a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

combinatorial entropy power inequalities a preliminary study of the stam region we initiate the study of the stam region defined as the subset of the positive orthant in r 2 n 1 that arises from considering the entropy powers of subset sums of n independent random vectors in a euclidean space of finite dimension we show that the class of fractionally superadditive set functions provides an outer bound to the stam region resolving a conjecture of barron and madiman on the other hand the entropy power of a sum of independent random vectors is not supermodular in any dimension we also develop some qualitative properties of the stam region showing for instance that its closure is a logarithmically convex cone

choquet weak convergence of capacity functionals of random sets the results in this paper are about the convergence of capacity functionals of random sets the motivation stems from asymptotic aspects in inference and decision making with coarse data in biostatistics set valued observations as well as connections between random sets with several emerging uncertainty calculi in intelligent systems such as fuzziness belief functions and possibility theory specifically we study the counter part of billingsley s portmanteau theorem for weak convergence of probability measures namely convergence of capacity functionals of random sets in terms of choquet integrals

linear rank tests for interval censored data with application to pcb levels in adipose tissue of transformer repair workers linear rank statistics are described for testing for differences between groups when the data are interval censored the statistics are closely related to those described by prentice for right censored data problems in calculating the statistics are discussed and several approaches to computation including estimation of the efficient rank scores are described results from a small simulation study are presented the methods are applied to data from a study relating tissue levels of pcbs to occupational exposure

ignorability in general incomplete data models summary rubin 1976 defined ignorability conditions for frequentist and bayes likelihood analyses of data subject to missing observations more recently heitjan rubin 1991 and heitjan 1993 generalised the rubin model to encompass other forms of incompleteness establishing ignorability conditions for bayes likelihood inferences only this paper extends the heitjan rubin model by explicitly defining the observed degree of coarseness as a data element this permits the development of a frequentist theory including a generalisation of missing completely at random the frequentist ignorability condition for missing data the model is applied in a number of incomplete data problems of general interest

bias reduction for an explicit solution of source localization using tdoa this paper proposes two methods to reduce the bias of the well known algebraic explicit solution chan and ho a simple and efficient estimator for hyperbolic location ieee trans signal process vol 42 pp 1905 1915 aug 1994 for source localization using tdoa bias of a source location estimate is significant when the measurement noise is large and the geolocation geometry is poor bias also dominates performance when multiple times of independent measurements are available such as in uwb localization or in target tracking the paper starts by deriving the bias of the source location estimate from chan and ho the bias is found to be considerably larger than that of the maximum likelihood estimator two methods called biassub and biasred are developed to reduce the bias the biassub method subtracts the expected bias from the solution of chan and ho s work where the expected bias is approximated by the theoretical bias using the estimated source location and noisy data measurements the biasred method augments the equation error formulation and imposes a constraint to improve the source location estimate the biassub method requires the exact knowledge of the noise covariance matrix and biasred only needs the structure of it analysis shows that both methods reduce the bias considerably and achieve the crlb performance for distant source when the noise is gaussian and small the biassub method can nearly eliminate the bias and the biasred method is able to lower the bias to the same level as the maximum likelihood estimator the biasred method is extended for tdoa and fdoa positioning simulations corroborate the performance of the proposed methods

survival curve estimation for informatively coarsened discrete event time data interval censored or more generally coarsened event time data arise when study participants are observed at irregular time periods and experience the event of interest in between study observations such data are often analysed assuming non informative censoring which can produce biased results if the assumption is wrong this paper extends the standard approach for estimating survivor functions to allow informatively interval censored data by incorporating various assumptions about the censoring mechanism into the model we include a bayesian extension in which final estimates are produced by mixing over a distribution of assumed censoring mechanisms we illustrate these methods with a natural history study of hiv infected individuals using assumptions elicited from an aids expert

dual time frequency domain system identification in this paper we obtain the maximum likelihood estimate of the parameters of discrete time linear models by using a dual time frequency domain approach we propose a formulation that considers a reduced rank linear transformation of the available data such a transformation may correspond to different options selection of time domain data transformation to the frequency domain or selection of frequency domain data obtained from time domain samples we use the proposed approach to identify multivariate systems represented in state space form by using the expectation maximisation algorithm we illustrate the benefits of the approach via numerical examples

gaussian particle filtering sequential bayesian estimation for nonlinear dynamic state space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations this paper introduces a new filter called the gaussian particle filter it is based on the particle filtering concept and it approximates the posterior distributions by single gaussians similar to gaussian filters like the extended kalman filter and its variants it is shown that under the gaussianity assumption the gaussian particle filter is asymptotically optimal in the number of particles and hence has much improved performance and versatility over other gaussian filters especially when nontrivial nonlinearities are present simulation results are presented to demonstrate the versatility and improved performance of the gaussian particle filter over conventional gaussian filters and the lower complexity than known particle filters

linear sparse differential resultant formulas abstract let p be a system of n linear nonhomogeneous ordinary differential polynomials in a set u of n 1 differential indeterminates differential resultant formulas are presented to eliminate the differential indeterminates in u from p these formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in p or in a linear perturbation p e of p in particular the formula fres p is the determinant of a matrix m p having no zero columns if the system p is super essential as an application if the system p is sparse generic such formulas can be used to compute the differential resultant res p introduced by li et al 2011 19

robust kalman filtering for discrete time varying uncertain systems with multiplicative noises in this paper a robust finite horizon kalman filter is designed for discrete time varying uncertain systems with both additive and multiplicative noises the system under consideration is subject to both deterministic and stochastic uncertainties sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete riccati difference equations a numerical example is given to show the applicability of the presented method

