tree structured proportional hazards regression modeling a method for fitting piecewise proportional hazards models to censored survival data is described stratification is performed recursively using a combination of statistical tests and residual analysis the bootstrap is employed to keep the probability of a type i error the error of discovering two or more strata when there is only one of the method close to a predetermined value the proposed method can thus also serve as a formal goodness of fit test for the proportional hazards model real and simulated data are used for illustration

geometric extensions of many particle hardy inequalities certain many particle hardy inequalities are derived in a simple and systematic way using the so called ground state representation for the laplacian on a subdomain of this includes geometric extensions of the standard hardy inequalities to involve volumes of simplices spanned by a subset of points clifford multilinear algebra is employed to simplify geometric computations these results and the techniques involved are relevant for classes of exactly solvable quantum systems such as the calogero sutherland models and their higher dimensional generalizations as well as for membrane matrix models and models of more complicated particle interactions of geometric character

reply to comment exact solution of an n body problem in one dimension it is pointed out that apart from the classic calogero problem the n body potential discussed in reference 1 of the preceding comment is the only one for which the n body problem as given by equation 1 of the comment is analytically solvable for all partial waves in that sense the n body potential is indeed unique

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

partially solvable quantum many body problems in d dimensional space d 1 2 3 a simple technique employed almost three decades ago to manufacture partially solvable quantum many body problems is revisited a quantum problem is partially solvable if only some of its eigenvalues and eigenfunctions can be exhibited the models thereby generated are characterized by hamiltonians of normal form i e standard kinetic plus momentum independent potential energy in most cases the latter features three body in addition to two body and one body interactions the setting refers to d dimensional space the examples focus on d 1 d 2 and d 2 and include generalizations of and additional results on cases recently discussed in the literature as well as new models

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

identification of linear stochastic models with covariance restrictions abstract the purpose of this paper is to provide a systematic treatment of the problem of identification in systems of linear structural equations where some of the disturbances are uncorrelated

novel correlations in two dimensions two body problem we discuss a many body hamiltonian with two and three body interactions in two dimensions introduced recently by murthy bhaduri and sen apart from an analysis of some exact solutions in the many body system we analyse in detail the two body problem which is completely solvable we show that the solution of the two body problem reduces to solving a known differential equation due to heun we show that the two body spectrum becomes remarkably simple for large interaction strengths and the level structure resembles that of the landau levels we also clarify the ultraviolet regularization which is needed to define an inverse square potential properly and discuss its implications for our model

multiple imputation of missing blood pressure covariates in survival analysis this paper studies a non response problem in survival analysis where the occurrence of missing data in the risk factor is related to mortality in a study to determine the influence of blood pressure on survival in the very old 85 years blood pressure measurements are missing in about 12 5 per cent of the sample the available data suggest that the process that created the missing data depends jointly on survival and the unknown blood pressure thereby distorting the relation of interest multiple imputation is used to impute missing blood pressure and then analyse the data under a variety of non response models one special modelling problem is treated in detail the construction of a predictive model for drawing imputations if the number of variables is large risk estimates for these data appear robust to even large departures from the simplest non response model and are similar to those derived under deletion of the incomplete records

new algebraic quantum many body problems we develop a systematic procedure for constructing quantum many body problems whose spectrum can be partially or totally computed by purely algebraic means the exactly solvable models include rational and hyperbolic potentials related to root systems in some cases with an additional external field the quasi exactly solvable models can be considered as deformations of the previous ones which share their algebraic character

efficient estimation and identification of simultaneous equation models with covariance restrictions this paper is a revision of an earlier version presented at the european econometric meetings 1982

piecewise exponential survival trees with time dependent covariates survival trees methods are nonparametric alternatives to the semiparametric cox regression in survival analysis in this paper a tree based method for censored survival data with time dependent covariates is proposed the proposed method assumes a very general model for the hazard function and is fully nonparametric the recursive partitioning algorithm uses the likelihood estimation procedure to grow trees under a piecewise exponential structure that handles time dependent covariates in a parallel way to time independent covariates in general the estimated hazard at a node gives the risk for a group of individuals during a specific time period both cross validation and bootstrap resampling techniques are implemented in the tree selection procedure the performance of the proposed survival trees method is shown to be good through simulation and application to real data

