Search

Joinpoint regression can model trends in time-specific estimates from aggregated data. These methods have been developed mainly for nonsurvey data such as cancer registry data assuming that the time-specific estimates are uncorrelated from time point to time point. This independence assumption can be violated for trends in time-specific estimates from complex survey samples due to using the same primary sampling units across time and, therefore, the full variance–covariance matrix of the time-specific estimates should be incorporated into the regression model fitting. This article extends these joinpoint methods for analyzing complex survey data within the National Cancer Institute’s Joinpoint software and empirically compares the extended method to existing methods for analyses of time trends in three surveys.

Selecting the number of change points in segmented line regression is an important problem in trend analysis, and there have been various approaches proposed in the literature. We first study the empirical properties of several model selection procedures and propose a new method based on two Schwarz type criteria, a classical Bayes Information Criterion (BIC) and the one with a harsher penalty than BIC ( [Image: see text] ). The proposed rule is designed to use the former when effect sizes are small and the latter when the effect sizes are large and employs the partial [Image: see text] to determine the weight between BIC and [Image: see text] . The proposed method is computationally much more efficient than the permutation test procedure that has been the default method of Joinpoint software developed for cancer trend analysis, and its satisfactory performance is observed in our simulation study. Simulations indicate that the proposed method performs well in keeping the probability of correct selection at least as large as that of [Image: see text] , whose performance is comparable to that of the permutation test procedure, and improves [Image: see text] when it performs worse than [Image: see text] The proposed method is applied to the U.S. prostate cancer incidence and mortality rates.

Since its release of Version 1.0 in 1998, Joinpoint software developed for cancer trend analysis by a team at the US National Cancer Institute has received a considerable attention in the trend analysis community and it became one of most widely used software for trend analysis. The paper published in Statistics in Medicine in 2000 (a previous study) describes the permutation test procedure to select the number of joinpoints, and Joinpoint Version 1.0 implemented the permutation procedure as the default model selection method and employed parametric methods for the asymptotic inference of the model parameters. Since then, various updates and extensions have been made in Joinpoint software. In this paper, we review basic features of Joinpoint, summarize important updates of Joinpoint software since its first release in 1998, and provide more information on two major enhancements. More specifically, these enhancements overcome prior limitations in both the accuracy and computational efficiency of previously used methods. The enhancements include: (i) data driven model selection methods which are generally more accurate under a broad range of data settings and more computationally efficient than the permutation test and (ii) the use of the empirical quantile method for construction of confidence intervals for the slope parameters and the location of the joinpoints, which generally provides more accurate coverage than the prior parametric methods used. We show the impact of these changes in cancer trend analysis published by the US National Cancer Institute.

This paper studies asymptotic properties of the estimators of the regression coefficients in segmented line regression, focusing on the multi-phase regression model with the continuity constraint a...

This paper considers an improved confidence interval for the average annual percent change in trend analysis, which is based on a weighted average of the regression slopes in the segmented line regression model with unknown change points. The performance of the improved confidence interval proposed by Muggeo is examined for various distribution settings, and two new methods are proposed for further improvement. The first method is practically equivalent to the one proposed by Muggeo, but its construction is simpler, and it is modified to use the t-distribution instead of the standard normal distribution. The second method is based on the empirical distribution of the residuals and the resampling using a uniform random sample, and its satisfactory performance is indicated by a simulation study. Copyright © 2017 John Wiley & Sons, Ltd.

Analysis of trends in health data collected over time can be affected by instantaneous changes in coding that cause sudden increases/decreases, or “jumps,” in data. Despite these sudden changes, the underlying continuous trends can present valuable information related to the changing risk profile of the population, the introduction of screening, new diagnostic technologies, or other causes. The joinpoint model is a well-established methodology for modeling trends over time using connected linear segments, usually on a logarithmic scale. Joinpoint models that ignore data jumps due to coding changes may produce biased estimates of trends. In this article, we introduce methods to incorporate a sudden discontinuous jump in an otherwise continuous joinpoint model. The size of the jump is either estimated directly (the Joinpoint-Jump model) or estimated using supplementary data (the Joinpoint-Comparability Ratio model). Examples using ICD-9/ICD-10 cause of death coding changes, and coding changes in the staging of cancer illustrate the use of these models.