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

nonparametric estimation from current status data with competing risks summary a great deal of recent attention has focused on the estimation of survival distributions based on current status data an extreme form of interval censored data this particular data structure arises in a wide variety of applications where cross sectional observation either naturally occurs or is preferred to more traditional forms of follow up here we consider current status data in the context of competing risks we briefly consider simple parametric models as a backdrop to nonparametric procedures we make some brief comparisons and remarks regarding the nonparametric maximum likelihood estimator the ideas are illustrated on the data of krailo pike 1983 which considers estimation of the age distribution at both natural and operative menopause we also consider the case where there is exact observation of failure times due to one of the competing risks when failure occurs prior to the monitoring time basic techniques of survival analysis focus on estimation of the survival distribution based on various forms of censored data an extreme form of censoring arises where the only information on studied individuals is their survival status at a single monitoring time this particular data structure is known as current status data nonparametric estimation of the survival function and semiparametric techniques for related regression models based on current status data have been much studied of late here we consider estimation of sub survival functions based on current status observations in the presence of competing risks for simplicity we describe only two competing risks but the ideas are easily extended when there are more than two possible causes of failure let j denote the cause specific hazard function for cause j 1 2 kalbfleisch prentice 2002 p 252 if t and j are the random variables that measure time to failure and cause of failure respectively the two sub distribution functions of interest are

regression with bivariate grouped data the problem of accounting for the grouping of continuous bivariate data in regression analyses is considered reasons why grouping must be taken seriously are advanced and a strategy for accounting for grouping is demonstrated the specific model asserts that in the absence of grouping the data would be bivariate normal this model is used to adjust estimates of parameters in a regression relating disease severity to a grouped exposure variable using data on pneumoconiosis in english coal miners ashford 1959 biometrics 15 573 581 the choice of computing methods is discussed and likelihood formulas are presented

a subdivision based algorithm for the sparse resultant multivariate resultants generalize the sylvester resultant of two polynomials and characterize the solvability of a polynomial system they also reduce the computation of all common roots to a problem in linear algebra we propose a determinantal formula for the sparse resultant of an arbitrary system of n 1 polynomials in n variables this resultant generalizes the classical one and has significantly lower degree for polynomials that are sparse in the sense that their mixed volume is lower than their bezout number our algorithm uses a mixed polyhedral subdivision of the minkowski sum of the newton polytopes in order to construct a newton matrix its determinant is a nonzero multiple of the sparse resultant and the latter equals the gcd of at most n 1 such determinants this construction implies a restricted version of an effective sparse nullstellensatz for an arbitrary specialization of the coefficients there are two methods that use one extra variable and yield the sparse resultant this is the first algorithm to handle the general case with complexity polynomial in the resultant degree and simply exponential in n we conjecture its extension to producing an exact rational expression for the sparse resultant

addressing issues associated with evaluating prediction models for survival endpoints based on the concordance statistic prediction models for disease risk and prognosis play an important role in biomedical research and evaluating their predictive accuracy in the presence of censored data is of substantial interest the standard concordance c statistic has been extended to provide a summary measure of predictive accuracy for survival models motivated by a prostate cancer study we address several issues associated with evaluating survival prediction models based on c statistic with a focus on estimators using the technique of inverse probability of censoring weighting ipcw compared to the existing work we provide complete results on the asymptotic properties of the ipcw estimators under the assumption of coarsening at random car and propose a sensitivity analysis under the mechanism of noncoarsening at random ncar in addition we extend the ipcw approach as well as the sensitivity analysis to high dimensional settings the predictive accuracy of prediction models for cancer recurrence after prostatectomy is assessed by applying the proposed approaches we find that the estimated predictive accuracy for the models in consideration is sensitive to ncar assumption and thus identify the best predictive model finally we further evaluate the performance of the proposed methods in both settings of low dimensional and high dimensional data under car and ncar through simulations

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

macaulay style formulas for sparse resultants we present formulas for computing the resultant of sparse polynomials as a quotient of two determinants the denominator being a minor of the numerator these formulas extend the original formulation given by macaulay for homogeneous polynomials

regularized extended estimation with stabilized exponential forgetting this technical note concerns the problem of variable regularized estimation of time varying nonlinear systems from the bayesian viewpoint the questions of how to impose the posterior information being variably regularized and how to forget this information are carefully discussed the estimator design adopts the strategy of the iterated kalman filter but differs in that instead of the separated moments of the linearized system only the augmented covariance matrix is updated to suppress obsolete information a decision problem involving the kullback leibler divergence is solved the decision provides the best combination of a pair of time evolution model hypotheses in terms of the geometric mean as a result exponential forgetting with the adaptively tuned factor is inserted into the estimation process the regularization of the investigated statistics is induced through the processing of externally supplied information the presented estimator allows for absolute discarding or conversely retention of external information produced in terms of the normal wishart distribution

locally efficient estimation with current status data and time dependent covariates abstract in biostatistical applications interest often focuses on the estimation of the distribution of a failure time variable t if one observes only whether or not t exceeds an observed monitoring time c then the data structure is called current status data also known as interval censored data case i we extend the data structure by allowing the presence of a possibly time dependent covariate process which is observed up till the monitoring time c we follow the approach of robins and rotnitzky by modeling the hazard of c conditional on the failure time variable and the covariate process i e the missingness or censoring process under the restriction that the missingness monitoring process satisfies coarsening at random because of the curse of dimensionality no globally efficient nonparametric estimators with a good practical performance at moderate sample sizes exist we introduce an inverse probability of censoring weighted estimator of the distribution and of smooth functionals of this di

