precision of incidence predictions based on poisson distributed observations disease incidence predictions are useful for a number of administrative and scientific purposes the simplest ones are made using trend extrapolation on either an arithmetic or a logarithmic scale this paper shows how approximate confidence prediction intervals can be calculated for such predictions both for the total number of cases and for the age adjusted incidence rates by assuming poisson distribution of the age and period specific numbers of incident cases generalizations for prediction models for example using power families and extra poisson variation are also presented cancer incidence predictions for the stockholm gotland oncological region in sweden are used as an example

a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

isomorphism classes of short gorenstein local rings via macaulay s inverse system in this paper we study the isomorphism classes of artinian gorenstein local rings with socle degree three by means of macaulay s inverse system we prove that their classification is equivalent to the projective classification of the hypersurfaces of p n of degree three this is an unexpected result because it reduces the study of this class of local rings to the homogeneous case the result has applications in problems concerning the punctual hilbert scheme hilbd p n and

the estimation of age period and cohort effects for vital rates in models for vital rates which include effects due to age period and cohort there is aliasing due to a linear dependence among these three factors this dependence arises both when age and period intervals are equal and when they are not one solution to the dependence is to set an arbitrary constraint on the parameters estimable functions of the parameters are invariant to the particular constraint applied for evenly spaced intervals deviations from linearity are estimable but only a linear function of the three slopes is estimable when age and period intervals have different widths further aliasing occurs it is assumed that the number of deaths in the numerator of the rate equation has a poisson distribution the calculations are illustrated with data on mortality from prostate cancer among nonwhites in the u s

the gorenstein colength of an artinian local ring abstract in this paper we make the notion of approximating an artinian local ring by a gorenstein artin local ring precise using the concept of gorenstein colength we also answer the question of when the gorenstein colength is at most two

estimating cancer incidence using a bayesian back calculation approach we propose a bayesian hierarchical model for the calculation of incidence counts from mortality data by a convolution equation that expresses mortality through its relationship with incidence and the survival probability density the basic idea is to use mortality data together with an estimate of the survival distribution from cancer incidence to cancer mortality to reconstruct the numbers of individuals who constitute previously incident cases that give rise to the observed pattern of cancer mortality this model is novel because it takes into account the uncertainty from the survival distribution thus a bayesian mixture cure model for survival is introduced furthermore projections are obtained starting from a bayesian age period cohort model the main advantage of the proposed approach is its consideration of the three components of the model the convolution equation the survival mixture cure model and the age period cohort projection within a directed acyclic graph model furthermore the estimation are obtained through the gibbs sampler we applied the model to cases of women with stomach cancer using six age classes 15 45 45 55 55 65 65 75 75 85 and 85 95 and validated it by using data from the tuscany cancer registry the model proposed and the program implemented are convenient because they allow different cancer disease to be analysed because the survival time is modelled by flexible distributions that are able to describe different trends

a simple non linear model in incidence prediction a simple model is proposed for incidence prediction the model is non linear in parameters but linear in time following models in environmental cancer epidemiology assuming a poisson distribution for the age and period specific numbers of incident cases approximate confidence and prediction intervals are calculated the major advantage of this model over current models is that age specific predictions can be made with greater accuracy the model also preserves in the period of prediction the age pattern of incidence rates existing in the data it may be fitted with any package which includes an iteratively reweighted least squares algorithm for example glim cancer incidence predictions for the stockholm gotland oncological region in sweden are presented as an example

predictive model assessment for count data we discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for count data our proposals include a nonrandomized version of the probability integral transform marginal calibration diagrams and proper scoring rules such as the predictive deviance in case studies we critique count regression models for patent data and assess the predictive performance of bayesian age period cohort models for larynx cancer counts in germany the toolbox applies in bayesian or classical and parametric or nonparametric settings and to any type of ordered discrete outcomes