The Schwarz criterion or Bayes Information Criterion (BIC) is often used to select a model dimension, and some variations of the BIC have been proposed in the context of change-point problems. In this paper, we consider a segmented line regression model with an unknown number of change-points and study asymptotic properties of Schwarz type criteria in selecting the number of change-points. Noticing the overestimating tendency of the traditional BIC observed in some empirical studies and being motivated by asymptotic behavior of the modified BIC proposed by Zhang and Siegmund (2007), we consider a variation of the Schwarz type criterion that applies a harsher penalty equivalent to the model with one additional unknown parameter per segment. For the segmented line regression model without the continuity constraint, we prove the consistency of the number of change-points selected by the criterion with such type of a modification and summarize the simulation results that support the consistency. Further simulations are conducted for the model with the continuity constraint, and we empirically observe that the asymptotic behavior of this modified version of BIC is comparable to that of the criterion proposed by Liu, Wu, and Zidek (1997).

BACKGROUND. The current study was undertaken to evaluate the spatiotemporal projection models applied by the American Cancer Society to predict the number of new cancer cases. METHODS. Adaptations of a model that has been used since 2007 were evaluated. Modeling is conducted in 3 steps. In step I, ecologic predictors of spatiotemporal variation are used to estimate age-specific incidence counts for every county in the country, providing an estimate even in those areas that are missing data for specific years. Step II adjusts the step I estimates for reporting delays. In step III, the delay-adjusted predictions are projected 4 years ahead to the current calendar year. Adaptations of the original model include updating covariates and evaluating alternative projection methods. Residual analysis and evaluation of 5 temporal projection methods were conducted. RESULTS. The differences between the spatiotemporal model-estimated case counts and the observed case counts for 2007 were < 1%. After delays in reporting of cases were considered, the difference was 2.5% for women and 3.3% for men. Residual analysis indicated no significant pattern that suggested the need for additional covariates. The vector autoregressive model was identified as the best temporal projection method. CONCLUSIONS. The current spatiotemporal prediction model is adequate to provide reasonable estimates of case counts. To project the estimated case counts ahead 4 years, the vector autoregressive model is recommended to be the best temporal projection method for producing estimates closest to the observed case counts. Cancer 2012;118:1100–9. V C 2012 American Cancer Society.

A segmented line regression model has been used to describe changes in cancer incidence and mortality trends [Kim, H.-J., Fay, M.P., Feuer, E.J. and Midthune, D.N., 2000, Permutation tests for joinpoint regression with applications to cancer rates. Statistics in Medicine, 19, 335–351. Kim, H.-J., Fay, M.P., Yu, B., Barrett., M.J. and Feuer, E.J., 2004, Comparability of segmented line regression models. Biometrics, 60, 1005–1014.]. The least squares fit can be obtained by using either the grid search method proposed by Lerman [Lerman, P.M., 1980, Fitting segmented regression models by grid search. Applied Statistics, 29, 77–84.] which is implemented in Joinpoint 3.0 available at http://srab.cancer.gov/joinpoint/index.html, or by using the continuous fitting algorithm proposed by Hudson [Hudson, D.J., 1966, Fitting segmented curves whose join points have to be estimated. Journal of the American Statistical Association, 61, 1097–1129.] which will be implemented in the next version of Joinpoint software. Foll...