power and sample size calculations for discrete bounded outcome scores we consider power and sample size calculations for randomized trials with a bounded outcome score bos as primary response adjusted for a priori chosen covariates we define bos to be a random variable restricted to a finite interval typically a bos has a j or u shaped distribution hindering traditional parametric methods of analysis when no adjustment for covariates is needed a non parametric test could be chosen however there is still a problem with calculating the power since the common location shift alternative does not hold in general for a bos in this paper we consider a parametric approach and assume that the observed bos is a coarsened version of a true bos which has a logit normal distribution in each treatment group allowing correction for covariates a two step procedure is used to calculate the power firstly the power function is defined conditionally on the covariate values secondly the marginal power is obtained by averaging the conditional power with respect to an assumed distribution for the covariates using monte carlo integration a simulation study evaluates the performance of our method which is also applied to the ecass 1 stroke study

locally efficient estimation of the quality adjusted lifetime distribution with right censored data and covariates summary zhao and tsiatis 1997 consider the problem of estimation of the distribution of the quality adjusted lifetime when the chronological survival time is subject to right censoring the quality adjusted lifetime is typically defined as a weighted sum of the times spent in certain states up until death or some other failure time they propose an estimator and establish the relevant asymptotics under the assumption of independent censoring in this paper we extend the data structure with a covariate process observed until the end of follow up and identify the optimal estimation problem because of the curse of dimensionality no globally efficient nonparametric estimators which have a good practical performance at moderate sample sizes exist given a correctly specified model for the hazard of censoring conditional on the observed quality of life and covariate processes we propose a closed form one step estimator of the distribution of the quality adjusted lifetime whose asymptotic variance attains the efficiency bound if we can correctly specify a lower dimensional working model for the conditional distribution of quality adjusted lifetime given the observed quality of life and covariate processes the estimator remains consistent and asymptotically normal even if this latter submodel is misspecified the practical performance of the estimators is illustrated with a simulation study we also extend our proposed one step estimator to the case where treatment assignment is confounded by observed risk factors so that this estimator can be used to test a treatment effect in an observational study

discussion of the frangakis and rubin article in clinical survival studies conducted in the united states rich data are frequently available on variables recording time to drop out and the evolution over time of a patient s clinical signs symptoms and laboratory measurements motivated by a greek study frangakis and rubin fr consider estimation of a marginal survival curve under a double sampling design from severely impoverished reduced data that included none of the aforementioned variables due to confidentiality restrictions to make our discussion relevant to settings with and without confidentiality restrictions we shall consider survival curve estimation both from rich data that includes the aforementioned variables and from reduced data that does not let t l and c be continuous failure dropout and administrative censoring times respectively with time measured from date of enrollment the goal is to estimate the cumulative net marginal hazard of failure a t fj at u du and the survival function s t e a t under a double sampling design in which a subset of the dropouts is followed up in a secondphase sample in their analysis fr assumed a all dropouts had the same chance of being selected into the second stage sample b all dropouts selected into the second phase had their censoring indicator a 6 t c and their minimum x min t c of censoring and failure successfully ascertained and c c was independent of underlying variables such as t and l it was necessary for fr to impose these assumptions because fr s estimator of a t is inconsistent unless a c hold in practice one or more of assumptions a c may often fail to hold for instance in the first paragraph of their section 5 fr noted it will often happen that a subset of the dropouts pursued in the second phase will fail to have x i ascertained violating assumption b fr recommend that members of this subset be treated in the analysis as having been administratively censored however were this recommendation to be followed fr s survival estimator would be inconsistent and could be severely biased if the number of secondstage subjects who do not have x i ascertained is large assumption a will be false if a potentially more efficient design has been employed in which subjects who dropped out early are oversampled in the second phase assumption c will be false when there are secular trends in the distribution of t as was the case during the 1980s and 1990s for the survival time t of aids patients if only assumption a were false then as fr note identification of a t could be restored by addition of the known second phase sampling probabilities to fr s reduced data however when assumptions b and or c are false both additional assumptions and rich data are required to restore identification in this discussion we make the following points first we show in section 4 that if assumptions a c hold then i when only the reduced data are available for analysis fr s estimator is algebraically identical to the efficient inverse prow ability weighted ipw estimator but ii when rich data are available fr s estimator is inefficient for this case we provide in section 8 a locally semiparametric efficient lse estimator of s t that exploits the information in the rich data second we consider the more realistic setting in which i fr s estimator is inconsistent because one or more of assumptions a c fail to hold and ii rich data are available in sections 6 and 7 we derive doubly robust lse survival curve estimators under the assumption that the missingness process is ignorable in summary we describe aspects of a powerful methodology for the analysis of doubly sampled censored survival data that can resolve the three principal problems left open by fr i how to construct locally lse estimators of s t when fr s assumptions a c hold and as would typically be the case in the united states rich data are available for analysis ii how to construct lse doubly robust estimators of s t when fr s assumptions b and or c fail but missingness remains ignorable and iii how to conduct a sensitivity analysis when missingness may be nonignorable this methodology is in effect a subset of the general theory developed in robins and rotnitzky 1992 robins 1993a b robins rotnitzky and scharfstein 1999 and scharfstein rotnitzky and robins 1999a for the analysis of semiand nonparametric rightcensored data models specialized to the case of doubly sampled censored survival data because of space limitations our resolution of problem iii will be described elsewhere in order to successfully exploit our general theory in the context of doubly sampled data an additional problem must be faced specifically in this context the distribution of the censoring variable has both discrete and continuous components as a result none of the estimators of s t previously proposed in the aforementioned papers are directly applicable in section 6 and the appendix we provide a survival estimator that allows for a mixed discrete and continuous censor