exactly solvable three body systems with internal degrees of freedom the approach of multi dimensional susy quantum mechanics is used in an explicit construction of exactly solvable three body and quasi exactly solvable n body matrix problems on a line from intertwining relations with time dependent operators we build exactly solvable non stationary scalar and 2 2 matrix three body models which are time dependent extensions of the calogero model finally we investigate the invariant operators associated with these systems

tree structured logistic model for over dispersed binomial data with application to modeling developmental effects this article proposes tree structured logistic regression modeling for over dispersed binomial data recursive partitioning is performed using a combination of statistical tests and residual analysis the splitting criterion in cross validation is based on the deviance function a nested grid algorithm to estimate the bootstrap parameters is developed the regression tree procedure provides a new approach for exploring in detail the relationship between the binomial response and explanatory variables the proposed procedure is used to model the relationship between the incidence of malformation and dose and fetal weight using data from a developmental experiment conducted at the national center for toxicological research a conditional gaussian chain model is used to account for the effect of fetal weight by dose

binary partitioning for continuous longitudinal data categorizing a prognostic variable we investigate a binary partitioning algorithm in the case of a continuous repeated measures outcome the procedure is based on the use of the likelihood ratio statistic to evaluate the performance of individual splits the procedure partitions a set of longitudinal data into two mutually exclusive groups based on an optimal split of a continuous prognostic variable a permutation test is used to assess the level of significance associated with the optimal split and a bootstrap confidence interval is obtained for the optimal split

a note on the identification of restricted factor loading matrices it is shown that problems of rotational equivalence of restricted factor loading matrices in orthogonal factor analysis are equivalent to problems of identification in simultaneous equations systems with covariance restrictions a necessary under a regularity assumption and sufficient condition for local uniqueness is given and a counterexample is provided to a theorem by j algina concerning necessary and sufficient conditions for global uniqueness

time dependent tree structured survival analysis with unbiased variable selection through permutation tests incorporating time dependent covariates into tree structured survival analysis tssa may result in more accurate prognostic models than if only baseline values are used available time dependent tssa methods exhaustively test every binary split on every covariate however this approach may result in selection bias towards covariates with more observed values we present a method that uses unbiased significance levels from newly proposed permutation tests to select the time dependent or baseline covariate with the strongest relationship with the survival outcome the specific splitting value is identified using only the selected covariate simulation results show that the proposed time dependent tssa method produces tree models of equal or greater accuracy as compared to baseline tssa models even with high censoring rates and large within subject variability in the time dependent covariate to illustrate the proposed method is applied to data from a cohort of bipolar youth to identify subgroups at risk for self injurious behavior

testing goodness of fit for proportional hazards model with censored observations abstract a numerical omnibus test of fit for the two sample proportional hazards model is proposed for randomly censored observations the test is derived from cox s partial likelihood and does not need a dummy time dependent covariate or any partition of the time axis consistency of the test is established examples are provided for illustration

on the investigation of local identifiability a counterexample an assertion that the parameters of a covariance structure are locally identified at a certain point only if the rank of the jacobian matrix at that point equals the number of parameters is shown to be false by means of a counterexample

a regression tree approach to identifying subgroups with differential treatment effects in the fight against hard to treat diseases such as cancer it is often difficult to discover new treatments that benefit all subjects for regulatory agency approval it is more practical to identify subgroups of subjects for whom the treatment has an enhanced effect regression trees are natural for this task because they partition the data space we briefly review existing regression tree algorithms then we introduce three new ones that are practically free of selection bias and are applicable to data from randomized trials with two or more treatments censored response variables and missing values in the predictor variables the algorithms extend the guide approach by using three key ideas i treatment as a linear predictor ii chi squared tests to detect residual patterns and lack of fit and iii proportional hazards modeling via poisson regression importance scores with thresholds for identifying influential variables are obtained as by products a bootstrap technique is used to construct confidence intervals for the treatment effects in each node the methods are compared using real and simulated data