This article proposes a new test to detect interactions in replicated two-way ANOVA models, more powerful than the classical F -test and more general than the test of Terbeck and Davies (1998, Annals of Statistics 26, 1279-1305) developed for the case with unconditionally identifiable interaction pattern. We use the parameterization without the conventional restrictions on the interaction terms and base our test on the maximum of the standardized disturbance estimates. We show that our test is unbiased and consistent, and discuss how to estimate the p -value of the test. In a 3 x 3 case, which is our main focus in this article, the exact p -value can be computed by using four-dimensional integrations. For a general I x J case which requires an (I - 1) x (J - 1) dimensional integration for a numerical evaluation of the exact p -value, we propose to use an improved Bonferroni inequality to estimate an upperbound of the p -value and simulations indicate a reasonable accuracy of the upperbound. Via simulations, we show that our test is more powerful than the classical F -test and also that it can deal with both situations: unconditionally identifiable and non-unconditionally identifiable cases. An application to genetic data is presented in which the new test is significant, while the classical F -test failed to detect interactions.

When designing programs or software for the implementation of Monte Carlo (MC) hypothesis tests, we can save computation time by using sequential stopping boundaries. Such boundaries imply stopping resampling after relatively few replications if the early replications indicate a very large or very small p-value. We study a truncated sequential probability ratio test (SPRT) boundary and provide a tractable algorithm to implement it. We review two properties desired of any MC p-value, the validity of the p-value and a small resampling risk, where resampling risk is the probability that the accept/reject decision will be different than the decision from complete enumeration. We show how the algorithm can be used to calculate a valid p-value and confidence intervals for any truncated SPRT boundary. We show that a class of SPRT boundaries is minimax with respect to resampling risk and recommend a truncated version of boundaries in that class by comparing their resampling risk (RR) to the RR of fixed boundaries with the same maximum resample size. We study the lack of validity of some simple estimators of p-values and offer a new simple valid p-value for the recommended truncated SPRT boundary. We explore the use of these methods in a practical example and provide the MChtest R package to perform the methods.

In this paper, we propose methods to cluster groups of two-dimensional data whose mean functions are piecewise linear into several clusters with common characteristics such as the same slopes. To fit segmented line regression models with common features for each possible cluster, we use a restricted least squares method. In implementing the restricted least squares method, we estimate the maximum number of segments in each cluster by using both the permutation test method and the Bayes information criterion method and then propose to use the Bayes information criterion to determine the number of clusters. For a more effective implementation of the clustering algorithm, we propose a measure of the minimum distance worth detecting and illustrate its use in two examples. We summarize simulation results to study properties of the proposed methods and also prove the consistency of the cluster grouping estimated with a given number of clusters. The presentation and examples in this paper focus on the segmented line regression model with the ordered values of the independent variable, which has been the model of interest in cancer trend analysis, but the proposed method can be applied to a general model with design points either ordered or unordered.

During sepsis, catabolism of proteins and associated changes in plasma amino acids occur. Tryptophan and tyrosine, and their derivatives serotonin (5-HT) and dopamine (DA), influence hypothalamic feeding-related areas and are associated with the onset of anorexia. We hypothesized that anorexia of sepsis is associated with changes in serotonin and dopamine in the ventromedial nucleus (VMN) of the hypothalamus. The aim of this study was to test our hypothesis by measuring intra-VMN changes of these two neurotransmitters at the onset of anorexia during sepsis. Fischer 344 male rats had an intracerebral guide cannula stereotaxically implanted into the VMN. Ten days later, in awake, overnight-food-deprived rats, a microdialysis probe was inserted through the in situ VMN cannula. Two hours thereafter, serial baseline serotonin and dopamine concentrations were measured. Then cecal ligation and puncture to induce sepsis or a control laparotomy was performed under isoflurane anesthesia. VMN microdialysis samples were serially collected every 30 min for 8 h after the surgical procedure to determine 5-HT and DA changes in response to sepsis. During the hypermetabolic response to sepsis, a strong association occurred between anorexia and a significant reduction of VMN dopamine concentration (P < 0.05; constant rate of dopamine decrease in the Study group of 0.99 pg per 2 h); no changes occurred in 5-HT in association with anorexia of sepsis. Six hours after operation, a single meal was offered for 20 min to assess the response of neurotransmitters to food ingestion. Food intake was minimal in anorectic septic rats (mean size of the after food-deprived meal in the Septic group was 0.03 ± 0.01 g, that of the Control group was 1.27 ± 0.14 g; P = 0.0001), while Control rats demonstrated anticipated changes in neurotransmitters in response to eating. We conclude that the onset of anorexia in septic rats is associated with a reduction in VMN dopamine.