efficient estimation from right censored data when failure indicators are missing at random the kaplan meier estimator of a survival function is well known to be asymptotically efficient when cause of failure is always observed it has been an open problem however to find an efficient estimator when failure indicators are missing at random lo showed that nonparametric maximum likelihood estimators are inconsistent and this has led to several proposals of ad hoc estimators none of which are efficient we now introduce a sieved nonparametric maximum likelihood estimator and show that it is efficient our approach is related to the estimation of a bivariate survival function from bivariate right censored data 1 introduction suppose that we wish to estimate a survival distribution based on right censored data when cause of failure is always observed the method of nonparametric maximum likelihood leads to the well studied kaplan meier 1958 estimator which has many desirable properties including asymptotic efficiency wellner 1982 in this paper we address the problem of finding an asymptotically efficient estimator when cause of failure information is missing for some individuals

semiparametric estimation of proportional mean residual life model in presence of censoring summary a mean residual life function is the average remaining life of a surviving subject as it varies with time the proportional mean residual life model was proposed by oakes and dasu 1990 biometrika77 409 410 in regression analysis to study its association with related covariates in absence of censoring in this article we develop some semiparametric estimation procedures to take censoring into account the proposed methodology is evaluated via simulation studies and further applied to a clinical trial of chemotherapy in postoperative radiotherapy of lung cancer patients

approximations of upper and lower probabilities by measurable selections a random set can be regarded as the result of the imprecise observation of a random variable following this interpretation we study to which extent the upper and lower probabilities induced by the random set keep all the information about the values of the probability distribution of the random variable we link this problem to the existence of selectors of a multi valued mapping and with the inner approximations of the upper probability and prove that under fairly general conditions although not in all cases the upper and lower probabilities are an adequate tool for modelling the available information in doing this we generalise a number of results from the literature finally we study the particular case of consonant random sets and we also derive a relationship between aumann and choquet integrals

an algorithmic and a geometric characterization of coarsening at random we show that the class of conditional distributions satisfying the coarsening at random car property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers combinatorial objects generalizing the notion of partition of a set however the complexity of a given car mechanism can be large the maximal height of the needed multicovers can be exponential in the number of points in the sample space the results stem from a geometric interpretation of the set of car distributions as a convex polytope and a characterization of its extreme points the hierarchy of car models defined in this way could be useful in parsimonious statistical modeling of car mechanisms though the results also raise doubts in applied work as to the meaningfulness of the car assumption in its full generality

the height of the mixed sparse resultant we present an upper bound for the height of the mixed sparse resultant defined as the logarithm of the maximum modulus of its coefficients we obtain a similar estimate for its mahler measure

nonlinear estimation with state dependent gaussian observation noise we consider the problem of estimating the state of a system when measurement noise is a function of the system s state we propose generalizations of the extended kalman filter and the iterated extended kalman filter that can be utilized when the state estimate distribution is approximately gaussian the state estimate is computed by an iterative root searching method that maximizes a maximum likelihood function the new filter allows for the consistent treatment of a class of control problem involving nonlinear estimation from measurements with state dependent noise the effectiveness of the estimation algorithm is illustrated for a control problem with a mobile bearing only sensor

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

modeling heaping in self reported cigarette counts in studies of smoking behavior some subjects report exact cigarette counts whereas others report rounded off counts particularly multiples of 20 10 or 5 this form of data reporting error known as heaping can bias the estimation of parameters of interest such as mean cigarette consumption we present a model to describe heaped count data from a randomized trial of bupropion treatment for smoking cessation the model posits that the reported cigarette count is a deterministic function of an underlying precise cigarette count variable and a heaping behavior variable both of which are at best partially observed to account for an excess of zeros as would likely occur in a smoking cessation study where some subjects successfully quit we model the underlying count variable with zero inflated count distributions we study the sensitivity of the inference on smoking cessation by fitting various models that either do or do not account for heaping and zero inflation comparing the models by means of bayes factors our results suggest that sufficiently rich models for both the underlying distribution and the heaping behavior are indispensable to obtaining a good fit with heaped smoking data the analyses moreover reveal that bupropion has a significant effect on the fraction abstinent but not on mean cigarette consumption among the non abstinent

on the testability of the car assumption in recent years a popular nonparametric model for coarsened data is an assumption on the coarsening mechanism called coarsening at random car it has been conjectured in several papers that this assumption cannot be tested by the data that is the assumption does not restrict the possible distributions of the data in this paper we will show that this conjecture is not always true an example will be current status data we will also give conditions when the conjecture is true and in doing so we will introduce a generalized version of the car assumption as an illustration we retrieve the well known result that the car assumption cannot be tested in the case of right censored data

ignorability for categorical data we study the problem of ignorability in likelihood based inference from incomplete categorical data two versions of the coarsened at random assumption car are distinguished their compatibility with the parameter distinctness assumption is investigated and several conditions for ignorability that do not require an extra parameter distinctness assumption are established it is shown that car assumptions have quite different implications depending on whether the underlying complete data model is saturated or parametric in the latter case car assumptions can become inconsistent with observed data

rounding error in regression the appropriateness of sheppard s corrections abstract we consider three simple approaches to rounding error in least squares regression the first treats the rounded data as if they were unrounded the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal the third sheppard s corrections can be motivated as maximum likelihood with small rounding error and either 1 joint normal data or 2 normal residuals regular independent variables and large samples although an example and theory suggest that the third approach is usually preferable to the first two a generally satisfactory attack on rounding error in regression requires the specification of the full distribution of variables and convenient computational methods for this problem are not currently available author

estimation of the failure time distribution in the presence of informative censoring we present a method for estimating the survival curve of a continuous failure time random variable from right censored data our method allows adjustment for informative censoring due to measured prognostic factors for time to event and censoring while simultaneously quantifying the sensitivity of the inference to residual dependence between failure and censoring due to unmeasured factors we present the results of a simulation study and illustrate our approach using data from the aids clinical trial group 175 study

