a semiparametric approach for the two sample comparison of survival times with long term survivors summary in the two sample comparison of survival times with long term survivors the overall difference between the two distributions reflects differences occurring in early follow up for susceptible subjects and in long term follow up for nonsusceptible subjects in this setting we propose statistics for testing i no overall ii no short term and iii no long term difference between the two distributions to be compared the statistics are derived as follows a semiparametric model is defined that characterizes a short term effect and a long term effect by approximating this model about no difference in early survival a time dependent proportional hazards model is obtained the statistics are obtained from this working model the asymptotic distributions of the statistics for testing no overall or no short term effects are ascertained while that of the statistic for testing no long term effect is valid only when the short term effect is small simulation studies investigate the power properties of the proposed tests for different configurations the results show the interesting behavior of the proposed tests for situations where a short term effect is expected an example investigating the impact of progesterone receptors status on local tumor relapse for patients with early breast cancer illustrates the use of the proposed tests

fast and stable qr eigenvalue algorithms for generalized companion matrices and secular equations we introduce a class of n n structured matrices which includes three well known classes of generalized companion matrices tridiagonal plus rank one matrices comrade matrices diagonal plus rank one matrices and arrowhead matrices relying on the structure properties of we show that if a then a rq where a qr is the qr decomposition of a this allows one to implement the qr iteration for computing the eigenvalues and the eigenvectors of any a with o n arithmetic operations per iteration and with o n memory storage this iteration applied to generalized companion matrices provides new o n2 flops algorithms for computing polynomial zeros and for solving the associated rational secular equations numerical experiments confirm the effectiveness and the robustness of our approach

nonparametric estimation of the sojourn time distributions for a multipath model summary we use a multipath multistate model to describe data with multiple end points statistical inference based on the intermediate end point is challenging because of the problems of nonidentifiability and dependent censoring we study nonparametric estimation for the path probability and the sojourn time distributions between the states the methodology proposed can be applied to analyse cure models which account for the competing risk of death asymptotic properties of the estimators proposed are derived simulation shows that the methods proposed have good finite sample performance the methodology is applied to two data sets

a comparison of companion matrix methods to find roots of a trigonometric polynomial abstract a trigonometric polynomial is a truncated fourier series of the form f n t j 0 n a j cos jt j 1 n b j sin jt it has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the fourier coefficients the ccm method however previous work provided no examples so one goal of this new work is to experimentally test the ccm method a second goal is introduce a new alternative the elimination chebyshev algorithm and experimentally compare it with the ccm scheme the elimination chebyshev matrix ecm algorithm yields a companion matrix with real valued elements albeit at the price of usefulness only for real roots the new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables c s where c cos t and s sin t the elimination method next reduces the system to a single univariate polynomial p c we show that this same polynomial is the resultant of the system and is also a generator of the groebner basis with lexicographic ordering for the system both methods give very high numerical accuracy for real valued roots typically at least 11 decimal places in matlab ieee 754 16 digit floating point arithmetic the ccm algorithm is typically one or two decimal places more accurate though these differences disappear if the roots are newton polished by a single newton s iteration the complex valued matrix is accurate for complex valued roots too though accuracy decreases with the magnitude of the imaginary part of the root the cost of both methods scales as o n 3 floating point operations in spite of intimate connections of the elimination chebyshev scheme to two well established technologies for solving systems of equations resultants and groebner bases and the advantages of using only real valued arithmetic to obtain a companion matrix with real valued elements the ecm algorithm is noticeably inferior to the complex valued companion matrix in simplicity ease of programming and accuracy

brief paper identification of an additive nonlinear system and its applications in generalized hammerstein models an identification algorithm is developed for a class of nonlinear systems that are multi input and multi output in an additive form the convergence results are achieved and its applications to identification of a generalized hammerstein system is also discussed

cure rate model with mismeasured covariates under transformation cure rate models explicitly account for the survival fraction in failure time data when the covariates are measured with errors naively treating mismeasured covariates as error free would cause estimation bias and thus lead to incorrect inference under the proportional hazards cure model we propose a corrected score approach as well as its generalization and implement a transformation on the mismeasured covariates toward error additivity and or normality the corrected score equations can be easily solved through the backfitting procedure and the biases in the parameter estimates are successfully eliminated we show that the proposed estimators for the regression coefficients are consistent and asymptotically normal we conduct simulation studies to examine the finite sample properties of the new method and apply it to a real data set for illustration

linear life expectancy regression with censored data summary in the statistical literature life expectancy is usually characterised by the mean residual life function regression models are thus needed to study the association between the mean residual life functions and their covariates in this paper we consider a linear mean residual life model and develop inference procedures in the presence of potential censoring the new model and inference procedures are applied to the stanford heart transplant data semiparametric efficiency calculations and information bounds are also considered

