a stochastic model for the distribution of hiv latency time based on t4 counts summary a mathematical model is proposed for the description of the t4 level as a function of the time since initial infection in the blood of an hiv infected individual two random variables are defined for each infected individual the time t from the moment of infection to the moment when the infection is first discovered and the level r of t4 cells in the blood at the time of the discovery here t is the length of the latency period and is not typically observable on the basis of a stochastic model employing a stationary gaussian process the joint density of these two random variables is derived and hence the conditional distribution of t given r it is shown that if t has an exponential marginal distribution then the conditional distribution of t is a censored normal distribution the theory is applied to data collected from intravenous drug users in new york city

instantaneous helical axis estimation from 3 d video data in neck kinematics for whiplash diagnostics to date the diagnosis of whiplash injuries has been very difficult and largely based on subjective clinical assessment the work by winters and peles multiple muscle systems biomechanics and movement organization springer new york 1990 suggests that the use of finite helical axes fhas in the neck may provide an objective assessment tool for neck mobility thus the position of the fha describing head trunk motion may allow discrimination between normal and pathological cases such as decreased mobility in particular cervical joints for noisy unsmoothed data the fhas must be taken over rather large angular intervals if the fhas are to be reconstructed with sufficient accuracy in the winters and peles study these intervals were approximately 10 in order to study the movements microstructure the present investigation uses instantaneous helical axes ihas estimated from low pass smoothed video data here the small step noise sensitivity of the fha no longer applies and proper low pass filtering allows estimation of the iha even for small rotation velocity of the moving neck for marker clusters mounted on the head and trunk technical system validation showed that the ihas direction dispersions were on the order of one degree while their position dispersions were on the order of 1 mm for low pass cut off frequencies of a few hz the dispersions were calculated from weighted errors in order to account for the adverse effects of vanishing various simple planar models relating the instantaneous 2 d centre of rotation with the geometry and kinematics of a multi joint neck model are derived in order to gauge the utility of the fha and iha approaches some preliminary results on asymptomatic and pathological subjects are provided in terms of the ruled surface formed by sampled ihas and of their piercing points through the mid sagittal plane during a prescribed flexion extension movement of the neck

a modification of the redistribution to the right algorithm using disease markers summary disease markers are time dependent covariates which describe progression towards development of disease traditional methods in survival analysis do not make use of available data on these markers to recover additional information from censored individuals using a heuristic modification of the redistribution to the right algorithm efron 1967 a new approach for recovering information for censored individuals using disease markers is proposed additionally the statistical properties of the proposed method are examined there are two possible advantages to this modification i bias reduction when censoring is informative and ii an increase in efficiency in the case of truly noninformative censoring

an inverse gaussian process model for degradation data this paper studies the maximum likelihood estimation of a class of inverse gaussian process models for degradation data both the subject to subject heterogeneity and covariate information can be incorporated into the model in a natural way the em algorithm is used to obtain the maximum likelihood estimators of the unknown parameters and the bootstrap is used to assess the variability of the maximum likelihood estimators simulations are used to validate the method the model is fitted to laser data and corresponding goodness of fit tests are carried out failure time distributions in terms of degradation level passages are calculated and illustrated the supplemental materials for this article are available online

high order approximations of the eigenvalues of regular sturm liouville problems abstract in this article we provide high order approximations to the eigenvalues of regular sturm liouville problems with general separable boundary conditions together with their error bounds the approach is based on sampling theory

on fitting cox s proportional hazards models to survey data summary binder 1992 proposed a method of fitting cox s proportional hazards models to survey data with complex sampling designs he defined the regression parameter of interest as the solution to the partial likelihood score equation based on all the data values of the survey population under study and developed heuristically a procedure to estimate the regression parameter and the corresponding variance in this paper we provide a formal justification of binder s method furthermore we present an alternative approach which regards the survey population as a random sample from an infinite universe and accounts for this randomness in the statistical inference under the alternative approach the regression parameter retains its original interpretation as the log hazard ratio and the statistical conclusion applies to other populations the related problem of survival function estimation is also studied

inverse gaussian processes with random effects and explanatory variables for degradation data degradation models are widely used to assess the lifetime information of highly reliable products this study proposes a degradation model based on an inverse normal gamma mixture of an inverse gaussian process this article presents the properties of the lifetime distribution and parameter estimation using the em type algorithm in addition to providing a simple model checking procedure to assess the validity of different stochastic processes several case applications are performed to demonstrate the advantages of the proposed model with random effects and explanatory variables technical details data and r code are available online as supplementary materials