With progression of tumor growth, rats demonstrate anorexia and reduced food intake, a function of meal number and meal size. Tumor necrosis factor-α (TNF-α), a recognized anorectic agent, reacts with two different receptors (type I: 55 kDa; type II: 75 kDa). We used a dimeric, pegylated 55-kDa TNF receptor construct to test its effects on food intake, meal number, and meal size, which were continuously measured with a rat eater meter in 16 Fischer 344 male rats injected with 106 viable methylcholanthrene cells. When anorexia developed, rats received a subcutaneous injection of either 0.25 mg/kg body wt of soluble TNF receptor construct (study) or vehicle (tumor-bearing control). Before TNF inhibitor injection, no differences were observed in food intake, meal number, or meal size between the two groups. After the TNF inhibitor injection, study vs. control rats significantly improved food intake as a result of an increase in meal number and meal size. Rats also showed a significant improvement in body weight. These data suggest that TNF-α, in addition to other cytokines, contributes to the anorexia of tumor growth, probably mediated via the hypothalamus.

Background: Tobacco smoking reduces appetite and body weight. Cessation of smoking leads to hyperphagia and weight gain. Food intake is a function of meal number (MN) and meal size (MZ) (ie, Food intake = MN × MZ). The effect of nicotine on these feeding components and their relationships to dopamine and serotonin in the lateral hypothalamic area (LHA) were determined. Methods: In Fischer-344 rats the effect of 7 days of systemic nicotine infusion on the feeding patterns was measured by rat eater meter and changes in serotonin (5HT) and dopamine (DA) in the LHA were measured by in vivo microdialysis. Results: Nicotine infusion caused hypophagia through a significant decrease in MN with a smaller decrease in MZ, resulting in a body weight reduction. 5HT and DA concomitantly increased in LHA. Stopping nicotine resulted in hyperphagia by a significant increase in MZ. Body weight normalized. 5HT and DA in LHA decreased after nicotine was stopped. Conclusion: Nicotine's hypophagic effect was associated with increased 5HT and DA in LHA, whereas hyperphagia after nicotine cessation was accompanied by decreased concentrations of the neurotransmitters. These findings suggest that nicotine affects appetite regulation, in part by modulation of LHA-DA and 5HT. (Surgery 1999;126:255-63.)

Background. Normally the lateral hypothalamic area (LHA) and the ventromedial nucleus (VMN) interact to regulate food intake (FI), the product of meal number (MN) and meal size (MZ), by changes in neurotransmitters, mainly dopamine and serotonin. Change in LHA dopamine influences meal size; while in VMN, decreasing dopamine and increasing serotonin levels influence meal number. Whether this situation exists in early cancer anorexia was tested in a series of studies to examine the role of the hypothalamus in the pathogenesis of early cancer anorexia. Materials and Methods. In experiment 1, male Fischer tumor-bearing (TB) rats and weight-matched controls had FI, MN, and MZ measured continuously via a computerized rat eater meter. At onset of anorexia, feeding patterns were measured. In experiment 2, the VMN was temporarily blocked with 0.32 μg of colchicine in TB rats, while TB controls had an equal volume of intra-VMN saline, and changes in feeding patterns were measured. In experiment 3, changes in VMN dopamine and serotonin were measured via microdialysis at anorexia and after tumor resection. Results. In experiment 1, with the onset of anorexia, food intake decreased significantly in TB rats, initially by a decrease in MN and then by a decrease in both MN and MZ. No change occurred in controls, suggesting that VMN versus LHA played a more significant role in mediation of cancer anorexia. In experiment 2, following VMN block, FI increased significantly in anorectic TB rats, achieved by an almost exclusive increase in MN with minimal change in MZ, thus supporting the role of the VMN in anorexia. In experiment 3, at the onset of anorexia, FI decreased significantly in TB rats versus controls. TB rats had a significant increase in VMN serotonin and a significant decrease in VMN dopamine. After tumor resection, food intake improved and high levels of serotonin normalized with no change in dopamine. Conclusion. Serotoninergic and dopaminergic systems are involved in the etiology of cancer anorexia. The changes in food intake are mediated via the VMN by a decrease in meal number.