estimation in change point hazard rate models summary this paper discusses the estimation of parameters in hazard rate models with a changepoint due to the irregularity of the models the classical maximum likelihood method and the method of moments cannot be used a consistent estimator of the change point is obtained by examining the properties of the density represented as a mixture the performance of the estimator is checked via simulation

likelihood ratio based confidence intervals in survival analysis abstract confidence intervals for the survival function and the cumulative hazard function are considered these confidence intervals are based on an inversion of the likelihood ratio statistic to do this two extensions of the likelihood each of which yields meaningful likelihood ratio hypothesis tests and subsequent confidence intervals are considered the choice of the best extension is difficult in the failure time setting the binomial extension is best in constructing confidence intervals concerning the survival function and the poisson extension is best in constructing confidence intervals concerning the cumulative hazard simulations indicate that these two methods perform as well as or better than competitors based on the asymptotic normality of the estimator

estimating a treatment effect with repeated measurements accounting for varying effectiveness duration to assess treatment efficacy in clinical trials certain clinical outcomes are repeatedly measured over time for the same subject the difference in their means may characterize a treatment effect since treatment effectiveness lag and saturation times may exist erosion of treatment effect often occurs during the observation period instead of using models based on ad hoc parametric or purely nonparametric time varying coefficients we model the treatment effectiveness durations which are the time intervals between the lag and saturation times then we use some mean response models to include such treatment effectiveness durations our methodology is demonstrated by simulations and analysis of a landmark hiv aids clinical trial of short course nevirapine against mother to child hiv vertical transmission during labour and delivery

numerical experiments on the accuracy of the chebyshev frobenius companion matrix method for finding the zeros of a truncated series of chebyshev polynomials for a function f x that is smooth on the interval email protected a b but otherwise arbitrary the real valued roots on the interval can always be found by the following two part procedure first expand f x as a chebyshev polynomial series on the interval and truncate for sufficiently large n second find the zeros of the truncated chebyshev series the roots of an arbitrary polynomial of degree n when written in the form of a truncated chebyshev series are the eigenvalues of an nxn matrix whose elements are simple explicit functions of the coefficients of the chebyshev series this matrix is a generalization of the frobenius companion matrix we show by experimenting with random polynomials wilkinson s notoriously ill conditioned polynomial and polynomials with high order roots that the chebyshev companion matrix method is remarkably accurate for finding zeros on the target interval yielding roots close to full machine precision we also show that it is easy and cheap to apply newton s iteration directly to the chebyshev series so as to refine the roots to full machine precision using the companion matrix eigenvalues as the starting point lastly we derive a couple of theorems the first shows that simple roots are stable under small perturbations of magnitude e to a chebyshev coefficient the shift in the root x is bounded by e df dx x o e 2 for sufficiently small e second we show that polynomials with definite parity only even or only odd powers of x can be solved by a companion matrix whose size is one less than the number of nonzero coefficients a vast cost saving

finding the zeros of a univariate equation proxy rootfinders chebyshev interpolation and the companion matrix when a function f x is holomorphic on an interval x in a b its roots on the interval can be computed by the following three step procedure first approximate f x on a b by a poly

two sample goodness of fit tests for additive risk models with censored observations summary the additive risk model assumes that the hazard function associated with a set of covariates is the sum of the baseline hazard function and the regression function of covariates we propose two different test procedures for checking the adequacy of two sample additive risk models for randomly censored observations one is based on the martingale residuals and the other on the difference between weighted estimators of the excess risk the test statistics are shown to be asymptotically normal under appropriate regularity conditions and consistent under any model misspecifications finally two real examples are provided along with results of a simulation study

goodness of fit tests for the cure rate in a mixture cure model summary we consider models for time to event data that allow that an event e g a relapse of a disease never occurs for a certain percentage p of the population called the cure rate we suppose that these data are subject to random right censoring and we model the data using a mixture cure model in which the survival function of the uncured subjects is left unspecified the aim is to test whether the cure rate p as a function of the covariates satisfies a certain parametric model to do so we propose a test statistic that is inspired by a goodness of fit test for a regression function due to hardle mammen 1993 we show that the statistic is asymptotically normally distributed under the null hypothesis that the model is correctly specified and under local alternatives a bootstrap procedure is proposed to implement the test the good performance of the approach is confirmed with simulations for illustration we apply the test to data on the times between first and second births

estimating multiplicative and additive hazard functions by kernel methods we propose new procedures for estimating the component functions in both additive and multiplicativen onparametricm arker dependenht azard models we work with a full counting process framework that allows for left truncation and right censoring and time varying covariates our procedures are based on kernel hazard estimation as developed by nielsen and linton and on the idea of marginal integration we provide a central limit theorem for the marginal integration estimator we then define estimators based on finite step backfitting in both additive and multiplicative cases and prove that these estimators are asymptotically normal and have smaller variance than the marginal integration method