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

resolution des systemes d equations algebriques abstract let f1 fk be k multivariate polynomials which have a finite number of common zeros in the algebraic closure of the ground field counting the common zeros at infinity an algorithm is given and proved which reduces the computations of these zeros to the resolution of a single univariate equation which degree is the number of common zeros this algorithm gives the whole algebraic and geometric structure of the set of zeros multiplicities conjugate zeros when all the polynomials have the same degree the complexity of this algorithm is polynomial relatively to the generic number of solutions

a stochastic analysis of a modified gain extended kalman filter with applications to estimation with bearings only measurements a new globally convergent nonlinear observer called the modified gain extended kalman observer mgeko is developed for a special class of systems this observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended kalman filter mgekf a sufficient condition for the estimation errors of the mgekf to be exponentially bounded in the mean square is obtained finally the mgeko and the mgekf are applied to the three dimensional bearings only measurement problem where the extended kalman filter often shows erratic behavior

interval censoring identifiability and the constant sum property the constant sum property given in oller et al 2004 for censoring models justifies the use of a simplified likelihood to obtain the nonparametric maximum likelihood estimator of the lifetime distribution in this paper we study the relevance of the constant sum property in the identifiability of the lifetime distribution we show that the lifetime distribution is not identifiable outside the class of constant sum models we also show that the lifetime probabilities assigned to the observable intervals are identifiable inside the class of constant sum models we illustrate all these notions with several examples

the iterated kalman filter update as a gauss newton method it is shown that the iterated kalman filter ikf update is an application of the gauss newton method for approximating a maximum likelihood estimate an example is presented in which the iterated kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate whereas the extended kalman filter update does not

estimating incubation period distributions with coarse data the incubation period the time between infection and disease onset is important in the surveillance and control of infectious diseases but is often coarsely observed coarse data arises because the time of infection the time of disease onset or both are not known precisely accurate estimates of an incubation period distribution are useful in real time outbreak investigations and in modeling public health interventions we compare two methods of estimating such distributions the first method represents the data as doubly interval censored the second introduces a data reduction technique that makes the computation more tractable in a simulation study the methods perform similarly when estimating the median but the first method yields more reliable estimates of the distributional tails we conduct a sensitivity analysis of the two methods to violations of model assumption and we apply these methods to historical incubation period data on influenza a and respiratory syncytial virus the analysis of reduced data is less computationally intensive and performs well for estimating the median under a wide range of conditions however for estimation of the tails of the distribution the doubly interval censored analysis is the recommended procedure

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

explicit factors of some iterated resultants and discriminants in this paper the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed we consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into irreducible factors of several constructions involving two times iterated univariate resultants and discriminants over the integer universal ring of coefficients of the entry polynomials cases involving from two to four generic polynomials and resultants or discriminants in one of their variables are treated the decompositions into irreducible factors we get are obtained by exploiting fundamental properties of the univariate resultants and discriminants and induction on the degree of the polynomials as a consequence each irreducible factor can be separately and explicitly computed in terms of a certain multivariate resultant with this approach we also obtain as direct corollaries some results conjectured by collins and mccallum which correspond to the case of polynomials whose coefficients are themselves generic polynomials in other variables finally a geometric interpretation of the algebraic factorization of the iterated discriminant of a single polynomial is detailled

robust h_ infty filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts in this paper the robust h filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time varying communication delays and multiple packet dropouts a sequence of random variables all of which are mutually independent but obey bernoulli distribution are introduced to account for the randomly occurred communication delays the packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval the discrete time system under consideration is also subject to parameter uncertainties state dependent stochastic disturbances and sector bounded nonlinearities we aim to design a linear full order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the h performance index intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed h performance for the overall filtering error dynamics in the presence of random delays random dropouts nonlinearities and the parameter uncertainties these conditions are characterized in terms of the feasibility of a set of linear matrix inequalities lmis and then the explicit expression is given for the desired filter parameters simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper

technical communique h output feedback control of discrete time systems with state multiplicative noise linear discrete time systems with stochastic uncertainties in their state space model are considered the problem of dynamic output feedback control is solved via a new approach for both the finite horizon and the stationary cases in both cases a cost function is defined which is the expected value of the standard h performance index with respect to the uncertain parameters an example is given which demonstrates the applicability of the theory

linear transformation models for failure time data with covariate measurement error in medical studies patients biological parameters are often imprecisely measured due to the measuring mechanism or the biological variability in the presence of covariate measurement error survival analysis using the cox model with the observed covariate may yield a biased estimate for the regression parameter existing research on this topic has focused on adapting the cox model to covariates with measurement errors in this article we generalize linear transformation models to accommodate covariate measurement error we derive inference procedures for the regression coefficients of examining the covariate effects on survival times under a generalized estimating equation framework our method relaxes the normality assumption on the unobserved true covariates and the measurement errors and can be easily adopted to conduct sensitivity analyses when the magnitude of the measurement error variance is unknown the extra variation owing to the measurement error corrections is accounted for through an asymp

inverse probability weighted estimation for general missing data problems abstract i study inverse probability weighted m estimation under a general missing data scheme examples include m estimation with missing data due to a censored survival time propensity score estimation of the average treatment effect in the linear exponential family and variable probability sampling with observed retention frequencies i extend an important result known to hold in special cases estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation for the treatment effect case the setup allows a general characterization of a double robustness result due to scharfstein et al 1999 rejoinder journal of the american statistical association 94 1135 1146

