more than two response groups deriving the large sample distribution of the slope parameter estimates for each of the two proc

on the existence of maximum likelihood estimators for the binomial response models summary necessary and sufficient conditions are given for the existence of maximum likelihood estimators of the linear regression parameter in binomial response this includes logit and probit models the question of existence of maximum likelihood estimators mle for logit models arose in an analysis of the relationship of psychiatric caseness to scores on a psychiatric screening questionnaire tennant 1977 administered the ghq general health questionnaire goldberg 1972 to 120 patients attending a general practitioner s surgery and also gave each one a standardized psychiatric interview from the interview patients were classified as psychiatric case non case in a secondary analysis of tennant s data duncan jones and henderson 1978 fitted a logit regression of caseness on ghq score and obtained a good fit with the model

prognostic modelling with logistic regression analysis a comparison of selection and estimation methods in small data sets logistic regression analysis may well be used to develop a prognostic model for a dichotomous outcome especially when limited data are available it is difficult to determine an appropriate selection of covariables for inclusion in such models also predictions may be improved by applying some sort of shrinkage in the estimation of regression coefficients in this study we compare the performance of several selection and shrinkage methods in small data sets of patients with acute myocardial infarction where we aim to predict 30 day mortality selection methods included backward stepwise selection with significance levels alpha of 0 01 0 05 0 157 the aic criterion or 0 50 and the use of qualitative external information on the sign of regression coefficients in the model estimation methods included standard maximum likelihood the use of a linear shrinkage factor penalized maximum likelihood the lasso or quantitative external information on univariable regression coefficients we found that stepwise selection with a low alpha for example 0 05 led to a relatively poor model performance when evaluated on independent data substantially better performance was obtained with full models with a limited number of important predictors where regression coefficients were reduced with any of the shrinkage methods incorporation of external information for selection and estimation improved the stability and quality of the prognostic models we therefore recommend shrinkage methods in full models including prespecified predictors and incorporation of external information when prognostic models are constructed in small data sets

a semiparametric changepoint model a semiparametric changepoint model is considered and the empirical likelihood method is applied to detect the change from a distribution to a weighted distribution in a sequence of independent random variables the maximum likelihood changepoint estimator is shown to be consistent the empirical likelihood ratio test statistic is proved to have the same limit null distribution as that with parametric models a data based test for the validity of the models is also proposed simulation shows the sensitivity and robustness of the semiparametric approach the methods are applied to some classical datasets such as the nile river data and stock price data

a permutation test for inference in logistic regression with small and moderate sized data sets inference based on large sample results can be highly inaccurate if applied to logistic regression with small data sets furthermore maximum likelihood estimates for the regression parameters will on occasion not exist and large sample results will be invalid exact conditional logistic regression is an alternative that can be used whether or not maximum likelihood estimates exist but can be overly conservative this approach also requires grouping the values of continuous variables corresponding to nuisance parameters and inference can depend on how this is done a simple permutation test of the hypothesis that a regression parameter is zero can overcome these limitations the variable of interest is replaced by the residuals from a linear regression of it on all other independent variables logistic regressions are then done for permutations of these residuals and a p value is computed by comparing the resulting likelihood ratio statistics to the original observed value simulations of binary outcome data with two independent variables that have binary or lognormal distributions yield the following results a in small data sets consisting of 20 observations type i error is well controlled by the permutation test but poorly controlled by the asymptotic likelihood ratio test b in large data sets consisting of 1000 observations performance of the permutation test appears equivalent to that of the asymptotic test and c in small data sets the p value for the permutation test is usually similar to the mid p value for exact conditional logistic regression

penalized maximum likelihood estimation in logistic regression and discrimination summary maximum likelihood estimation of the parameters of the binary logistic regression model for pr h i x is discussed with separate discussion of sampling from i the conditional distribution of h given x ii the joint distribution of h and x and iii the conditional distribution of x given h difficulties associated with continuous x in the latter sampling scheme are discussed to avoid these penalized maximum likelihood estimates are introduced which give estimates of the logistic parameters and a nonparametric spline estimate of the marginal distribution of x extensions to multinomial logistic regression are outlined