student t processes for degradation analysis stochastic processes are widely used to analyze degradation data and the gaussian process is a particularly common one in this article we propose a robust statistical model using a student t pro

sinc interpolants in the energy plane for regular solution jost function and its zeros of quantum scattering in a remarkable note of chadan il nuovo cimento 39 697 703 1965 the author expanded both the regular wave function and the jost function of the quantum scattering problem using an interpolation theorem of valiron bull sci math 49 181 192 1925 these expansions have a very slow rate of convergence and applying them to compute the zeros of the jost function which lead to the important bound states gives poor convergence rates it is our objective in this paper to introduce several efficient interpolation techniques to compute the regular wave solution as well as the jost function and its zeros approximately this work continues and improves the results of chadan and other related studies remarkably several worked examples are given with illustrations and comparisons with existing methods

kernel estimation in a nonparametric marker dependent hazard model we introduce a new kernel hazard estimator in a nonparametric model where the stochastic hazard depends on the current value of time and on the current value of a time dependent covariate or marker we establish the pointwise and global convergence of our estimator

exploring the nature of covariate effects in the proportional hazards model we discuss an exploratory technique for investigating the nature of covariate effects in cox s proportional hazards model this technique features an additive term sigma p1 fj chi ij in place of the usual linear term sigma p1 chi ij beta j where chi i1 chi i2 chi ip are covariate values for the ith individual the fj are unspecified smooth functions that are estimated using scatterplot smoothers these functions can be used for descriptive purposes or to suggest transformations of the covariates the estimation technique is a variation of the local scoring algorithm for generalized additive models hastie and tibshirani 1986 statistical science 1 297 318

a framework for consistent prediction rules based on markers summary recently interest has developed regarding the statistical properties and uses of marker processes in the context of the analysis of failure time data or survival analysis a marker process is a stochastic process that acts as a time dependent covariate that is internal to the unit under study in the language of kalbfleisch prentice 1980 as such the sample path of the process up to a certain point in time may carry information about the subsequent hazard for failure uses of marker processes in the analysis of survival data are manifold here we consider the specific area of prediction of future failure times at a point in time based on various forms of information about the history of the marker process we provide a stochastic framework for the consideration of prediction functions demonstrate a simple consistency condition that such functions should satisfy and discuss construction of prediction functions in a general sense several examples are used to illustrate the ideas and we show that certain recently suggested imputation schemes fail to meet the consistency condition the consistency condition also elucidates the model assumed by cox 1983 in his work on surrogate responses we also briefly consider a closely related backward prediction problem

estimation of the axis of a screw motion from noisy data a new method based on plucker lines the problems of estimating the motion and orientation parameters of a body segment from two n point set patterns are analyzed using the plucker coordinates of a line plucker lines the aim is to find algorithms less complex than those in conventional use and thus facilitating more accurate computation of the unknown parameters all conventional techniques use point transformation to calculate the screw axis in this paper we present a novel technique that directly estimates the axis of a screw motion as a plucker line the plucker line can be transformed via the dual number coordinate transformation matrix this method is compared with schwartz and rozumalski 2005 a new method for estimating joint parameters from motion data journal of biomechanics 38 107 116 in simulations of random measurement errors and systematic skin movements simulation results indicate that the methods based on plucker lines plucker line method are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements this investigation yielded practical results which can be used to locate the axis of a screw motion in a noisy environment developing the dual transformation matrix dtm from noisy data and determining the screw axis from a given dtm is done in a manner analogous to that for handling simple rotations a more robust approach to solve for the dual vector associated with dtm is also addressed by using the eigenvector and the singular value decomposition

instantaneous moment arm determination of the cat knee the moment arm is an important parameter for calculating forces and pressures at a joint present techniques described in the literature are limited for joint studies in animals because of the invasive procedures required which destroy the joint integrity this paper describes a new application of the instantaneous helical axis iha for determination of the moment arm of the knee joint without compromising its integrity measurements based on the iha technique are compared to an established technique using six cadaveric cat hind limbs one experiment using the iha technique was performed to demonstrate its application in situ it was found that the moment arm determined by both techniques resulted in continuous estimations of similar magnitudes over the expected range of motion of the knee joint although the iha technique is sensitive to smoothing a trend toward increasing moment arm as a function of increasing knee angle was observed in four of six specimens the in situ experiment demonstrated the ability to use the iha technique without compromising the integrity of the knee joint so that further histological morphological or topological information could be investigated