on low gorenstein colength abstract the aim of this paper is to extend the characterization of teter rings of 9 to artin rings of gorenstein colength two and to improve and complete the result 1 theorem 5 5 on such rings by using macaulay s inverse system we provide several explicit examples and families of gorenstein colength two rings taking into account their analytic type

connected sums of gorenstein local rings given surjective homomorphisms r t s of local rings and ideals in r and s that are isomorphic to some t module v the connected sum r ts is defined to be ring obtained by factoring out the diagonal image of v in the fiber product r t s when t is cohen macaulay of dimension d and v is a canonical module of t it is proved that if r and s are gorenstein of dimension d then so is r ts this result is used to study how closely an artinian ring can be approximated by a gorenstein ring mapping onto it when t is regular it is shown that r ts almost never is a complete intersection ring the proof uses a presentation of the cohomology algebra extr ks k k as an amalgam of the algebras extr k k and ext s k k over isomorphic polynomial subalgebras generated by one element of degree 2

generalized linear models with unknown link functions function by incorporating it as an unknown in the model since the link function is usually taken to be strictly increasing by a strictly increasing transformation of its range to the unit interval we can model it as a strictly increasing cumulative distribution function the transformation results in a domain which is 0 1 we model the cumulative distribution function as a mixture of beta cumulative distribution functions noting that the latter family is dense within the collection of all continuous densities on 0 1 for the fitting of the model we take a bayesian approach encouraging vague priors to focus upon the likelihood we discuss choices of such priors as well as the integrability of the resultant posteriors implementation of the bayesian approach is carried out using sampling based methods in particular a tailored metropolis within gibbs algorithm an illustrative example utilising data involving wave damage to cargo ships is provided

an analysis of taguchi s on line process control procedure under a random walk model the assumptions of the on line process control methods presented by taguchi elsayed and hsiang 1989 are examined taguchi s method for obtaining control strategies is evaluated for the random walk case a method for approximating optimal control strategies is presented and compared with results obtained using taguchi s method with a new modification of taguchi s method and with simulation results

on semiparametric transformation cure models a general class of semiparametric transformation cure models is studied for the analysis of survival data with long term survivors it combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence included as special cases are the proportional hazards cure model farewell 1982 kuk chen 1992 sy taylor 2000 peng dear 2000 and the proportional odds cure model generalised estimating equations are proposed for parameter estimation it is shown that the resulting estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to data from a breast cancer study is given to illustrate the methodology

effects of dynamics on the properties of feedback adjustment schemes with dead band bounded adjustment schemes also called dead band schemes are analyzed assuming that delayed elfects of the adjustments occur the disturbance model is allowed to show a deterministic process drift per unit time interval the resulting average adjustment interval and mean squared deviation from target are obtained under this general framework

a bayesian generalized age period cohort power model for cancer projections age period cohort apc models are the state of art in cancer projections assessing past and recent trends and extrapolating mortality or incidence data into the future nordpred is a well established software assuming a poisson distribution for the counts and a log link or power link function with fixed power however its predictive performance is poor for sparse data bayesian models with log link function have been applied but they can lead to extreme estimates in this paper we address criticisms of the aforementioned models by providing bayesian formulations based on a power link and develop a generalized apc power link model which assumes a random rather than fixed power parameter in addition a power model with a fixed power parameter of five was formulated in the bayesian framework the predictive performance of the new models was evaluated on swiss lung cancer mortality data using model based estimates of observed periods results indicated that the generalized apc power link model provides best estimates for male and female lung cancer mortality the gender specific models were further applied to project lung cancer mortality in switzerland during the periods 2009 2013 and 2014 2018 copyright 2014 john wiley sons ltd