The ability of accurately predicting reliability for products is an invaluable asset for any manufacturing company. The United Technologies Carrier developed such a system based on Weibull distribution. However, predicting accurate reliability requires experienced person's special knowledge. Two expert systems were developed to capture such knowledge. The use of Weibull plots was critical in interpreting the results of failure rates. This interpretation process was imitated by employing multi-layer feed-forward neural networks. The expert systems and neural networks are integrated with the already existing Early Warning System (EWS) and databases. The resulting system, Automatic Early Warning System (AEWS), is currently deployed in United Technologies Carrier and has led to a significant boost in productivity by at least 8 times in terms of process time.

Our concern in this paper is a detection of a change in regression coefficients of a linear model. First, we examine the null and alternative distributions of the likelihood ratio statistic and study its asymptotic behavior. We then propose analytic approximations for the p-value and power of the test and perform simulations to assess the accuracy of the analytic approximations. Also, the test based on the cusum of the recursive residuals is discussed and its power is compared with that of the likelihood ratio test. We conclude that the likelihood ratio yest is much more powerful than the cusum test of Brown et al. (1975, J. Roy. Statist. Soc. Ser. B37, 149-192) and propose a test based on the backward cusum to improve the power of the cusum test.

In clinical trials we often need a sequential testing procedure for a difference between two medical treatments whose effectiveness is influenced by prognostoc factors. This article considers a repeated significance test on regression coefficients in a linear regression model. We first derive approximations for the overall significance level and power of the test and compare our test with a fixed sample test. We then discuss applications of these results to the sequential comparison of two treatments and also discuss the effect of allocation rules on the behavior of the test statistics.

Our concern in this paper is a group sequential test design for which the sample sizes between interim analyses are not identical. First, we consider a repeated significance test for comparing two treatments in a clinical trial, and study asymptotic properties of the test statistic. Using the arguments developed by Siegmund (1985, Chapters 8 and 9), we then obtain approximations for the overall significance level of the test and for the error level at each interim analysis. Simulation studies are performed to assess the accuracy of the approximations and the robustness of the approximations are examined using numerical examples.

This article examines the robustness of the likelihood ratio tests for a change point in simple linear regression. We first summarize the normal theory of Kim and Siegmund, who have considered the likelihood ratio tests for no change in the regression coefficients versus the alternatives with a change in the intercept alone and with a change in the intercept and slope. We then discuss the robustness of these tests. Using the convergence theory of stochastic processes, we show that the test statistics converge to the same limiting distributions regardless of the underlying distribution. We perform simulations to assess the distributional insensitivity of the test statistics to a Weibull, a lognormal, and a contaminated normal distribution in two different cases: fixed and random independent variables. Numerical examples illustrate that the test has a correct size and retains its power when the distribution is nonnormal. We also study the effects of the independent variable's configuration with the...

Likelihood ratio tests for a change in simple linear regression with unequal variances are studied. We first derive the likelihood ratio statistics assuming nonhomogeneous error variance. (We call such statistics the weighted likelihood ratio statistics.) We obtain analytic approximations for the p-values of these weighted tests, and assess the accuracy of the approximations via simulation. Using numerical examples, we also study the robustness to heteroscedasticity of the unweighted likelihood ratio tests considered in Kim and Siegmund (1989).