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

a poisson formula for the sparse resultant we present a poisson formula for sparse resultants and a formula for the product of the roots of a family of laurent polynomials which are valid for arbitrary families of supports to obtain these formulae we show that the sparse resultant associated to a family of supports can be identified with the resultant of a suitable multiprojective toric cycle in the sense of remond this connection allows to study sparse resultants using multiprojective elimination theory and intersection theory of toric varieties

missing at random likelihood ignorability and model completeness this paper provides further insight into the key concept of missing at random mar in incomplete data analysis following the usual selection modelling approach we envisage two models with separable parameters a model for the response of interest and a model for the missing data mechanism mdm if the response model is given by a complete density family then frequentist inference from the likelihood function ignoring the mdm is valid if and only if the mdm is mar this necessary and sufficient condition also holds more generally for models for coarse data such as censoring examples are given to show the necessity of the completeness of the underlying model for this equivalence to hold

ignorability and coarse data some biomedical examples heitjan and rubin 1991 annals of statistics 19 2244 2253 define data to be coarse when one observes not the exact value of the data but only some set a subset of the sample space that contains the exact value this definition covers a number of incomplete data problems arising in biomedicine including rounded heaped censored and missing data in analyzing coarse data it is common to proceed as though the degree of coarseness is fixed in advance in a word to ignore the randomness in the coarsening mechanism when coarsening is actually stochastic however inferences that ignore this randomness may be seriously misleading heitjan and rubin 1991 have proposed a general model of data coarsening and established conditions under which it is appropriate to ignore the stochastic nature of the coarsening the conditions are that the data be coarsened at random a generalization of missing at random rubin 1976 biometrika 63 581 592 and that the parameters of the data and the coarsening process be distinct this article presents detailed applications of the general model and the ignorability conditions to a variety of coarse data problems arising in biomedical statistics a reanalysis of the stanford heart transplant data crowley and hu 1977 journal of the american statistical association 72 27 36 reveals significant evidence that censoring of pretransplant survival times by transplantation was nonignorable suggesting a greater benefit from cardiac transplantation than previous analyses had found

sensitivity of the discrete time kaplan meier estimate to nonignorable censoring application in a clinical trial untestable assumptions about association between survival and censoring times can affect the validity of estimates of the survival distribution including the kaplan meier km nonparametric mle this article explores the sensitivity of the km curve to nonignorable censoring by extending the index of local sensitivity to nonignorability isni troxel et al 2004 zhang and heitjan 2006 to the case of a nonparametric survival model the method involves first specifying a coarse data selection model to describe the association between the failure and censoring processes then evaluating the slope of the nonparametric survival mle ordinate with respect to a nonignorability parameter in the neighborhood of the ignorable model we define the nonparametric mle of the survival curve for a fixed value of the nonignorability parameter and show in a simulation that isni analysis effectively captures local sensitivity to nonignorability the method measures sensitivity in the sense of identifying functionals of the nonparametric mle that nonignorability if present can affect substantially we demonstrate the method with an application to a trial comparing mechanical assistance to optimal medical management in the treatment of end stage heart failure

a polyhedral method for solving sparse polynomial systems a continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations we introduce mixed subdivisions of newton polytopes and we apply them to give a new proof and algorithm for bernstein s theorem on the expected number of roots this results in a numerical homotopy with the optimal number of paths to be followed in this homotopy there is one starting system for each cell of the mixed subdivision and the roots of these starting systems are obtained by an easy combinatorial construction

sharp estimates for the arithmetic nullstellensatz we present sharp estimates for the degree and the height of the polynomials in the nullstellensatz over the integer ring zz the result improves previous work of philippon berenstein yger and krick pardo we also present degree and height estimates of intrinsic type which depend mainly on the degree and the height of the input polynomial system as an application we derive an effective arithmetic nullstellensatz for sparse polynomial systems the proof of these results relies heavily on the notion of local height of an affine variety defined over a number field we introduce this notion and study its basic properties

learning reliable classifiers from small or incomplete data sets the naive credal classifier 2 in this paper the naive credal classifier which is a set valued counterpart of naive bayes is extended to a general and flexible treatment of incomplete data yielding a new classifier called naive credal classifier 2 ncc2 the new classifier delivers classifications that are reliable even in the presence of small sample sizes and missing values extensive empirical evaluations show that by issuing set valued classifications ncc2 is able to isolate and properly deal with instances that are hard to classify on which naive bayes accuracy drops considerably and to perform as well as naive bayes on the other instances the experiments point to a general problem they show that with missing values empirical evaluations may not reliably estimate the accuracy of a traditional classifier such as naive bayes this phenomenon adds even more value to the robust approach to classification implemented by ncc2