forecasting age specific breast cancer mortality using functional data models accurate estimates of future age specific incidence and mortality are critical for allocation of resources to breast cancer control programmes and evaluation of screening programmes the purpose of this study is to apply functional data analysis techniques to model age specific breast cancer mortality time trends and forecast entire age specific mortality functions using a state space approach we use annual unadjusted breast cancer mortality rates in australia from 1921 to 2001 in 5 year age groups 45 to 85 we use functional data analysis techniques where mortality and incidence are modelled as curves with age as a functional covariate varying by time data are smoothed using non parametric smoothing methods then decomposed using principal components analysis to estimate basis functions that represent the functional curve period effects from the fitted coefficients are forecast then multiplied by the basis functions resulting in a forecast mortality curve with prediction intervals to forecast we adopt a state space approach and an automatic modelling framework for selecting among exponential smoothing methods overall breast cancer mortality rates in australia remained relatively stable from 1960 to the late 1990s but have declined over the last few years a set of four basis functions minimized the mean integrated squared forecasting error and account for 99 3 per cent of variation around the mean mortality curve twenty year forecasts suggest a continuing decline but at a slower rate and stabilizing beyond 2010 forecasts show a decline in all age groups with the greatest decline in older women the proposed methods have the potential to incorporate important covariates such as hormone replacement therapy and interventions to represent mammographic screening this would be particularly useful for evaluating the impact of screening on mortality and incidence from breast cancer

permutation tests for joinpoint regression with applications to cancer rates the identification of changes in the recent trend is an important issue in the analysis of cancer mortality and incidence data we apply a joinpoint regression model to describe such continuous changes and use the grid search method to fit the regression function with unknown joinpoints assuming constant variance and uncorrelated errors we find the number of significant joinpoints by performing several permutation tests each of which has a correct significance level asymptotically each p value is found using monte carlo methods and the overall asymptotic significance level is maintained through a bonferroni correction these tests are extended to the situation with non constant variance to handle rates with poisson variation and possibly autocorrelated errors the performance of these tests are studied via simulations and the tests are applied to u s prostate cancer incidence and mortality rates

selection of sampling interval and action limit for discrete feedback adjustment an important problem in process adjustment using feedback is how often to sample the process and when to apply an adjustment schemes designed to minimize the overall cost were developed by box and kramer but unfortunately it is not always easy to assign values to the individual costs required to define such schemes these are the costs of making an adjustment of taking an observation and of being off target in this article charts are provided in which the same schemes are alternatively characterized by the mean squared deviation from target they produce the frequency with which they require observations to be made and the resulting overall length of time between adjustments this characterization allows a particular scheme to be chosen by judging the advantages and disadvantages of alternative options in the light of the special circumstances of the application the schemes arc derived on certain assumptions relating in particular to the model for the disturbance affecting the process an invest

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

prediction of cancer incidence in the nordic countries empirical comparison of different approaches prediction of the future number of cancer cases is of great interest to society the classical approach is to use the age period cohort model for making cancer incidence predictions we made an empirical comparison of different versions of this model using data from cancer registries in the nordic countries for the period 1958 1997 we have applied 15 different methods to 20 sites for each sex in denmark finland norway and sweden median absolute value of the relative difference between observed and predicted numbers of cases for these 160 combinations of site sex and country was calculated the medians varied between 10 4 per cent and 15 3 per cent in predictions 10 years ahead and between 15 1 per cent and 32 0 per cent for 20 year predictions we have four main conclusions i projecting current trends worked better than assuming that future rates are equal to present rates ii the method based on the multiplicative apc model often overestimated the number of cancer cases due to its exponential growth over time but using a power function to level off this growth improved the predictions iii projecting only half of the trend after the first 10 years also gave better long term predictions iv methods that emphasize trends in the last decade seem to perform better than those that include earlier time trends

a spatiotemporal back calculation approach to estimate cancer incidence measures incidence rates are an important population level disease risk measure cancer incidence data in the united states which are collected by disease registries have been spatiotemporally sparse back calculation methods can yield incidence estimates for a spatial domain by solving a convolution equation that relates mortality to incidence through survival estimates we propose a novel back calculation approach that uses spatiotemporal age period cohort apc modeling to estimate incidence for spatial units within a region the method is applied to state specific lung cancer data in the united states for males ages 30 to 84 in years 1975 2004 seer data are used to model cancer progression from incidence to mortality along three timescales apc and across four regions using mortality data from national vital statistics system incidence is back calculated for unique birth cohorts in 49 states a conditionally autoregressive model with cubic splines for temporal effects is used to smooth back calculated estimates bayesian estimates of model parameters are obtained using integrated nested laplace approximation results show varying time trends in lung cancer risk across states which may quantify effects of state policies