a multistate markov chain model for longitudinal categorical quality of life data subject to non ignorable missingness summary quality of life qol is an important outcome in clinical research particularly in cancer clinical trials typically data are collected longitudinally from patients during treatment and subsequent follow up missing data are a common problem and missingness may arise in a non ignorable fashion in particular the probability that a patient misses an assessment may depend on the patient s qol at the time of the scheduled assessment we propose a markov chain model for the analysis of categorical outcomes derived from qol measures our model assumes that transitions between qol states depend on covariates through generalized logit models or proportional odds models to account for non ignorable missingness we incorporate logistic regression models for the conditional probabilities of observing measurements given their actual values the model can accommodate time dependent covariates estimation is by maximum likelihood summing over all possible values of the missing measurements we

relevance of mandibular helical axis analysis in functional and dysfunctional tmjs the helical axis ha or motion screw yields a comprehensive description of joint motion the perspective representation of this axis clearly visualizes the regularity of mandibular functional movements yatabe et al 1997 journal of dentist research 76 714 719 and gallo et al 2000 journal of dental research 79 1566 1572 in this study the sensitivity of the ha representation was investigated relative to a irregularities in pathologic motion of clicking temporomandibular joints tmjs for jaw opening closing and b differences in food bolus size and consistency for unilateral mastication in subjects with normal tmjs mandibular motion relative to the head was acquired using a jaw tracker with six degrees of freedom with a sampling frequency of 70 hz the ha was calculated according to an eigenvalue method spoor and veldpaus 1980 journal of biomechanics 13 391 393 and parameters were defined describing its position and orientation relative to the anatomy we analyzed 39 subjects with unilateral or bilateral reciprocal tmj clicking during jaw opening closing and seven asymptomatic subjects during unilateral mastication of five different types of soft and hard food in two different bolus sizes the results showed a greater variability of the ha parameters in the group of clicking joints than in the asymptomatic group in particular the area in which the ha moved was wider in clicking joints than in normal ones and the ha in clicking tmjs had a much greater fluctuation than in normal ones during unilateral mastication for more consistent food or a bigger bolus the ha showed a significantly greater excursion of the orientation parameters furthermore a significantly greater excursion of the dorsoventral and of the craniocaudal component of the distance vector from the ha to the condyle were found the helical axis analysis of mandibular movements was sensitive to kinematic irregularities of the mandible due to an internal joint derangement as well as to differences in food bolus size and consistency

optimal average path of the instantaneous helical axis in planar motions with one functional degree of freedom this paper presents a model for determining the path of the instantaneous helical axis iha that optimally represents human planar motions with one functional degree of freedom fdof a human movement is said to have one fdof when all degrees of freedom dofs are coordinated such that all the kinematic variables can be expressed across movement repetitions as functions of only one independent dof except for a small natural intercycle variability quantified as lower than a prespecified value the concept of fdof allows taking into account that due to motor coordination human movements are executed in a repeatable manner our method uses the measurement of several repetitions of a given movement to obtain the optimal average iha path the starting point is a change of variables from time to a joint position magnitude generally an angle in this way instead of operating with the time dependent single valued trajectory of the successive cycles our model permits the representation of any motion variable e g positions and their time derivatives as a cloud of points dependent on the joint angle this allows the averaging to be performed over the displacements and their derivatives before determining the mean iha path we thus avoid the nonlinear magnification of errors and variability inherent in the iha computation moreover the iha path can be considered as a geometric attribute of the joint and the type of motion rather than of each single movement execution an experiment was performed that show the accuracy and usefulness of the method

a general approach to the predictability issue in survival analysis with applications very often in survival analysis one has to study martingale integrals where the integrand is not predictable and where the counting process theory of martingales is not directly applicable as for example in nonparametric and semiparametric applications where the integrand is based on a pilot estimate we call this the predictability issue in survival analysis the problem has been resolved by approximations of the integrand by predictable functions which have been justified by ad hoc procedures we present a general approach to the solution of this problem the usefulness of the approach is shown in three applications in particular we argue that earlier ad hoc procedures do not work in higher dimensional smoothing problems in survival analysis