Sequential designs can be used to save computation time in implementing Monte Carlo hypothesis tests. The motivation is to stop resampling if the early resamples provide enough information on the significance of the p-value of the original Monte Carlo test. In this paper, we consider a sequential design called the B-value design proposed by Lan and Wittes and construct the sequential design bounding the resampling risk, the probability that the accept/reject decision is different from the decision from complete enumeration. For the B-value design whose exact implementation can be done by using the algorithm proposed in Fay, Kim and Hachey, we first compare the expected resample size for different designs with comparable resampling risk. We show that the B-value design has considerable savings in expected resample size compared to a fixed resample or simple curtailed design, and comparable expected resample size to the iterative push out design of Fay and Follmann. The B-value design is more practical than the iterative push out design in that it is tractable even for small values of resampling risk, which was a challenge with the iterative push out design. We also propose an approximate B-value design that can be constructed without using a specially developed software and provides analytic insights on the choice of parameter values in constructing the exact B-value design.

We derive a first order approximation for the probability that a general two-dimensional random walk crosses a circular boundary. Simulations are performed to assess the accuracy of the approximation, and statistical applications are discussed.

Les modeles de regression lineaire segmentes, composes de phases lineaires continues, ont ete appliques pour decrire des changements de tendance de taux. Dans cet article nous proposons une procedurepour comparer deux fonctions de regression lineaires segmentees, afin de tester soit a) si les deux fonctions de regression lineaires segmentees sont identiques ou ii) si les deux fonctions moyennes sont paralleles et admettent des intercepts differents. Une forme generale de la statistique de test est decrite, et on propose alors une procedure par permutation pour estimer la p-value du test. Le test de permutation est compare a un test F approche en terme d'estimation de la p-value, et les performances du test de permutation sont etudiees par simulation. Les tests sont appliques pour comparer les taux de mortalite par cancer du poumon chez les femmes, entre deux regions de recensement, et egalement pour comparer les taux de mortalite par cancer du sein chez la femme entre deux stades.

Background: Cross-sectional analysis was performed to study the trend in weight loss following surgery. Methods: Among 194 patients involved in the study during the period 1990-1995, 86.6% were female and 87.1% were white. Median values for the initial cohort of 194 patients were as follows: age 32.5 years; height 163.8 cm; preoperative weight 122.81 kg. Of these patients 67%, 30%, and 3% of the patients were categorized as morbidly obese, super obese, and obese respectively. They all underwent gastric bypass surgery. Results: Follow-up rates were 67.9% at 1 year, 55.8% at 2 years, 62.8% at 3 years, and 70.0% at 4 years postoperation. Median BMI was reduced from 45.18 to 28.40, and median percentage loss of excess weight was 68.5% after 1 year. After 2, 3, and 4 years, median BMI values were 27.69, 28.63, and 29.40, and median percentages of excess weight loss were 71.18%, 69.28%, and 57.49%, respectively. Although the analysis at 4 years indicates that some patients experience slight weight gain, the increase was not significant and further analysis will be performed when more data points are available. Conclusion: Postoperative weight loss has been satisfactory.

This paper examines the robustness of the likelihood ratio tests for a change-point in simple linear regression. We first summarize the normal theory of Kim and Siegmund (1989) and then study the robustness of the tests to nonnormality and heteroscedasticity.

The original article to which this Correction refers was published in Statistics in Medicine 2000; 19:335–351.

SUMMARY We consider likelihood ratio tests to detect a change-point in simple linear regression (a) when the alternative specifies that only the intercept changes and (b) when the alternative permits the intercept and the slope to change. Approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable. The approximations are compared with simulations in order to assess their accuracy. For the model in which only the intercept is allowed to change, a confidence region for the change-point and an approximate joint confidence region for the change-point, the difference in intercepts, and the slope are obtained by inversion of the appropriate likelihood ratio tests.