dose response signal detection under model uncertainty we investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty when several competing regression models are available to describe the dose response relationship the proposed approach uses the complete structure of the regression models but does not require knowledge of the parameters of the competing models standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters however for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values we thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on gaussian processes the new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

maximin designs for exponential growth models and heteroscedastic polynomial models this paper is concerned with nonsequential optimal designs for a class of nonlinear growth models which includes the asymptotic regression model this design problem is intimately related to the problem of finding optimal designs for polynomial regression models with only partially known heteroscedastic structure in each case a straightforward application of the usual d optimality criterion would lead to designs which depend on the unknown underlying parameters to overcome this undesirable dependence a maximin approach is adopted the theorem of perron and frobenius on primitive matrices plays a crucial role in the analysis

equivalence of regression curves sharing common parameters in clinical trials the comparison of two different populations is a common problem nonlinear parametric regression models are commonly used to describe the relationship between covariates such as concentration or dose and a response variable in the two groups in some situations it is reasonable to assume some model parameters to be the same for instance the placebo effect or the maximum treatment effect in this paper we develop a parametric bootstrap test to establish the similarity of two regression curves sharing some common parameters we show by theoretical arguments and by means of a simulation study that the new test controls its significance level and achieves a reasonable power moreover it is demonstrated that under the assumption of common parameters a considerably more powerful test can be constructed compared with the test that does not use this assumption finally we illustrate the potential applications of the new methodology by a clinical trial example

optimal weights for experimental designs on linearly independent support points an explicit formula is derived to compute the a optimal design weights on linearly independent regression vectors for the mean parameters in a linear model with homoscedastic variances the formula emerges as a special case of a general result which holds for a wide class of optimality criteria there are close links to iterative algorithms for computing optimal weights

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

optimal designs for quantile regression models despite their importance optimal designs for quantile regression models have not been developed so far in this article we investigate the d optimal design problem for nonlinear quantile regression analysis we provide a necessary condition to check the optimality of a given design and use it to determine bounds for the number of support points of locally d optimal designs the results are illustrated determining locally bayesian and standardized maximin d optimal designs for quantile regression analysis in the michaelis menten and emax model which are widely used in such important fields as toxicology pharmacokinetics and dose response modeling

optimal designs for dose finding studies with an active control summary dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control in the past however research has focused mostly on experimental designs for placebo controlled dose finding studies to the best of our knowledge optimal designs for dose finding studies with an active control have not been considered so far as the statistical analysis for an active controlled dose finding study can be formulated in terms of a mixture of two regression models the related design problem is different from what has been investigated before in the literature we present a rigorous approach to the problem of determining optimal designs for estimating the smallest dose achieving the same treatment effect as the active control we determine explicitly the locally optimal designs for a broad class of models employed in such studies we also discuss robust design strategies and determine related bayesian and standardized minimax optimal designs we illustrate the results by investigating alternative designs for a clinical trial which has recently appeared in a consulting project of one of the authors

on the efficiency of two stage response adaptive designs in this paper we investigate the efficiency of response adaptive locally optimum designs we focus on two stage adaptive designs where after the first stage the accrued data are used to determine a locally optimum design for the second stage on the basis of an explicit expansion of the information matrix we compare the variance of the maximum likelihood estimates obtained from a two stage adaptive design and a fixed design without adaptation for several one parameter models we provide explicit expressions for the relative efficiency of these two designs which is seen to depend sensitively on the statistical problem under investigation in particular we show that in non linear regression models with moderate or large variances the first stage sample size of an adaptive design should be chosen sufficiently large in order to address variability in the interim parameter estimates these findings support the results of recent simulation studies conducted to compare adaptive designs in more complex situations we finally present an application to a real clinical dose finding trial aiming at the estimation of the smallest dose achieving a certain percentage of the maximum treatment effect by using a three parameteremax model copyright 2012 john wiley sons ltd

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

optimal designs for the emax log linear and exponential models we derive locally d and edp optimal designs for the exponential log linear and three parameter emax models for each model the locally d and ed p optimal designs are supported at the same set of points while the corresponding weights are different this indicates that for a given model d optimal designs are efficient for estimating the smallest dose that achieves 100p of the maximum effect in the observed dose range conversely ed p optimal designs also yield good d efficiencies we illustrate the results using several examples and demonstrate that locally d and ed p optimal designs for the emax log linear and exponential models are relatively robust with respect to misspecification of the model parameters

maximum likelihood analysis of a general latent variable model with hierarchically mixed data summary a general two level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels nonlinear relationships among the latent variables in the structural equations at both levels as well as the effects of fixed covariates in the measurement and structural equations at both levels can be analyzed within the framework moreover the methodology can be applied to hierarchically mixed continuous dichotomous and polytomous data a monte carlo em algorithm is implemented to produce the maximum likelihood estimate the e step is completed by approximating the conditional expectations through observations that are simulated by markov chain monte carlo methods while the m step is completed by conditional maximization a procedure is proposed for computing the complicated observed data log likelihood and the bic for model comparison the methods are illustrated by using a real data set

a general approach to categorical data analysis with missing data using generalized linear models with composite links a general approach for analyzing categorical data when there are missing data is described and illustrated the method is based on generalized linear models with composite links the approach can be used among other applications to fill in contingency tables with supplementary margins fit loglinear models when data are missing fit latent class models without or with missing data on observed variables fit models with fused cells including many models from genetics and to fill in tables or fit models to data when variables are more finely categorized for some cases than others both newton like and em methods are easy to implement for parameter estimation

designing experiments with respect to standardized optimality criteria we introduce a new class of standardized optimality criteria which depend on standardized covariances of the least squares estimators and provide an alternative to the commonly used criteria in design theory besides a nice statistical interpretation the new criteria satisfy an extremely useful invariance property which allows an easy calculation of optimal designs on many linearly transformed design spaces