fitting cox s proportional hazards models from survey data summary the proportional hazards model makes a number of assumptions which may not always be completely satisfied however fitting such models can have both descriptive and analytical value we discuss the implications of the survey design for large scale studies we propose a weighted estimator and derive a design based estimator for the variance of the estimated parameters the derivation requires using methods not previously used in the context of analysis of survey data we conduct a small simulation study comparing the proposed method with others in the literature

mixed effects logistic regression models for longitudinal binary response data with informative drop out a shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop out the model consists of observed longitudinal and missing response components that share random effects parameters to our knowledge this is the first presentation of such a model for longitudinal binary response data comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations the naive mixed effects logit model that does not account for informative drop out is also compared the simulation based differences among the models with respect to coverage of confidence intervals bias and mean squared error mse depend on at least two factors whether an effect is a between or within subject effect and the amount of between subject variation as exhibited by variance components of the random effects distributions when the shared parameter model holds the approximate conditional model provides confidence intervals with good coverage for within cluster factors but not for between cluster factors the converse is true for the naive model under a different drop out mechanism when the probability of drop out is dependent only on the current unobserved observation all three models behave similarly by providing between subject confidence intervals with good coverage and comparable mse and bias but poor within subject confidence intervals mse and bias the naive model does more poorly with respect to the within subject effects than do the shared parameter and approximate conditional models the data analysis which entails a comparison of two pain relievers and a placebo with respect to pain relief conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome driven drop out process this comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data

models for variable stress accelerated life testing experiments based on wiener processes and the inverse gaussian distribution variable stress accelerated life testing trials are experiments in which each of the units in a random sample of units of a product is run under increasingly severe conditions to get information quickly on its life distribution we consider a fatigue failure model in which accumulated decay is governed by a continuous gaussian process w y whose distribution changes at certain stress change points to t l t k continuously increasing stress is also considered failure occurs the first time w y crosses a critical boundary the distribution of time to failure for the models can be represented in terms of time transformed inverse gaussian distribution functions and the parameters in models for experiments with censored data can be estimated using maximum likelihood methods a common approach to the modeling of failure times for experimental units subject to increased stress at certain stress change points is to assume that the failure times follow a distribution that consists of segments of weib

on precision limits for derivatives numerically calculated from noisy data abstract this paper has three purposes 1 1 to verify an error formula from which the maximal precision in derivatives obtained from noisy measurement data can be calculated the formula is verified by comparison with the resulting noise in derivatives obtained by local least squares polynomial fitting it is also verified that differentiation by fourier series expansion gives noise exceeding the minimum value according to the error formula 2 2 an index called the relative noise amplification rna is introduced for an arbitrary differentiating filter it is defined as the noise transmission of the filter divided by the minimal noise transmission according to the above mentioned error formula when the filter produces unbiased estimates the value of the rna always exceeds one the rna can be used as a quality index for differentiating filters the filter with the smallest value on the rna also has the smallest amount of noise superimposed on the calculated derivatives provided the input noise is white and additive 3 3 the bandwidth and the relative noise amplification of differentiating filters obtained by local least squares polynomial fitting are presented the 0th 1st and 2nd order derivatives have been investigated for polynomials up to 8th order these results can be used for the determination of suitable filter parameters in various applications

models for nonresponse in sample surveys abstract the literature on the analysis of incomplete data using models is reviewed in the context of nonresponse in sample surveys the modeling approach provides a large body of methods for handling unit and item nonresponse some of which cannot be derived from the randomization theory of inference for surveys key concepts from the literature on incomplete data such as factorizations of the likelihood for special data patterns the em algorithm for general data patterns and ignorability of the response mechanism are discussed within the survey context model based procedures are related to common methods for handling nonresponse in surveys such as weighting or imputation of means within subclasses of the population

super efficient hazard estimation based on high quality marker information we show that a nonparametric one dimensional hazard as a function of time can be estimated n consistently if a high quality marker is observed