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

almost everywhere complexity hierarchies for nondeterministic time abstract we present an almost everywhere complexity hierarchy for nondeterministic time and show that it is essentially the best result of this sort that can be proved using relativizable proof techniques

weighted kaplan meier statistics a class of distance tests for censored survival data a class of statistics based on the integrated weighted difference in kaplan meier estimators is introduced for the two sample censored data problem with positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering the standard weighted log rank statistics are not always sensitive against this alternative particularly if the hazard functions cross qualitative comparisons are made between the weighted log rank statistics and these weighted kaplan meier wkm statistics a statement of null asymptotic distribution theory is given and the choice of weight function is discussed in some detail results from small sample simulation studies indicate that these statistics compare favorably with the log rank procedure even under the proportional hazards alternative and may perform better than it under the crossing hazards alternative

computing the zeros of a fourier series or a chebyshev series or general orthogonal polynomial series with parity symmetries in recent years good algorithms have been developed for finding the zeros of trigonometric polynomials and of ordinary polynomials when written in the form of a truncated chebyshev polynomial or legendre polynomial series in each case the roots can be found from the eigenvalues of a generalized frobenius companion matrix whose elements are trivial functions of the fourier coefficients or chebyshev coefficients however the qr method for computing the companion matrix eigenvalues has a cost that grows proportionally to n 3 where n is the polynomial degree by exploiting the special structure of the companion matrices the cost can be reduced to o n 2 but only for large n here we show that if the polynomial has definite parity such as a trigonometric polynomial composed only of cosines or a polynomial that is a sum only of chebyshev polynomials of odd degree one can exploit these symmetries to halve the size of the problem this reduces costs in the companion matrix method by a factor ranging between four and eight for trigonometric polynomials we give transformations that dramatically reduce costs even if the roots are found by an algorithm other than the companion matrix procedure we further give reductions for trigonometric polynomials with double parity symmetries which save a factor of sixteen to a factor of sixty four in the companion matrix algorithm special functions such as spherical harmonics mathieu functions prolate spheroidal wavefunctions and hough functions all represented by truncated fourier series with double parity are a rich source of applications

computing zeros on a real interval through chebyshev expansion and polynomial rootfinding robust polynomial rootfinders can be exploited to compute the roots on a real interval of a nonpolynomial function f x by the following i expand f as a chebyshev polynomial series ii convert to a polynomial in ordinary series of powers form and iii apply the polynomial rootfinder complex valued roots and real roots outside the target interval are discarded the expansion is most efficiently done by adaptive chebyshev interpolation with n equal to a power of two where n is the degree of the truncated chebyshev series all previous evaluations of f can then be reused when n is increased adaption stops when n is sufficiently large so that further increases produce no significant change in the interpolant we describe two conversion strategies the convert to powers method uses multiplication by mildly ill conditioned matrices to create a polynomial of degree n the degree doubling strategy defines a polynomial of larger degree 2n but is very well conditioned the convert to powers method although faster restricts n to moderate values this can always be accomplished by subdividing the target interval both these strategies allow simultaneous approximation of many roots on an interval whether simple or multiple for nonpolynomial f x

almost every set in exponential time is p bi immune a set a is p bi immune if neither a nor its complement has an infinite subset in p we investigate here the abundance of p bi immune languages in linear exponential time e using resource bounded measure we prove that the class of p bi immune sets has measure 1 in e this implies that almost every language in e is p bi immune a bit further we show that every p random pseudorandom language is e bi immune regarding the existence of p bi immune sets in np we show that if np does not have measure 0 in e then np contains a p bi immune set another consequence is that the class of 1 tt p complete languages for e has measure 0 in e in contrast using the approach of resource bounded category it is shown that in e the class of p bi immune languages lacks the property of baire the baire category analogue of lebesgue measurability

a new bayesian model for survival data with a surviving fraction abstract we consider bayesian methods for right censored survival data for populations with a surviving cure fraction we propose a model that is quite different from the standard mixture model for cure rates we provide a natural motivation and interpretation of the model and derive several novel properties of it first we show that the model has a proportional hazards structure with the covariates depending naturally on the cure rate second we derive several properties of the hazard function for the proposed model and establish mathematical relationships with the mixture model for cure rates prior elicitation is discussed in detail and classes of noninformative and informative prior distributions are proposed several theoretical properties of the proposed priors and resulting posteriors are derived and comparisons are made to the standard mixture model a real dataset from a melanoma clinical trial is discussed in detail