is the minimum chi square estimator the winner in logit regression abstract amemiya 1980 showed that the bias corrected maximum likelihood estimator has a smaller n 2 order mse matrix than minimum chi square in a general logit model in this paper the exact mse is calculated for both estimators for berkson s 1995 examples the bias corrected maximum likelihood has a smaller exact mse provided that berkson s 2n rule is used in the calculation of the exact results the margin by which the exact mse of minimum chi square exceeds that of bias corrected maximum likelihood is small and hence there may be no practical advantage in using the latter estimator

kernel estimation in wicksell s corpuscle problem summary we consider the estimation of the probability density function of the radii of spheres in a medium given the radii of their profiles in a random cross section this problem is known as wicksell s corpuscle problem we present a new estimator related to the classical kernel density estimator and discuss its properties a comparison is made with other estimators related to the kernel estimator

predictive value of statistical models a review is given of different ways of estimating the error rate of a prediction rule based on a statistical model a distinction is drawn between apparent optimum and actual error rates moreover it is shown how cross validation can be used to obtain an adjusted predictor with smaller error rate a detailed discussion is given for ordinary least squares logistic regression and cox regression in survival analysis finally the splitsample approach is discussed and demonstrated on two data sets

mixtures of g priors in generalized linear models abstractmixtures of zellner s g priors have been studied extensively in linear models and have been shown to have numerous desirable properties for bayesian variable selection and model averaging

adjusted score functions for monotone likelihood in the cox regression model standard inference procedures for the cox model involve maximizing the partial likelihood function monotone partial likelihood is an issue that frequently happens in the analysis of health science studies monotone likelihood mainly occurs in samples with substantial censoring of survival times and is associated with categorical covariates in particular and more frequently it usually happens when one level of a categorical covariate has just experienced censoring times in order to overcome this problem heinze and schemper proposed an adjusted partial likelihood score function obtained by suitably adapting the general approach of firth for mean bias reduction the procedure is effective in preventing infinite estimates as an alternative solution we propose an approach based on the adjusted score function recently suggested by kenne pagui et al for median bias reduction this procedure also solves the infinite estimate problem and has an additional advantage of being invariant under componentwise reparameterizations this latter fact is fundamental under cox model since hazards ratio interpretation is obtained by exponentiating parameter estimates numerical studies of the proposed method suggest better inference properties than those of the mean bias reduction a real data application related to a melanoma skin dataset is used as illustration for a comparison basis of the methods

efficient design for estimation of median lethal dose and quantal dose response curves summary the results of quantal dose response experiments are often summarized by an estimate of the median lethal dose denoted ld50 and many sequential designs have been proposed for efficient estimation of ld50 these designs strive to produce a sequence of trials at dose levels that get closer and closer to ld50 consequently they may not provide very good estimates of the overall shape of the dose response curve in this paper we propose guidelines for the design of experiments that estimate ld50 fairly efficiently and that also allow for efficient global estimation of the curve

propriety of the posterior distribution and existence of the mle for regression models with covariates missing at random characterizing model identifiability in the presence of missing covariate data is a very important issue in missing data problems in this article we characterize the propriety of the posterior distribution of the regression coefficients for some general classes of regression models including the class of generalized linear models glm s and parametric survival models with right censored data toward this goal we derive some very general and easy to check conditions for the matrix of covariates we also derive sufficient conditions for the existence of the maximum likelihood estimates and establish novel results for checking propriety of the posterior when the sample size is large several theorems are given to establish propriety of the posterior and the existence of the maximum likelihood estimator the conditions reduce to solving a system of linear equations which can be carried out using software such as maple imsl or sas we assume that the missing covariates are missing at random and assume

power of tests in binary response models most hypotheses in binary response models are composite the null hypothesis is usually that one or more slope coefficients are zero typically the sequence of alternatives of interest is one in which the slope coefficients are increasing in absolute value in this papar we prove that the power goes to zero for this sequence of alternatives of interest in cases which often occur in practice this abstract was borrowed from another version of this item