resultants and chow forms via exterior syzygies let w be a vector space of dimension n 1 over a field k the chow divisor of a k dimensional variety x in p p w is the hypersurface in the grassmannian gk 1 of planes of codimension k 1 in p whose points over the algebraic closure of k are the planes that meet x the chow form of x is the defining equation of the chow divisor for example the resultant of k 1 forms of degree e in k 1 variables is the chow form of p embedded by the e th veronese mapping in p with n k e k 1 more generally the chow divisor of a k cycle i ni vi on projective space is defined to be i nidi where di is the chow divisor of vi the chow divisor of a sheaf f with k dimensional support is the chow divisor of the associated k cycle of f in this paper we will give a new expression for the chow divisor and apply it to give explicit formulas in many new cases starting with a sheaf f on p we use exterior algebra methods to define a canonical and effectively computable chow complex of f on each grassmannian of planes in p if f has k dimensional support we show that the chow form of f is the determinant of the chow complex of f on the grassmannian of planes of codimension k 1 the beilinson monad of f beilinson 1978 is the chow complex of f on the grassmannian of 0 planes that is on p itself in particular we are able to give explicit determinantal and pfaffian formulas for resultants in some cases where no polynomial formulas were known for example the horrocks mumford bundle gives rise to polynomial formulas for the resultant of five homogeneous forms of degrees 4 6 or 8 in five variables the easiest of our new formulas to write down is for the resultant of 3 quadratic forms in three variables the chow form of the veronese surface in p using the tangent bundle of p conclude that it can be written in bezout form described below as the pfaffian of the matrix 0 245 345 135 045 035 145 235

logistic quantile regression for bounded outcomes when research interest lies in continuous outcome variables that take on values within a known range e g a visual analog scale for pain within 0 and 100 mm the traditional statistical methods such as least squares regression mixed effects models and even classic nonparametric methods such as the wilcoxon s test may prove inadequate frequency distributions of bounded outcomes are often unimodal u shaped and j shaped to the best of our knowledge in the biomedical and epidemiological literature bounded outcomes have seldom been analyzed by appropriate methods that for one correctly constrain inference to lie within the feasible range of values in many respects continuous bounded outcomes can be likened to probabilities or propensities yet what has long been heeded when modeling the probability of binary outcomes with the widespread use of logistic and probit regression so far appears to have been overlooked with continuous bounded outcomes with consequences at times disastrous logistic quantile regression constitutes an effective method to fill this gap

efficient estimation in the bivariate censoring model and repairing npmle the npmle in the bivariate censoring model is not consistent the problem is caused by the singly censored observations in this paper we prove that the npmle based on interval censoring the singly censored observations is ecient for this reduced data and moreover if we let the width of the interval converge to zero slowly enough then the npmle is also ecient for the original data we are able to determine a lower bound for the rate at which the bandwidth should converge to zero the eciency proof uses the general identity which holds for npmle of a linear parameter in convex models as proved in van der laan 1993a

on topological properties of the choquet weak convergence of capacity functionals of random sets in view of the recent interests in random sets in information technology such as models for imprecise data in intelligent systems morphological analysis in image processing we present in this paper some contributions to the foundation of random set theory namely a complete study of topological properties of capacity functionals of random sets generalizing weak convergence of probability measures these results are useful for investigating the concept of choquet weak convergence of capacity functionals leading to tractable criteria for convergence in distribution of random sets the weak topology is defined on the space of all capacity functionals on r d we show that this topological space is separable and metrizable

double robust semiparametric estimator for differences in restricted mean lifetimes in observational studies restricted mean lifetime is often of direct interest in epidemiologic studies involving censored survival times differences in this quantity can be used as a basis for comparing several groups for example transplant surgeons nephrologists and of course patients are interested in comparing posttransplant lifetimes among various types of kidney transplants to assist in clinical decision making as the factor of interest is not randomized covariate adjustment is needed to account for imbalances in confounding factors in this report we use semiparametric theory to develop an estimator for differences in restricted mean lifetimes although accounting for confounding factors the proposed method involves building working models for the time to event and coarsening mechanism i e group assignment and censoring we show that the proposed estimator possesses the double robust property i e when either the time to event or coarsening process is modeled correctly the estimator is consistent and asymptotically normal simulation studies are conducted to assess its finite sample performance and the method is applied to national kidney transplant data

linear estimation of continuous discrete linear state space models with multiplicative noise this paper deals with the estimation of the state variable of continuous discrete linear state space models with multiplicative noise specifically the optimal minimum variance linear filter for that class of models is constructed moreover the solutions of the differential equations that describe the evolution of the two first conditional moments between observations are obtained and an algorithm for their numerical computation is also given the performance of the linear filter is illustrated by means of numerical experiments

polynomial filtering of discrete time stochastic linear systems with multiplicative state noise the problem of finding an optimal polynomial state estimate for the class of stochastic linear models with a multiplicative state noise term is studied for such models a technique of state augmentation is used leading to the definition of a general polynomial filter the theory is developed for time varying systems with nonstationary and non gaussian noises moreover the steady state polynomial filter for stationary systems is also studied numerical simulations show the high performances of the proposed method with respect to the classical linear filtering techniques

inference for events with dependent risks in multiple endpoint studies abstract kaplan meier and cumulative incidence functions are not sufficient descriptive devices for studies that have multiple time to event endpoints for example in cancer treatment research the probability of tumor recurrence conditional on not having died from treatment related toxicities and the prevalence of graft versus host disease among leukemia free patients surviving a bone marrow transplant are of interest these quantities can be estimated nonparametrically using simple functions of several kaplan meier and cumulative incidence estimates for events with possibly dependent risks we derive asymptotic distribution theory for such functions by representing kaplan meier cumulative incidence and cumulative hazard estimators as sums of iid random variables variance estimation also follows directly from this representation two sample test statistics with asymptotic null distribution theory are presented several examples illustrate the utility of these results