calibrating parametric subject specific risk estimation for modern evidence based medicine decisions on disease prevention or management strategies are often guided by a risk index system for each individual the system uses his her baseline information to estimate the risk of experiencing a future disease related clinical event such a risk scoring scheme is usually derived from an overly simplified parametric model to validate a model based procedure one may perform a standard global evaluation via for instance a receiver operating characteristic analysis in this article we propose a method to calibrate the risk index system at a subject level specifically we developed point and interval estimation procedures for t year mortality rates conditional on the estimated parametric risk score the proposals are illustrated with a dataset from a large clinical trial with post myocardial infarction patients

inference from nonrandomly missing categorical data an example from a genetic study on turner s syndrome abstract the process leading to partial classification with categorical data is sometimes nonrandom a particular model accounting for incomplete data which allows the probability of uncertain classification to depend on category identity is utilized for an analysis of data obtained from a genetic study on turner s syndrome estimates of population proportions are obtained from maximum likelihood a method for handling nonrandomly missing data arrayed in contingency tables is discussed sensitivity analyses incorporating parameters related to the missing data mechanism are recommended for estimation and testing

registration of 6 dofs electrogoniometry and ct medical imaging for 3d joint modeling the paper describes a method in which two data collecting systems medical imaging and electrogoniometry are combined to allow the accurate and simultaneous modeling of both the spatial kinematics and the morphological surface of a particular joint the joint of interest joi is attached to a plexiglas jig that includes four metallic markers defining a local reference system r gonio for the kinematics data volumetric data of the joi and the r gonio markers are collected from medical imaging the spatial location and orientation of the markers in the global reference system r ct of the medical imaging environment are obtained by applying object recognition and classification methods on the image dataset segmentation and 3d isosurfacing of the joi are performed to produce a 3d model including two anatomical objects the proximal and distal joi segments after imaging one end of a custom made 3d electrogoniometer is attached to the distal segment of the joi and the other end is placed at the r gonio origin the joi is displaced and the spatial kinematics data is recorded by the goniometer after recording data registration from r gonio to r ct occurred prior to simulation data analysis was performed using both joint coordinate system jcs and instantaneous helical axis iha finally the 3d joint model is simulated in real time using the experimental kinematics data the system is integrated into a computer graphics interface allowing free manipulation of the 3d scene the overall accuracy of the method has been validated with two other kinematics data collection methods including a 3d digitizer and interpolation of the kinematics data from discrete positions obtained from medical imaging validation has been performed on both superior and inferior radio ulna joints i e prono supination motion maximal rms error was 1 degrees and 1 2mm on the helical axis rotation and translation respectively prono supination of the forearm showed a total rotation of 132 degrees for 0 8mm of translation the method reproducibility using jcs parameters was in average 1 degrees maximal deviation 2 degrees for rotation and 1mm maximal deviation 2mm for translation in vitro experiments have been performed on both knee joint and ankle joint averaged jcs parameters for the knee were 109 degrees 17 degrees and 4 degrees for flexion internal rotation and abduction respectively averaged maximal translation values for the knee were 12 3 and 4mm posteriorly medially and proximally respectively averaged jcs parameters for the ankle were 43 degrees 9 degrees and 3 degrees for plantarflexion adduction and internal rotation respectively averaged maximal translation values for the ankle were 4 2 and 1mm anteriorly medially and proximally respectively

finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics abstract recent work on joint kinematics indicates that the finite centroid centre of rotation and the finite helical axis axis of rotation screw axis twist axis are highly susceptible to measurement errors when they are experimentally determined from landmark position data this paper presents an analytical model to describe these effects under isotropic conditions for the measurement errors and for the spatial landmark distribution it appears that the position and direction errors are inversely proportional to the rotation magnitude and that they are much more error prone than the relatively well determined rotation and translation magnitudes furthermore the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis for the planar centroid the use of rigid body constraints results in considerable precision improvement relative to the classical finite reuleaux method for centroid reconstruction these analytical results can be used to define suitable measurement configurations and they are used in this paper to explain experimental results on rontgenphotogrammetrically acquired in vitro wrist joint movement

