an overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death we propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors the baseline hazard was modelled until 10 years follow up using parametric continuous functions six models including cubic regression splines were considered and the akaike information criterion was used to select the final model this approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information splines were also used to model simultaneously non linear effects of continuous covariates and time dependent hazard ratios this led to a graphical representation of the hazard ratio that can be useful for clinical interpretation estimates of these models were obtained by likelihood maximization we showed that these estimates could be also obtained using standard algorithms for poisson regression

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

smoothing spline anova frailty model for recurrent event data summary gap time hazard estimation is of particular interest in recurrent event data this article proposes a fully nonparametric approach for estimating the gap time hazard smoothing spline analysis of variance anova decompositions are used to model the log gap time hazard as a joint function of gap time and covariates and general frailty is introduced to account for between subject heterogeneity and within subject correlation we estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the newton raphson procedure the stochastic approximation algorithm saa and the markov chain monte carlo mcmc method the convergence of the algorithm is guaranteed by decreasing the step size of parameter update and or increasing the mcmc sample size along iterations model selection procedure is also developed to identify negligible components in a functional anova decomposition of the log gap time hazard we evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data

reml and ml estimation for clustered grouped survival data clustered grouped survival data arise naturally in clinical medicine and biological research for example in a randomized clinical trial the variable of interest is the time to occurrence of a certain event with or without a new treatment and the data are collected from possibly correlated subjects from independent clusters however it is sometimes impossible or too expensive to monitor the experimental subjects continuously the subjects are examined regularly and the continuous survival data are thus grouped into a discrete time scale with such a design researchers are mainly interested in the effectiveness of the new treatment as well as the correlation among subjects from the same cluster namely the intracluster correlation this paper suggests a random effects approach to the estimation of the regression parameter with various choices of regression model and also the dependence parameter which characterizes the intracluster correlation time dependent covariates can be accommodated in the proposed model and the estimation procedure will not be further complicated with large cluster sizes the proposed method is applied to the data from the diabetic retinopathy study the objective of which is to evaluate the effectiveness of laser photocoagulation in delaying or preventing the onset of blindness in the left and right eyes of individuals with diabetes associated retinopathy the intracluster correlation using a grouped proportional hazards regression model can be estimated and the relationship between the regression parameter estimates based on the random effects approach and the marginal approach using a dynamic logistic regression model are discussed results from a simulation study of the proposed method are also presented

a note on gauss hermite quadrature summary for gauss hermite quadrature we consider a systematic method for transforming the variable of integration so that the integrand is sampled in an appropriate region the effectiveness of the quadrature then depends on the ratio of the integrand to some gaussian density being a smooth function well approximated by a low order polynomial it is pointed out that in this approach order one gauss hermite quadrature becomes the laplace approximation thus the quadrature as implemented here can be thought of as a higher order laplace approximation

probabilistic multidimensional scaling complete and incomplete data simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the hefner model this model is a probabilistic multidimensional scaling model which assigns a multivariate normal distribution to each stimulus point it is shown that for such a model standard nonmetric and metric algorithms are not appropriate

flexible regression models with cubic splines we describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates this simple method can help prevent the problems that result from inappropriate linearity assumptions we compare restricted cubic spline regression to non parametric procedures for characterizing the relationship between age and survival in the stanford heart transplant data we also provide an illustrative example in cancer therapeutics

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

using the bootstrap to improve estimation and confidence intervals for regression coefficients selected using backwards variable elimination applied researchers frequently use automated model selection methods such as backwards variable elimination to develop parsimonious regression models statisticians have criticized the use of these methods for several reasons amongst them are the facts that the estimated regression coefficients are biased and that the derived confidence intervals do not have the advertised coverage rates we developed a method to improve estimation of regression coefficients and confidence intervals which employs backwards variable elimination in multiple bootstrap samples in a given bootstrap sample predictor variables that are not selected for inclusion in the final regression model have their regression coefficient set to zero regression coefficients are averaged across the bootstrap samples and non parametric percentile bootstrap confidence intervals are then constructed for each regression coefficient we conducted a series of monte carlo simulations to examine the performance of this method for estimating regression coefficients and constructing confidence intervals for variables selected using backwards variable elimination we demonstrated that this method results in confidence intervals with superior coverage compared with those developed from conventional backwards variable elimination we illustrate the utility of our method by applying it to a large sample of subjects hospitalized with a heart attack