stabilized finite element approximations for a generalized boussinesq problem a posteriori error analysis abstract the purpose of this work is the design and analysis of a posteriori error estimators for low order stabilized finite element approximations of a generalized boussinesq problem we consider standard stabilization procedures over conforming finite element spaces and a nonconforming one that delivers a divergence free discrete velocity field the analysis that is valid for two and three dimensional domains relies on a smallness assumption on the solution and is based on a technique that involves the ritz projection of the residuals the devised a posteriori error estimators are proven to be globally reliable and locally efficient three dimensional numerical experiments reveal a competitive performance of adaptive procedures driven by the designed a posteriori error estimators

the equivalence of two models for ordinal data summary the equivalence of the grouped continuous and continuation ratio models for ordinal data when the complementary log log link is used is demonstrated recent experience using two regression models for ordinal data gave essentially identical results when the complementary log log transform was used for the probabilities pregibon 1980 implies that these models are the same the present note makes the equivalence explicit suppose that y is an ordinal response variable whose values are labelled 1 k let 7rj x pr y j i x for an observation with covariate vector x and yj x 1 x rj x pr y k j i x and set bj x pr y ij y j x 7tj x i yj l x j 1 k 1 grouped continuous models fit a linear predictor to some monotonic function f of the cumulative probabilities yj x namely f 7j x oj oc x continuation ratio models use the probabilities bj x instead of the yj s that is

locally optimal designs for errors in variables models we consider the construction of optimal designs for nonlinear regression models when there are measurement errors in the covariates corresponding approximate design theory is developed for maximum likelihood and least squares estimation with the latter leading to nonconcave optimization problems analytical characterizations of the locally d optimal saturated designs are provided for the michaelis menten e rm max and exponential regression models through concrete applications we illustrate how measurement errors in the covariates affect the optimal choice of design and show that the locally d optimal saturated designs are highly efficient for relatively small misspecifications of the parameter values

a general model for the analysis of multilevel data a general model is developed for the analysis of multivariate multilevel data structures special cases of the model include repeated measures designs multiple matrix samples multilevel latent variable models multiple time series and variance and covariance component models

optimal designs for dose finding studies understanding and properly characterizing the dose response relationship is a fundamental step in the investigation of a new compound be it a herbicide or fertilizer a molecular entity an environmental toxin or an industrial chemical in this article we investigate the problem of deriving efficient designs for the estimation of target doses in the context of clinical dose finding we propose methods to determine the appropriate number and actual levels of the doses to be administered to patients as well as their relative sample size allocations more specifically we derive local optimal designs that minimize the asymptotic variance of the minimum effective dose estimate under a particular dose response model we investigate the small sample properties of these designs together with their sensitivity to a misspecification of the true parameter values and of the underlying dose response model through simulation finally we demonstrate that the designs derived for a fixed model are rather sensitive

on the relationship between item response theory and factor analysis of discretized variables equivalence of marginal likelihood of the two parameter normal ogive model in item response theory irt and factor analysis of dichotomized variables fa was formally proved the basic result on the dichotomous variables was extended to multicategory cases both ordered and unordered categorical data pair comparison data arising from multiple judgment sampling were discussed as a special case of the unordered categorical data a taxonomy of data for the irt and fa models was also attempted

robust and efficient designs for the michaelis menten model for the michaelis menten model we determine designs that maximize the minimum of the d efficiencies over a certain interval for the nonlinear parameter the best two point designs can be found explicitly and a characterization is given when these designs are optimal within the class of all designs in most cases of practical interest the determined designs are highly efficient and robust with respect to misspecification of the nonlinear parameter the results are illustrated and applied in an example of a hormone receptor assay

multilevel and latent variable modeling with composite links and exploded likelihoods composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models applications considered include survival or duration models models for rankings small area estimation with census information models for ordinal responses item response models with guessing randomized response models unfolding models latent class models with random effects multilevel latent class models models with log normal latent variables and zero inflated poisson models with random effects some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation

e optimal designs for rational models in this paper experimental designs for a rational model y p x q x e are investigated where p x o 1 x p x p and q x 1 p 1 x p q x q are polynomials and e is a random error two approaches bayesian d optimal and bayesian optimal design for extrapolation are examined the first criterion maximizes the expected increase in shannon information provided by the experiment asymptotically and the second minimizes the asymptotic variance of the maximum likelihood estimator mle of the mean response at an extrapolation point x e corresponding locally optimal designs are also discussed conditions are derived under which a p q 1 point design is a locally d optimal design the bayesian d optimal design is shown to be independent of the parameters in p x and to be equally weighted at each support point if the number of support points is the same as the number of parameters in the model the existence and uniqueness of the locally optimal design for extrapolation are proven the number of support points for the locally optimal design for extrapolation is exactly p q 1 these p q 1 design points are proved to be independent of the extrapolation point x e and the parameters in p x the corresponding weights are also independent of the parameters in p x but depend on x e and are not equal

optimal designs for dose response curves with common parameters a common problem in phase ii clinical trials is the comparison of dose response curves corresponding to different treatment groups if the effect of the dose level is described by parametric regression models and the treatments differ in the administration frequency but not in the sort of drug a reasonable assumption is that the regression models for the different treatments share common parameters this paper develops optimal design theory for the comparison of different regression models with common parameters we derive upper bounds on the number of support points of admissible designs and explicit expressions for d optimal designs are derived for frequently used dose response models with a common location parameter if the location and scale parameter in the different models coincide minimally supported designs are determined and sufficient conditions for their optimality in the class of all designs derived the results are illustrated in a dose finding study comparing monthly and weekly administration