a model for markers and latent health status summary we extend the bivariate wiener process considered by whitmore and co workers and model the joint process of a marker and health status the health status process is assumed to be latent or unobservable the time to reach the primary end point or failure death onset of disease etc is the time when the latent health status process first crosses a failure threshold level inferences for the model are based on two kinds of data censored survival data and marker measurements covariates such as treatment variables risk factors and base line conditions are related to the model parameters through generalized linear regression functions the model offers a much richer potential for the study of treatment efficacy than do conventional models treatment effects can be assessed in terms of their influence on both the failure threshold and the health status process parameters we derive an explicit formula for the prediction of residual failure times given the current marker level also we discuss model validation this model does not require the proportional hazards assumption and hence can be widely used to demonstrate the usefulness of the model we apply the methods in analysing data from protocol 116a of the aids clinical trials group

sampling and eigenvalues of non self adjoint sturm liouville problems in this work we extend the sampling method to the case of non self adjoint sturm liouville problems generated by complex valued potentials and boundary conditions it is shown that the function which is recovered by sampling on the real line extends analytically into the complex plane a direct connection with polynomial approximation is established

time dependent predictive accuracy in the presence of competing risks competing risks arise naturally in time to event studies in this article we propose time dependent accuracy measures for a marker when we have censored survival times and competing risks time dependent versions of sensitivity or true positive tp fraction naturally correspond to consideration of either cumulative or prevalent cases that accrue over a fixed time period or alternatively to incident cases that are observed among event free subjects at any select time time dependent dynamic specificity 1 false positive fp can be based on the marker distribution among event free subjects we extend these definitions to incorporate cause of failure for competing risks outcomes the proposed estimation for cause specific cumulative tp dynamic fp is based on the nearest neighbor estimation of bivariate distribution function of the marker and the event time on the other hand incident tp dynamic fp can be estimated using a possibly nonproportional hazards cox model for the cause specific hazards and riskset reweighting of the marker distribution the proposed methods extend the time dependent predictive accuracy measures of heagerty lumley and pepe 2000 biometrics 56 337 344 and heagerty and zheng 2005 biometrics 61 92 105

on intrinsic equivalences of the finite helical axis the instantaneous helical axis and the sara approach a mathematical perspective accurate determination of joint axes is essential for understanding musculoskeletal function whilst numerous algorithms to compute such axes exist the conditions under which each of the methods performs best remain largely unknown typically algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance we derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data finite helical axes fha instantaneous helical axes iha and sara symmetrical axis of rotation approach including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the fha and sara approach are equivalent for the analysis of two time frames moreover we show that the position of a helical axis derived from the iha using positional data is affected by a systematic error perpendicular to the true axis direction whereas the axis direction is identical to those computed with either the fha or sara approach true direction finally with an appropriate choice of weighting factors the mean fha mfha method is equivalent to the symmetrical centre of rotation estimation score algorithm for determination of a centre of rotation cor and similarly equivalent to the sara algorithm for determination of an axis of rotation aor the deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient robust methods for determining aors and cors with confidence

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

high precision three dimensional photogrammetric calibration and object space reconstruction using a modified dlt approach two modified dlt algorithms are presented that improve the accuracy of three dimensional object space reconstruction by almost an order of magnitude when compared with conventional methods the improvement in the linear modified dlt mdlt algorithm is achieved by satisfying certain orthogonality conditions in the form of a non linear constraint thereby effectively eliminating a redundant dlt parameter in the non linear mdlt algorithm the improvement and computational stability results from the appropriate elimination of implicit variables from one side of the approximating relations and the corresponding reformulation of the objective function to be minimized the highest reconstruction accuracy of 0 733 mm rms mean error was obtained with the non linear mdlt algorithm this corresponds to a spatial resolution of about one part in 2860 or 0 035 overall accuracy the accuracy obtainable with the linear mdlt was found to be slightly less and about 0 041 0 833 mm rms mean error

the inverse gaussian process as a degradation model this article systematically investigates the inverse gaussian ig process as an effective degradation model the ig process is shown to be a limiting compound poisson process which gives it a meaningful physical interpretation for modeling degradation of products deteriorating in random environments treated as the first passage process of a wiener process the ig process is flexible in incorporating random effects and explanatory variables that account for heterogeneities commonly observed in degradation problems this flexibility makes the class of ig process models much more attractive compared with the gamma process which has been thoroughly investigated in the literature of degradation modeling the article also discusses statistical inference for three random effects models and model selection it concludes with a real world example to demonstrate the applicability of the ig process in degradation analysis supplementary materials for this article are available online