nonparametric estimation and testing in a cure model nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship one two and k sample likelihood ratio tests for inference on the cure rates are developed in the two sample case its power is compared to the power of several alternatives including the log rank and gray and tsiatis 1989 biometrics 45 899 904 tests implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed

inference for a class of transformed hazards models a new class of transformed hazard rate models is considered that contains both the multiplicative hazards model and the additive hazards model as special cases the sieve maximum likelihood estimators are derived for the model parameters and the estimators for the regression coefficients are shown to be consistent and asymptotically normal with variance achieving the semiparametric efficiency bound simulation studies are conducted to examine the small sample properties of the proposed estimates and a real dataset is used to illustrate our approach

additive hazards models with latent treatment effectiveness lag time summary in many clinical trials for evaluating treatment efficacy it is believed that there may exist latent treatment effectiveness lag times after which medical treatment procedure or chemical compound would be in full effect in this paper semiparametric regression models are proposed and studied for estimating the treatment effect accounting for such latent lag times the new models take advantage of the invariant property of the additive hazards model in marginalising over an additive latent variable parameters in the models are thus easily estimated and interpreted while the flexibility of not having to specify the baseline hazard function is preserved monte carlo simulation studies demonstrate the appropriateness of the proposed semiparametric estimation procedure the methodology is applied to data collected in a randomised clinical trial which evaluates the efficacy of biodegradable carmustine polymers for treatment of recurrent brain tumours

a note on almost everywhere complex sets and separating deterministic time complexity classes abstract for each time bound t input strings natural numbers that is some machine s exact running time there is a 0 1 valued function ft that can be computed within time proportional to t but that cannot be computed within any time bound t that is infinitely often significantly smaller than t t t typically equivalently every algorithm to compute ft requires time t on almost every input if t is almost everywhere significantly smaller than t t o t typically

testing if a nonlinear system is additive or not abstract additive nonlinear systems are one of the most widely used nonlinear and non parametric models to describe nonlinear behaviors a number of analysis and identification techniques have been developed in the literature for such systems to apply however one has to make sure that the system is additive or can be approximated well by an additive system this is a nontrivial problem and has eluded researchers for a long time to the best of our knowledge only scatter results are reported in the literature the difficulties lie in the fact that the function and its structure are unknown so estimating its derivatives under an unknown multidimensional density function could be subject to the curse of dimensionality in this paper we present two methods to check if a system is additive the first one estimates the squared derivative average via the fourier transform the other one directly estimates the squared derivative average in a reproducing kernel hilbert space rkhs setting for both methods convergence results are established and practical numerical algorithms are developed

pseudomartingale estimating equations for modulated renewal process models summary we adapt martingale estimating equations based on gap time information to a gen eral intensity model for a single realization of a modulated renewal process the consistency and asymptotic normality of the estimators is proved under ergodicity conditions previous work has considered either parametric likelihood analysis or semiparametric multiplicative models using partial likelihood the framework is generally applicable to semiparametric and paramet ric models including additive and multiplicative specifications and periodic models it facilitates a semiparametric extension of a popular parametric earthquake model simulations and empir ical analyses of taiwanese earthquake sequences illustrate the methodology s practical utility

fine separation of average time complexity classes we extend levin s definition of average polynomial time to arbitrary time bounds in accordance with the following general principles 1 it essentially agrees with levin s notion when applied to polynomial time bounds 2 if a language l belongs to dtime t n for some time bound t n then every distributional problem l mu is t on the mu average 3 if l does not belong to dtime t n almost everywhere then no distributional problem l mu is t on the mu average we present hierarchy theorems for average case complexity for arbitrary time bounds that are as tight as the well known hartmanis stearns hierarchy theorem for deterministic complexity as a consequence for every time bound t n there are distributional problems l mu that can be solved using only a slight increase in time but that cannot be solved on the mu average in time t n

numerical perturbative and chebyshev inversion of the incomplete elliptic integral of the second kind abstract the incomplete elliptic integral of the second kind e sin t m 0 t 1 m sin 2 t dt where m 0 1 is the elliptic modulus can be inverted with respect to angle t by solving the transcendental equation e sin t m z 0 we show that newton s iteration t n 1 t n e sin t m z 1 m sin 2 t always converges to t z m e 1 z m within a relative error of less than 10 10 in three iterations or less from the first guess t 0 z m 2 r 2 where defining 1 z e 1 m r 1 m 2 2 and atan 1 m we briefly discuss three alternative initialization strategies homotopy initialization t 0 z m 1 m z 0 mt z m m 1 perturbation series in powers of m and inversion of the chebyshev interpolant of the incomplete elliptic integral although all work well and are general strategies applicable to a very wide range of problems none of these three alternatives is as efficient as the empirical initialization which is completely problem specific this illustrates tai tsun wu s maxim usefulness is often inversely proportional to generality