implicitization of curves and hyper surfaces using predicted support we reduce implicitization of rational planar parametric curves and hyper surfaces to linear algebra by interpolating the coefficients of the implicit equation given a superset of its terms for predicting these terms we focus on methods that exploit input and output structure in the sense of sparse or toric elimination theory namely by computing the newton polytope of the implicit polynomial via sparse resultant theory our algorithm works even in the presence of base points but in this case the implicit equation shall be obtained as a factor of the produced polynomial we implement our methods in maple and some in matlab as well and study their numerical stability and efficiency on several classes of curves and surfaces we apply our approach to approximate implicitization and quantify the accuracy of the approximate output which turns out to be satisfactory on all tested examples in building a square or rectangular interpolation matrix an important issue is over sampling the given curve or surface we conclude that unitary complex numbers offer the best tradeoff between speed and accuracy when numerical methods are employed namely svd whereas for exact kernel computation random integers is the method of choice we compare our prototype to existing software and find that it is rather competitive

remission duration an example of interval censored observations remission duration data from two observational studies the german all aul study on acute lymphoblastic and acute undifferentiated leukaemia and the kiel lymphoma study are used to demonstrate the adequacy of an interval censoring approach the turnbull estimator is contrasted with the conventionally used kaplan meier estimator in addition a parametric model is used for estimation or simulation of the delay times of complete remission diagnosis and relapse diagnosis two possible consequences of the conventional approach are discussed biased estimation for example overestimation of remission duration and underestimation of the true error variance which may lead to false positive results on the other hand the applicability of the interval censoring approach is doubtful when the censoring mechanism examination pattern patient s behaviour is confounded with the endpoints

bayesian selection of decomposable models with incomplete data this article describes a new approach to bayesian selection of decomposable models with incomplete data this approach requires the characterization of new ignorability conditions for the missing data mechanism and the development of new computational methods both issues are considered and solutions are proposed theory and methods are assessed in controlled experiments and in the analysis of one real life incomplete dataset

flexible modeling of longitudinal highly skewed outcomes the analysis of data from epidemiologic and environmental studies presents challenges such as skewness of distribution rounding and multiple measurements over time to model trends over time based on repeated measurements we propose a general latent model suitable for highly skewed data the model assumes that the observed outcome is determined by an unobservable outcome that follows a weibull distribution to accommodate correlations among repeated responses over time we introduce a general random effect from the power variance function pvf family of distributions including the gamma distribution often employed in the literature the resulting marginal likelihood has a closed form without resorting to numerical or approximation methods we study estimation and hypothesis testing under these models with different choices of random effect distributions simulation studies are conducted to evaluate their performance finally we apply the proposed method to exposure data collected from the michigan polybrominated biphenyl mipbb study

bivariate current status data with univariate monitoring times summary for bivariate current status data with univariate monitoring times the identifiable part of the joint distribution is three univariate cumulative distribution functions namely the two marginal distributions and the bivariate cumulative distribution function evaluated on the diagonal we show that smooth functionals of these univariate cumulative distribution functions can be efficiently estimated with easily computed nonparametric maximum likelihood estimators based on reduced data consisting of univariate current status observations this theory is then applied to functionals that address independence of the two survival times and the goodness of fit of a copula model used by wang ding 2000 some brief simulations are provided along with an illustration based on data on hiv transmission extension of the ideas to incorporate covariates possibly time dependent are discussed

robust estimation in non linear state space models with state dependent noise in this paper we present a robust estimation algorithm for non linear state space models driven by state dependent noise the algorithm is robust to outliers in the data we derive the algorithm step by step from first principles from theory to implementation the implementation is straightforward and consists mainly of two components 1 a slightly modified version of the rauch tung striebel recursions and 2 a backtracking line search strategy since it preserves the underlying chain structure of the problem its computational complexity grows linearly with the number of data the algorithm is iterative and is guaranteed to converge under mild assumptions to a local optimum from any starting point we validate our approach via experiments on synthetic data from a multi variate stochastic volatility model

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

ignorability sufficiency and ancillarity this paper explores the relationship between ignorability sufficiency and ancillarity in the coarse data model of heitjan and rubin bayes or likelihood ignorability has a natural relationship to sufficiency and frequentist ignorability an analogous relationship to ancillarity weaker conditions termed observed likelihood sufficiency observed specific sufficiency and observed ancillarity expand the concepts to models where the coarsening mechanism is sometimes but not always ignorable

generalized iterated kalman filter and its performance evaluation in this paper we present a generalized iterated kalman filter gikf algorithm for state estimation of a nonlinear stochastic discrete time system with state dependent multiplicative observation noise the gikf algorithm adopts the newton raphson iterative optimization steps to yield an approximate maximum a posteriori estimate of the states the mean square estimation error mse and the cramer rao lower bound crlb of the state estimates are also derived in particular the local convergence of mse of gikf is rigorously established it is also proved that the gikf yields a smaller mse than those of the generalized extended kalman filter and the traditional extended kalman filter the performance advantages and convergence of gikf are demonstrated using monte carlo simulations on a target tracking application in a range measuring sensor network

inference in randomized studies with informative censoring and discrete time to event endpoints summary in this article we present a method for estimating and comparing the treatment specific distributions of a discrete time to event variable from right censored data our method allows for 1 adjustment for informative censoring due to measured prognostic factors for time to event and censoring and 2 quantification of the sensitivity of the inference to residual dependence between time to event and censoring due to unmeasured factors we develop our approach in the context of a randomized trial for the treatment of chronic schizophrenia we perform a simulation study to assess the practical performance of our methodology