proportional hazards tests and diagnostics based on weighted residuals summary nonproportional hazards can often be expressed by extending the cox model to include time varying coefficients e g for a single covariate the hazard function for subject i is modelled as exp fl t zi t a common example is a treatment effect that decreases with time we show that the function 3 t can be directly visualized by smoothing an appropriate residual plot also many tests of proportional hazards including those of cox 1972 gill schumacher 1987 harrell 1986 lin 1991 moreau o quigley mesbah 1985 nagelkerke oosting hart 1984 o quigley pessione 1989 schoenfeld 1980 and wei 1984 are related to time weighted score tests of the proportional hazards hypothesis and can be visualized as a weighted least squares line fitted to the residual plot

parametric latent class joint model for a longitudinal biomarker and recurrent events a joint model for a longitudinal biomarker and recurrent events is proposed this general model accommodates the effects of covariates on the biomarker and event processes the effects of accumulating event occurrences and effects caused by interventions after each event occurrence association between the biomarker and recurrent event processes is captured through a latent class structure which also serves to handle an underlying heterogeneous population we use the em algorithm for maximum likelihood estimation of the model parameters and a penalized likelihood measure to determine the number of latent classes this joint model is validated by simulation and illustrated with a data set from epileptic seizure study

a least squares algorithm for the equiform transformation from spatial marker co ordinates the present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co ordinates of at least three non collinear markers a sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution the implementation of the proposed algorithm in a fortran subroutine is appended

a semi parametric threshold regression analysis of sexually transmitted infections in adolescent women time to event analysis of sexually transmitted infection data is often complicated by the existence of nonproportional hazards and nonlinear independent variable effects methods without the proportional hazards assumption such as threshold regression models have been successfully used in many applications this paper seeks to extend the existing threshold regression models to accommodate the nonlinear independent variable effects specifically we incorporated penalized and regression splines to the threshold regression models for added modeling flexibility cross validation methods were used for the selection of the number of knots and for the determination of smoothing parameters variance estimates were proposed for inference purposes simulation results showed that the proposed methods were able to achieve nonparametric function and parametric coefficient estimates that are close to their true values simulation also demonstrated satisfactory performance of variance estimates using the proposed methods we analyzed time from sexual debut to the first infection with chlamydia trachomatis infection in a group of young women analysis shows that the lifetime number of sexual partners has a nonlinear effect on the risk of c trachomatis infection and the infection risks were differential by ethnicity and age of sexual debut

inference in generalized additive mixed modelsby using smoothing splines generalized additive mixed models are proposed for overdispersed and correlated data which arise frequently in studies involving clustered hierarchical and spatial designs this class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression while accounting for correlation between observations by using random effects we estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi likelihood because numerical integration is often required by maximizing the objective functions double penalized quasi likelihood is proposed to make approximate inference frequentist and bayesian inferences are compared a key feature of the method proposed is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model by using existing statistical software a bias correction procedure is also proposed to improve the performance of double penalized quasi likelihood for sparse data we illustrate the method with an application to infectious disease data and we evaluate its performance through simulation

using threshold regression to analyze survival data from complex surveys with application to mortality linked nhanes iii phase ii genetic data the cox proportional hazards ph model is a common statistical technique used for analyzing time to event data the assumption of ph however is not always appropriate in real applications in cases where the assumption is not tenable threshold regression tr and other survival methods which do not require the ph assumption are available and widely used these alternative methods generally assume that the study data constitute simple random samples in particular tr has not been studied in the setting of complex surveys that involve 1 differential selection probabilities of study subjects and 2 intracluster correlations induced by multistage cluster sampling in this paper we extend tr procedures to account for complex sampling designs the pseudo maximum likelihood estimation technique is applied to estimate the tr model parameters computationally efficient taylor linearization variance estimators that consider both the intracluster correlation and the differential selection probabilities are developed the proposed methods are evaluated by using simulation experiments with various complex designs and illustrated empirically by using mortality linked third national health and nutrition examination survey phase ii genetic data

on sinc based method in computing eigenvalues of boundary value problems we aim in this paper to give a complete treatment of the error analysis of the use of the sinc method in computing eigenvalues of second order birkhoff regular eigenvalue problems for this task we study truncation and amplitude errors on bbb c associated with cardinal series representation of band limited functions as well as those of their derivatives these results which seem to be considered for the first time give us the possibility to establish the error analysis when the eigenvalues are not real or not algebraically simple