aalen additive hazards change point model we study a test comparing the full aalen additive hazards model and the change point model and suggest how to estimate the parameters of the change point model we also study a test for no change point effect both tests are provided with large sample properties and a resampling method is applied to obtain p values the finite sample properties of the proposed inference procedures and estimators are assessed through a simulation study the methods are further applied to a dataset concerning myocardial infarction

a linear rank test for use when the main interest is in differences in cure rates for diseases with a positive probability of being cured a family of alternatives to the null hypothesis of equality of survival distributions is introduced which is designed to focus power against alternatives with differences in cure rates the optimal linear rank test for this alternative is derived and found to be substantially more efficient than the log rank test for this alternative when cure rates are less than 50 while there is little difference between the tests if the cure rates are 50 or greater the simple test based on the difference of kaplan meier estimates of the proportion cured is also examined and found to be fully efficient for this alternative with no censoring while its efficiency rapidly drops as censoring is increased the new test is not a pure test of equality of cure rates when the data are censored but rather is a test of equality of survival distributions that focuses power against late differences in the survival curves

variable selection and identification of high dimensional nonparametric additive nonlinear systems this paper considers variable selection and identification of dynamic additive nonlinear systems via kernel based nonparametric approaches where the number of variables and additive functions may be large variable selection aims to find which additive functions contribute and which do not the proposed variable selection consists of two successive steps at the first step one estimates each additive function by kernel based nonparametric identification approaches without suffering from the curse of dimensionality at the second step a nonnegative garrote estimator is applied to identify which additive functions are nonzero by utilizing the obtained nonparametric estimates of each function under weak conditions the nonparametric estimates of each additive function can achieve the same asymptotic properties as for 1d nonparametric identification based on kernel functions it is also established that the nonnegative garrote estimator turns a consistent estimate for each additive function into a consistent variable selection with probability one as the number of samples tends to infinity two simulation examples are presented to verify the effectiveness of the variable selection and identification approaches proposed in the paper

identification of nonlinear additive fir systems in this paper we consider identification of a nonlinear additive system an input signal is designed in such a way that the problem of identification of nonlinear additive systems is reduced to a problem of identification of static nonlinear functions then three approaches are established to estimate the order of the system the methods exploit the structure of the nonlinear additive model so that their implementations are easy

complete distributional problems hard languages and resource bounded measure we say that a distribution is reasonable if there exists a constant s 0 such that x x n 1 ns we prove the following result which suggests that all distnp complete problems have reasonable distributions if np contains a dtime 2n bi immune set then every distnp complete set has a reasonable distribution it follows from work of mayordomo 19 that the consequent holds if the p measure of np is not zero cai and selman 6 defined a modification and extension of levin s notion of average polynomial time to arbitrary time bounds and proved that if l is p bi immune then l is distributionally hard meaning that for every polynomial time computable distribution the distributional problem l is not polynomial on the average we prove the following results which suggest that distributional hardness is closely related to more traditional notions of hardness 1 if np contains a distributionally hard set then np contains a p immune set 2 there exists a language l that is distributionally hard but not p bi immune if and only if p contains a set that is immune to all p printable sets the following corollaries follow readily 1 if the p measure of np is not zero then there exists a language l that is distributionally hard but not p bi immune 2 if the p2 measure of np is not zero then there exists a language l in np that is distributionally hard but not p bi immune

cure rate models power of the logrank and generalized wilcoxon tests this paper reports the results of simulations that compare the power of the logrank and generalized wilcoxon tests in situations where the cure rate model is appropriate

accelerated failure time regression models with a regression model of surviving fraction an application to the analysis of permanent employment in japan abstract accelerated failure time regression models with an additional regression model for the surviving fraction are proposed for the analysis of events that may never occur regardless of censoring for some people in the population risk set the models attempt to estimate simultaneously the effects of covariates on the acceleration deceleration of the timing of a given event and the surviving fraction that is the proportion of the population for which the event never occurs the extended family of the generalized gamma distribution is used for the accelerated failure time regression model the logistic function is used for the regression model of the surviving fraction the models are applied to the data of interfirm job mobility in japan to assess variability in permanent employment among white collar and blue collar employees in firms of different sizes independent from their variability in the timing of interfirm job separations