the use of gaussian quadrature for estimation in frailty proportional hazards models in this paper we propose a novel gaussian quadrature estimation method in various frailty proportional hazards models we approximate the unspecified baseline hazard by a piecewise constant one resulting in a parametric model that can be fitted conveniently by gaussian quadrature tools in standard software such as sas proc nlmixed we first apply our method to simple frailty models for correlated survival data e g recurrent or clustered failure times then to joint frailty models for correlated failure times with informative dropout or a dependent terminal event such as death simulation studies show that our method compares favorably with the well received penalized partial likelihood method and the monte carlo em mcem method for both normal and gamma frailty models we apply our method to three real data examples 1 the time to blindness of both eyes in a diabetic retinopathy study 2 the joint analysis of recurrent opportunistic diseases in the presence of death for hiv infected patients and 3 the joint modeling of local distant tumor recurrences and patients survival in a soft tissue sarcoma study the proposed method greatly simplifies the implementation of the joint frailty models and makes them much more accessible to general statistical practitioners

strengthening analytical thinking for observational studies the stratos initiative the validity and practical utility of observational medical research depends critically on good study design excellent data quality appropriate statistical methods and accurate interpretation of results statistical methodology has seen substantial development in recent times unfortunately many of these methodological developments are ignored in practice consequently design and analysis of observational studies often exhibit serious weaknesses the lack of guidance on vital practical issues discourages many applied researchers from using more sophisticated and possibly more appropriate methods when analyzing observational studies furthermore many analyses are conducted by researchers with a relatively weak statistical background and limited experience in using statistical methodology and software consequently even standard analyses reported in the medical literature are often flawed casting doubt on their results and conclusions an efficient way to help researchers to keep up with recent methodological developments is to develop guidance documents that are spread to the research community at large these observations led to the initiation of the strengthening analytical thinking for observational studies stratos initiative a large collaboration of experts in many different areas of biostatistical research the objective of stratos is to provide accessible and accurate guidance in the design and analysis of observational studies the guidance is intended for applied statisticians and other data analysts with varying levels of statistical education experience and interests in this article we introduce the stratos initiative and its main aims present the need for guidance documents and outline the planned approach and progress so far we encourage other biostatisticians to become involved

analysis of pairwise preference data using integrated b splines pairwise preference data are represented as a monotone integral transformation of difference on the underlying stimulus object or utility scale the class of monotone transformations considered is that in which the kernel of the integral is a linear combination of b splines two types of data are analyzed binary and continuous the parameters of the transformation and the underlying scale values or utilities are estimated by maximum likelihood with inequality constraints on the transformation parameters various hypothesis tests and interval estimates are developed examples of artificial and real data are presented

on the robustness of maximum likelihood scaling for violations of the error model a monte carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling data sets generated according to the lognormal the normal and the rectangular distribution were analysed with the log normal error model in ramsay s multiscale program package the results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters in a comparison among several dimensionality tests the corrected version of thex2 test as proposed by ramsay yielded the best results and turned out to be quite robust against violations of the error model

a penalized likelihood approach for arbitrarily censored and truncated data application to age specific incidence of dementia the cos model is the model of choice when analyzing survival data presenting only right censoring and left truncation there is a need for methods that can accommodate more complex observation schemes involving general censoring and truncation in addition it is important in many epidemiological applications to have a smooth estimate of the hazard function we show that the penalized likelihood approach gives a solution to these problems the solution of the maximum of the penalized likelihood is approximated on a basis of splines the smoothing parameter is estimated using approximate cross validation confidence bands can be given a simulation study shows that this approach gives better results than the smoothed nelson aalen estimator we apply this method to the analysis of data from a large cohort study on cerebral aging the age specific incidence of dementia is estimated and risk factors of dementia studied

semiparametric transformation models with random effects for recurrent events in this article we study a class of semiparametric transformation models with random effects for the intensity function of the counting process these models provide considerable flexibility in formulating the effects of possibly time dependent covariates on the developments of recurrent events while accounting for the dependence of the recurrent event times within the same subject we show that the nonparametric maximum likelihood estimators npmles for the parameters of these models are consistent and asymptotically normal the limiting covariance matrices for the estimators of the regression parameters achieve the semiparametric efficiency bounds and can be consistently estimated the limiting covariance function for the estimator of any smooth functional of the cumulative intensity function also can be consistently estimated we develop a simple and stable em algorithm to compute the npmles as well as the variance and covariance estimators simulation studies demonstrate that the proposed methods per

maximum likelihood estimation for the proportional odds model with random effects in this article we study the semiparametric proportional odds model with random effects for correlated right censored failure time data we establish that the maximum likelihood estimators for the parameters of this model are consistent and asymptotically gaussian furthermore the limiting variances achieve the semiparametric efficiency bounds and can be consistently estimated simulation studies show that the asymptotic approximations are accurate for practical sample sizes and that the efficiency gains of the proposed estimators over those of cai cheng and wei can be substantial a real example is provided to illustrate the proposed methods