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

comparison of different approaches to incidence prediction based on simple interpolation techniques the paper compares three different methods for performing disease incidence prediction based on simple interpolation techniques the first method assumes that the age period specific numbers of observed cases follow a poisson distribution and the other two methods assume a normal distribution for the incidence rates the main emphasis of the paper is on assessing the reliability of the three methods for this purpose ex post predictions produced by each method are checked for different cancer sites using data from the cancer control region of turku in finland in addition the behaviour of the estimators of predicted expected values and prediction intervals crucial for investigation of the reliability of prediction are assessed using a simulation study the prediction method making use of the poisson assumption appeared to be the most reliable of the three approaches the simulation study found that the estimator of the length of the prediction interval produced by this method has the smallest coverage error and is the most precise

performance of discrete feedback adjustment schemes with dead band under stationary versus nonstationary stochastic disturbance discrete dead band adjustment schemes are often analyzed assuming that the disturbance may be approximately represented by a nonstationary integrated moving average ima model sometimes however stationary autoregressive moving average arma models have been used for the same purpose this article shows a that the ima model leads to a much easier analysis b that almost exactly the same average adjustment intervals aai s and mean squared deviations msd s are obtained under both disturbance models in the region of interest of the action limits c that for wider action limits the arma disturbance overestimates the aa1 and underestimates the msd with respect to the results provided by the ima disturbance and d that the ima disturbance model is robust against model misspecification but the arma model is not

uncertainty of aids incubation time and its effects on back calculation estimates incubation time is the period from the onset of hiv infection to aids the distribution of the incubation time is one of the main parameters of the back calculation method for the estimation of incidence of hiv infection because of the long and variable incubation time the assessment of its distribution is uncertain and this uncertainty spreads through the back calculation method and affects the estimation of the precision of incidence of hiv infection we propose a method to investigate the sensitivity of the estimates to variations of the incubation times with particular regard to the covariate age in the modelling of the incubation period making use of the parametric bootstrap an application to the hiv epidemic in italy is presented the amplification of the uncertainty of the hiv incidence estimates resulting from the implementation of our proposed method tends to concentrate around the earlier periods of the epidemic corresponding to the right tail of the incubation time distribution which is very sensitive to small perturbations

a hierarchical bayesian approach to age specific back calculation of cancer incidence rates we propose a bayesian hierarchical model to estimate age specific cancer incidence per year from age specific cancer mortality the model is based upon the empirical bayesian approach of liao and brookmeyer 1995 and extends that model by consideration of the dependence on age the incident cases per year are considered as observations from a discrete time stochastic process following an autoregressive structure within a poisson regression model the model assumes that the survival probability among those with cancer is known we have investigated the sensitivity of the model to the choice of this distribution and have found that this is the most sensitive part of the model by comparison the predictions of the model are relatively robust to changes in other key areas such as the number of years an incident case contributes before death assumptions about parameter equality for identification and the initial prior distributions the proposed methodology has been investigated using lung cancer mortality data from scotland parameter estimates were obtained through markov chain monte carlo methods implemented using bugs

a simple method for studying run length distribution of exponentially weighted moving average charts a numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average ewma charts both average run lengths arl s and standard deviations of run lengths sdrl s are presented for the twosided ewma chart assuming normal observations along with an example illustrating how to design such a chart the procedure given extends easily to many nonnormal cases and to one sided versions of the ewma chart