nonparametric covariate hypothesis tests for the cure rate in mixture cure models in lifetime data like cancer studies there may be long term survivors which lead to heavy censoring at the end of the follow up period since a standard survival model is not appropriate to handle these data a cure model is needed in the literature covariate hypothesis tests for cure models are limited to parametric and semiparametric methods we fill this important gap by proposing a nonparametric covariate hypothesis test for the probability of cure in mixture cure models a bootstrap method is proposed to approximate the null distribution of the test statistic the procedure can be applied to any type of covariate and could be extended to the multivariate setting its efficiency is evaluated in a monte carlo simulation study finally the method is applied to a colorectal cancer dataset

semiparametric estimation for the additive hazards model with left truncated and right censored data survival data from prevalent cases collected under a cross sectional sampling scheme are subject to left truncation when fitting an additive hazards model to left truncated data the conditional estimating equation method lin ying 1994 obtained by modifying the risk sets to account for left truncation can be very inefficient as the marginal likelihood of the truncation times is not used in the estimation procedure in this paper we use a pairwise pseudolikelihood to eliminate nuisance parameters from the marginal likelihood and by combining the marginal pairwise pseudo score function and the conditional estimating function propose an efficient estimator for the additive hazards model the proposed estimator is shown to be consistent and asymptotically normally distributed with a sandwich type covariance matrix that can be consistently estimated simulation studies show that the proposed estimator is more efficient than its competitors a data analysis illustrates application of the method

multiple testing for a combination drug with two study endpoints a combination drug product with two or more active compounds may be superior to each of its components with higher dose levels and therefore is preferred in terms of efficacy cost and safety to study a combination drug researchers often conduct trials by using a factorial design with combinations of dose levels of each drug component by applying some bootstrap methods we construct multiple testing procedures to simultaneously identify combinations superior to each drug component with any dose level these multiple testing procedures are more powerful than holm s step down procedure that is known to be very conservative when there is only one study endpoint applying the bootstrap is straightforward in many studies however there are two or more study endpoints and it is not simple to apply the bootstrap we apply one version of the bootstrap and then use an upper bound to control the familywise error defined as the probability of rejecting at least one true null hypothesis properties of the bootstrap multiple testing procedures are discussed and examined in some simulation studies

regression analysis with multiplicative and time varying additive regression coefficients with examples from breast and colon cancer regression analysis may be used to simplify the representation of mortality rates when there are many significant prognostic covariates or to adjust for confounding effects the principal request of the regression model in this range of use is to have unbiased parameter estimates a model with constant multiplicative and time varying additive regression coefficients is discussed the model allows some covariate effects to be multiplicative while allowing others to have a time varying additive effect thus it is a mix of classical cox regression and aalen s additive risk model a major characteristic of cancer mortality rates in contrast to general mortality rates is that hazard rates after a potentially initial increase decrease although not always tending to zero cancer diseases like breast and colon cancer have significantly increased cause specific mortality rates even 20 years after diagnosis another major feature in cancer survival analysis is that many covariate effects are time varying some covariate effects like age at diagnosis may only be significant for a limited time after diagnosis furthermore some treatment procedures may initially decrease the mortality while the long term effect may be opposite a third issue is that average covariate effects are very often not multiplicative estimation is carried out iteratively the cumulative additive regression functions are estimated non parametrically using a least squares method and the multiplicative parameters are estimated from the partial likelihood the method is applied on 3201 female breast cancer and 1372 male colon cancer patients

weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatment summary in certain long term treatment trials one expects some lag period before the treatment is fully effective this paper presents two weighted log rank type statistics designed to have good efficiency over a wide range of lags a maximin efficiency robust statistic and a simplified version of this statistic both statistics can be computed as easily as the log rank statistic asymptotic efficiency calculations supported by small sample simulations show that the two proposed statistics are substantially more efficient than the conventional log rank statistic in certain lag situations with comparatively little efficiency loss relative to the log rank statistic when no lag exists we recommend the maximin statistic for situations where a lag is expected but cannot be specified precisely in advance

almost everywhere superiority for quantum polynomial time simon as extended by brassard and hoyer shows that there are tasks on which polynomial time quantum machines are exponentially faster than each classical machine infinitely often the present paper shows that there are tasks on which polynomial time quantum machines are exponentially faster than each classical machine almost everywhere

a model combining excess and relative mortality for population based studies considering expected mortality provides an attractive approach to analyse mortality of population based cohorts of patients presenting with a chronic disease two classes of methods are available either modelling the excess mortality using an additive hazard model or modelling the relative mortality using a multiplicative hazard model because these two models are informative to look for factors associated with mortality related to a chronic disease we developed an alternative model modelling both the excess and the relative mortality we generalised andersen and vaeth s model to fit covariates and obtain directly an estimation of the excess mortality ratio and relative mortality ratio for each covariate we assessed the performances of the combined model by using simulations and it appeared satisfactorily we illustrate the combined model by data collected in patients presenting with end stage renal disease and treated by dialysis the combined model offers the possibility of performing pure additive and multiplicative models and thus to compare their log likelihoods the combined model appears useful to select one of these pure models or to conclude to the need of modelling both excess and relative mortality in this latter case our model enabled better describing the effect of covariates on the excess and relative mortality