cox regression analysis of multivariate failure time data the marginal approach multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated in this paper i present a general methodology for analysing such data which is analogous to that of liang and zeger for longitudinal data analysis this approach formulates the marginal distributions of multivariate failure times with the familiar cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified the baseline hazard functions for the marginal models may be identical or different simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators and robust variance covarinace estimators are constructed to account for the intra class correlation simulation results demonstrate that the large sample approximations are adequate for practical use and that ignoring the intra class correlation could yield rather misleading variance estimators the proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches detailed illustrations with data from four clinical or epidemiologic studies are provided

nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities a maximum likelihood estimation procedure is developed for multidimensional scaling when dis similarity measures are taken by ranking procedures such as the method of conditional rank orders or the method of triadic combinations the central feature of these procedures may be termed directionality of ranking processes that is rank orderings are performed in a prescribed order by successive first choices those data have conventionally been analyzed by shepard kruskal type of nonmetric multidimensional scaling procedures we propose as a more appropriate alternative a maximum likelihood method specifically designed for this type of data a broader perspective on the present approach is given which encompasses a wide variety of experimental methods for collecting dissimilarity data including pair comparison methods such as the method of tetrads and the pick m method of similarities an example is given to illustrate various advantages of nonmetric maximum likelihood multidimensional scaling as a statistical method at the moment the approach is limited to the case of one mode two way proximity data but could be extended in a relatively straightforward way to two mode two way two mode three way or even three mode three way data under the assumption of such models as indscal or the two or three way unfolding models

hardy space infinite elements for scattering and resonance problems this paper introduces a new type of infinite element for scattering and resonance problems that is derived from a variant of the pole condition as radiation condition this condition states that a certain transform of the exterior solution belongs to the hardy space of l 2 boundary values of holomorphic functions on the unit disc if and only if the solution is outgoing we obtain a symmetric variational formulation of the problem in this hardy space our infinite elements correspond to a galerkin discretization with respect to the standard monomial orthogonal basis of this hardy space and lead to simple element matrices hardy space infinite elements are particularly well suited for solving resonance problems since they preserve the eigenvalue structure of the problem we prove superalgebraic convergence for a separated problem numerical experiments exhibit fast convergence over a wide range of wave numbers

generalized survival models for correlated time to event data our aim is to develop a rich and coherent framework for modeling correlated time to event data including 1 survival regression models with different links and 2 flexible modeling for time dependent and nonlinear effects with rich postestimation we extend the class of generalized survival models which expresses a transformed survival in terms of a linear predictor by incorporating a shared frailty or random effects for correlated survival data the proposed approach can include parametric or penalized smooth functions for time time dependent effects nonlinear effects and their interactions the maximum penalized marginal likelihood method is used to estimate the regression coefficients and the variance for the frailty or random effects the optimal smoothing parameters for the penalized marginal likelihood estimation can be automatically selected by a likelihood based cross validation criterion for models with normal random effects gauss hermite quadrature can be used to obtain the cluster level marginal likelihoods the akaike information criterion can be used to compare models and select the link function we have implemented these methods in the r package rstpm2 simulating for both small and larger clusters we find that this approach performs well through 2 applications we demonstrate 1 a comparison of proportional hazards and proportional odds models with random effects for clustered survival data and 2 the estimation of time varying effects on the log time scale age varying effects for a specific treatment and two dimensional splines for time and age

joint estimation of time dependent and non linear effects of continuous covariates on survival in order to yield more flexible models the cox regression model lambda t x lambda 0 t exp betax has been generalized using different non parametric model estimation techniques one generalization is the relaxation of log linearity in x lambda t x lambda 0 t exp r x another is the relaxation of the proportional hazards assumption lambda t x lambda 0 t exp beta t x these generalizations are typically considered independently of each other we propose the product model lambda t x lambda 0 t exp beta t r x which allows for joint estimation of both effects and investigate its properties the functions describing the time dependent beta t and non linear r x effects are modelled simultaneously using regression splines and estimated by maximum partial likelihood likelihood ratio tests are proposed to compare alternative models simulations indicate that both the recovery of the shapes of the two functions and the size of the tests are reasonably accurate provided they are based on the correct model by contrast type i error rates may be highly inflated and the estimates considerably biased if the model is misspecified applications in cancer epidemiology illustrate how the product model may yield new insights about the role of prognostic factors

the irrelevance of distributional assumptions on reaction times in multidimensional scaling of same different judgment tasks takane and sergent developed a model maxrt for scaling same different judgments and response times rts simultaneously the model assumes that rts are distributed lognormally our experiment showed that the rt distribution of the judgments might be task dependent it is shown that lognormal rts provide a far better fit than exponential normal and pareto distributed rts with the same means and variances but that the final parameter estimates from the data set with lognormal rts hardly differ from the alternatively distributed rts finally despite the robustness of the distributional assumption of the rts with respect to the parameter estimates it is shown that rts have an informational value that is not contained in the same different judgments alone