group sequential designs for cure rate models with early stopping in favour of the null hypothesis ewell and ibrahim derived the large sample distribution of the logrank statistic under general local alternatives their asymptotic results enable us to extend several group sequential designs which allow for early stopping in favour of the null hypothesis to the setting in which the cure rate model is appropriate in particular we derive stopping rules for the cure rate model using conditional power predictive power and repeated confidence intervals methods we illustrate the methods proposed using a hypothetical phase iii clinical trial which is typical for melanoma studies

an extension of matlab to continuous functions and operators an object oriented matlab system is described for performing numerical linear algebra on continuous functions and operators rather than the usual discrete vectors and matrices about eighty matlab functions from plot and sum to svd and cond have been overloaded so that one can work with our chebfun objects using almost exactly the usual matlab syntax all functions live on 1 1 and are represented by values at sufficiently many chebyshev points for the polynomial interpolant to be accurate to close to machine precision each of our overloaded operations raises questions about the proper generalization of familiar notions to the continuous context and about appropriate methods of interpolation differentiation integration zerofinding or transforms applications in approximation theory and numerical analysis are explored and possible extensions for more substantial problems of scientific computing are mentioned

on a general class of semiparametric hazards regression models a general class of semiparametric hazards regression models for survival data is proposed and studied this general class includes some popular classes of models as subclasses such as cox s proportional hazards model the accelerated failure time model and a recently proposed class of models called the accelerated hazards model in the general class of models a covariate s effect is identified as having two separate components namely a time scale change on hazard progression and a relative hazards ratio the new model is flexible in modelling survival data and may yield more accurate prediction of an individual s survival process by way of the nested structure that includes the proportional hazards model the accelerated failure time model and the accelerated hazards model the general class of models may provide a numerical tool for determining which of them is more appropriate for a given dataset

a chebyshev polynomial interval searching method lanczos economization for solving a nonlinear equation with application to the nonlinear eigenvalue problem to search a given real interval for roots our algorithm is to replace f by fn its n term chebyshev expansion on the search interval min max and compute the roots of this proxy this strategy is efficient if and only if f itself is expensive to evaluation such as when f is the determinant of a large matrix whose elements depend nonlinearly on for such expensive functions it is much cheaper to search for zeros of fn which can be evaluated in o n operations than to iterate or look for sign changes on a fine grid with f itself it is possible to systematically increase n until the chebyshev series converges acceptably fast without wasting previously computed values of f by imitating the clenshaw curtis quadrature our strategy of replacing f by fn is similar to lanczos economization of power series which also replaces an expensive function by a chebyshev approximation that is more rapidly evaluated the errors induced by the chebyshev approximation can be eliminated by a final step of one or two iterations with f itself using the zeros of fn as initial guesses we show through numerical examples that the algorithm works well the only sour note is that it is sometimes necessary to split the search interval into subintervals each with a separate chebyshev expansion when f varies by many orders of magnitude on the search interval

a comparison of tests of the difference in the proportion of patients who are cured we compared by simulation the likelihood ratio wald and score tests based on a mixture model similar to that proposed by farewell 1982 biometrics 38 1041 1046 and a simple nonparametric test based on the plateau value of the product limit estimate for testing the difference in cured proportions between two groups the parametric tests obtained their asymptotic properties even in small samples provided that one could assume equal failure rates in the two groups otherwise good agreement with predictions required that essentially all potential failures had been observed the comparative properties of the parametric tests depended on whether the population survival functions crossed with the power of the wald test as good as or better than the others in the common situation when the survival functions do not cross however its size was sometimes less than nominal the score test was often not defined and is therefore of limited value the product limit test often performed as well as the parametric tests and despite being biased in some circumstances may be a useful alternative to these especially in small samples when some potential failures have not been observed

roots of polynomials expressed in terms of orthogonal polynomials a technique is presented for determining the roots of a polynomial p x that is expressed in terms of an expansion in orthogonal polynomials the roots are expressed as the eigenvalues of a nonstandard companion matrix b n whose coefficients depend on the recurrence formula for the orthogonal polynomials and on the coefficients of the orthogonal expansion some questions on the numerical stability of the eigenvalue problem to which they give rise are discussed the problem of finding the roots of a transcendental function f x can be reduced to the problem considered by approximating f x by a chebyshev polynomial we illustrate the effectiveness of this convert to chebyshev strategy by solving several transcendental equations using this plus our new algorithm we analyze the numerical stability through both linear algebra theory and numerical experiments and find that this method is very well conditioned

transfer functionals and semiparametric regression models summary a general approach to semiparametric regression model construction is proposed using the notation of a transfer functional estimators of unknown regression parameters are proposed generalising the estimators of the parameters of the proportional hazards and the additive risk models

bayesian estimators for conditional hazard functions summary this article introduces a new bayesian approach to the analysis of right censored survival data the hazard rate of interest is modeled as a product of conditionally independent stochastic processes corresponding to 1 a baseline hazard function and 2 a regression function representing the temporal influence of the covariates these processes jump at times that form a time homogeneous poisson process and have a pairwise dependency structure for adjacent values the two processes are assumed to be conditionally independent given their jump times features of the posterior distribution such as the mean covariate effects and survival probabilities conditional on the covariate are evaluated using the metropolis hastings green algorithm we illustrate our methodology by an application to nasopharynx cancer survival data

maximum likelihood methods for cure rate models with missing covariates we propose maximum likelihood methods for parameter estimation for a novel class of semiparametric survival models with a cure fraction in which the covariates are allowed to be missing we allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions we propose a novel em algorithm for maximum likelihood estimation and derive standard errors by using louis s formula louis 1982 journal of the royal statistical society series b 44 226 233 computational techniques using the monte carlo em algorithm are discussed and implemented a real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology

semiparametric transformation models for survival data with a cure fraction we propose a class of transformation models for survival data with a cure fraction the class of transformation models is motivated by biological considerations and includes both the proportional hazards and the proportional odds cure models as two special cases an efficient recursive algorithm is proposed to calculate the maximum likelihood estimators mles furthermore the mles for the regression coefficients are shown to be consistent and asymptotically normal and their asymptotic variances attain the semiparametric efficiency bound simulation studies are conducted to examine the finite sample properties of the proposed estimators the method is illustrated on data from a clinical trial involving the treatment of melanoma

computing real roots of a polynomial in chebyshev series form through subdivision with linear testing and cubic solves abstract an arbitrary polynomial of degree n f n x can always be represented as a truncated chebyshev polynomial series chebyshev form this representation is much better conditioned than the usual power form of a polynomial we describe a new method for finding the real roots of f n x in chebyshev form the canonical interval x 1 1 is subdivided into n s subintervals each is tested for zeros using the error bound for linear interpolation on zero possible intervals f n is approximated by a cubic polynomial whose roots are then found by the usual sixteenth century formulas

semiparametric analysis of general additive multiplicative hazard models for counting processes the additive multiplicative hazard model specifies that the hazard function for the counting process associated with a multidimensional covariate process z w t x t t takes the form of t z g 0 t w t 0 t h 0 t x t where 0 0 t 0 t t is a vector of unknown regression parameters g and h are known link functions and 0 is an unspecified baseline hazard function in this paper we develop a class of simple estimating functions for 0 which contains the partial likelihood score function in the special case of proportional hazards models the resulting estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions weak convergence of the aalen breslow type estimators for the cumulative baseline hazard function 0 t 0 t 0 u du is also established furthermore we construct adaptive estimators for 0 and o that achieve the semiparametric information bounds finally a real example is provided along with some simulation results

new series for the cosine lemniscate function and the polynomialization of the lemniscate integral we discuss the numerical computation of the cosine lemniscate function and its inverse the lemniscate integral these were previously studied by bernoulli euler gauss abel jacobi and ramanujan we review general elliptic formulas for this special case and provide some novelties we show that a fourier series by ramanujan converges twice as fast as the standard elliptic cosine fourier series specialized to this case the so called imbricate series however converges geometrically fast over the entire complex plane we derive two new expansions the rational plus fourier series converges much faster than ramanujan s for real z each term is asymptotically 12 400 times smaller than its immediate predecessor coslem z 4b q 1 q cos bz 1 q 2 4qcos 2 bz n 1 q n 1 2 1 1 q 2 n 1 1 cos 2n 1 bz where q exp p is the elliptic nome k 1 85 is the complete elliptic integral of the first kind for a modulus m 1 2 and b p k2 the rational imbricate series is uniformly valid over the complex plane but converges twice as fast as the sech imbricate series coslem z 4bq 1 q j q 1 q cos bz 1 q 2 4qcos 2 b z jpi where p 4 2 k is the period in both the real and imaginary directions we devise a new approximation for the lemniscate integral for real argument as the arccosine of a chebyshev series and show that 17 terms yield about 15 digits of accuracy for complex argument we show that the lemniscate integral can be found to near machine precision assumed as sixteen decimal digits by computing the roots of a polynomial of degree thirteen alternatively newton s iteration converges in three iterations with an initialization accurate to four decimal places that is the chosen root of a cubic equation