multidimensional scaling models for reaction times and same different judgments a method for joint analysis of reaction times and same different judgments is discussed a set of stimuli is assumed to have some parametric representation which uniquely defines dissimilarities between the stimuli those dissimilarities are then related to the observed reaction times and same different judgments through a model of psychological processes three representation models of dissimilarities are considered the minkowski power distance model the linear model and tversky s feature matching model maximum likelihood estimation procedures are developed and implemented in the form of a fortran program an example is given to illustrate the kind of analyses that can be performed by the proposed method

penalized partial likelihood for frailties and smoothing splines in time to first insemination models for dairy cows in many epidemiological studies time to event data are clustered and the physiological relationship between time dependent covariates and the log hazard is often not linear as assumed in the cox model introducing frailties in the cox model can account for the clustering of the data and smoothing splines can be used to describe nonlinear relations these two extensions of the cox model are introduced jointly and it is shown how penalized partial likelihood techniques can be used to fit the extended model we demonstrate the need for such a model to study the relation between the physiological covariates milk ureum and protein concentration and the log hazard of first insemination in dairy cows with the farms as clusters

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

penalized likelihood in cox regression in a cox regression model instability of the estimated regression coefficients can be reduced by maximizing a penalized partial log likelihood where a penalty function of the regression coefficients is substracted from the partial log likelihood in this paper we choose the optimal weight of the penalty function by maximizing the predictive value of the model as measured by the crossvalidated partial log likelihood our methods are illustrated by a study of ovarian cancer survival and by a study of centre effects in kidney graft survival

a semiparametric recurrent events model with time varying coefficients we consider a recurrent events model with time varying coefficients motivated by two clinical applications a random effects gaussian frailty model is used to describe the intensity of recurrent events the model can accommodate both time varying and time constant coefficients the penalized spline method is used to estimate the time varying coefficients laplace approximation is used to evaluate the penalized likelihood without a closed form the smoothing parameters are estimated in a similar way to variance components we conduct simulations to evaluate the performance of the estimates for both time varying and time independent coefficients we apply this method to analyze two data sets a stroke study and a child wheeze study

multidimensional successive categories scaling a maximum likelihood method a single step maximum likelihood estimation procedure is developed for multidimensional scaling of dissimilarity data measured on rating scales the procedure can fit the euclidian distance model to the data under various assumptions about category widths and under two distributional assumptions the scoring algorithm for parameter estimation has been developed and implemented in the form of a computer program practical uses of the method are demonstrated with an emphasis on various advantages of the method as a statistical procedure

a maximum likelihood method for fitting the wandering vector model after introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed the possibility of testing various hypotheses by means of likelihood ratio tests is discussed finally the algorithm is applied to some existing data sets for illustrative purposes

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

proportional hazards model with random effects we propose a general proportional hazards model with random effects for handling clustered survival data this generalizes the usual frailty model by allowing a multivariate random effect with arbitrary design matrix in the log relative risk in a way similar to the modelling of random effects in linear generalized linear and non linear mixed models the distribution of the random effects is generally assumed to be multivariate normal but other preferably symmetrical distributions are also possible maximum likelihood estimates of the regression parameters the variance components and the baseline hazard function are obtained via the em algorithm the e step of the algorithm involves computation of the conditional expectations of functions of the random effects for which we use markov chain monte carlo mcmc methods approximate variances of the estimates are computed by louis formula and posterior expectations and variances of the individual random effects can be obtained as a by product of the estimation the inference procedure is exemplified on two data sets

modeling clustered discrete or grouped time survival data with covariates summary we have developed methods for modeling discrete or grouped time right censored survival data collected from correlated groups or clusters we assume that the marginal hazard of failure for individual items within a cluster is specified by a linear log odds survival model and the dependence structure is based on a gamma frailty model the dependence can be modeled as a function of cluster level covariates likelihood equations for estimating the model parameters are provided generalized estimating equations for the marginal hazard regression parameters and pseudolikelihood methods for estimating the dependence parameters are also described data from two clinical trials are used for illustration purposes

nonparametric estimation of a recurrent survival function abstract recurrent event data are frequently encountered in studies with longitudinal designs let the recurrence time be the time between two successive recurrent events recurrence times can be treated as a type of correlated survival data in statistical analysis in general because of the ordinal nature of recurrence times statistical methods that are appropriate for standard correlated survival data in marginal models may not be applicable to recurrence time data specifically for estimating the marginal survival function the kaplan meier estimator derived from the pooled recurrence times serves as a consistent estimator for standard correlated survival data but not for recurrence time data in this article we consider the problem of how to estimate the marginal survival function in nonparametric models a class of nonparametric estimators is introduced the appropriateness of the estimators is confirmed by statistical theory and simulations simulation and analysis from schizophrenia data are pre