Sample size modifications in the interim analyses of an adaptive design can inflate the type 1 error rate, if test statistics and critical boundaries are used in the final analysis as if no modification had been made. While this is already true for designs with an overall change of the sample size in a balanced treatment-control comparison, the inflation can be much larger if in addition a modification of allocation ratios is allowed as well. In this paper, we investigate adaptive designs with several treatment arms compared to a single common control group. Regarding modifications, we consider treatment arm selection as well as modifications of overall sample size and allocation ratios. The inflation is quantified for two approaches: a naive procedure that ignores not only all modifications, but also the multiplicity issue arising from the many-to-one comparison, and a Dunnett procedure that ignores modifications, but adjusts for the initially started multiple treatments. The maximum inflation of the type 1 error rate for such types of design can be calculated by searching for the “worst case” scenarios, that are sample size adaptation rules in the interim analysis that lead to the largest conditional type 1 error rate in any point of the sample space. To show the most extreme inflation, we initially assume unconstrained second stage sample size modifications leading to a large inflation of the type 1 error rate. Furthermore, we investigate the inflation when putting constraints on the second stage sample sizes. It turns out that, for example fixing the sample size of the control group, leads to designs controlling the type 1 error rate.

]]>This is a discussion around the paper “Overview of object oriented data analysis” by J. Steve Marron and Andrés M. Alonso.

]]>This is a discussion of the following paper: “Overview of object oriented data analysis” by J. Steve Marron and Andrés M. Alonso.

]]>The generalized estimating equations (GEEs) method has become quite useful in modeling correlated data. However, diagnostic tools to check that the selected final model fits the data as accurately as possible have not been explored intensively. In this paper, an outlier detection technique is developed based on the use of the “working” score test statistic to test an appropriate mean-shift model in the context of longitudinal studies based on GEEs. Through a simulation study it has been shown that this method correctly singled out the outlier when the data set had a known outlier. The method is applied to a set of data to illustrate the outlier detection procedure in GEEs.

]]>The logrank test is the most popular choice for testing the equality of two survival distributions with time-to-event data. It is based on the comparison of the Nelson–Aalen estimates of the corresponding cumulative hazard functions. The improvements of the logrank test in the literature have been accomplished using weighted logrank tests, with the weight chosen appropriately to maximize power. Notwithstanding, power also depends on the efficiency of the estimation of the cumulative hazard function. The presmoothed estimator has been shown to be more efficient than the Nelson–Aalen estimator under some general assumptions. We introduce a new logrank-type test that, instead of the Nelson–Aalen estimator, is based on its presmoothed counterpart. An extensive simulation study has been conducted to compare the performance of this new test with the classical one. This study shows that the new test has the proper size under the null hypothesis, while improving the power over a wide range of alternatives. The new test is illustrated with several real data examples.

]]>This is a discussion of the paper: ‘Overview of object oriented data analysis’ by J. Steve Marron and Andrés M. Alonso.

]]>This is a discussion of the paper: “Overview of object oriented data analysis” by J. Steve Marron and Andrés M. Alonso.

]]>This is a discussion of the paper “Overview of object oriented data analysis” by J. Steve Marron and Andrés M. Alonso.

]]>This paper presents systematic methods for the detection of influential individuals that affect the log odds (LOD) score curve. We derive general formulas of influence functions for profile likelihoods and introduce them into two standard quantitative trait locus detection methods—the interval mapping method and single marker analysis. Besides influence analysis on specific LOD scores, we also develop influence analysis methods on the shape of the LOD score curves. A simulation-based method is proposed to assess the significance of the influence of the individuals. These methods are shown useful in the influence analysis of a real dataset of an experimental population from an F_{2} mouse cross. By receiver operating characteristic analysis, we confirm that the proposed methods show better performance than existing diagnostics.

This is the reply to the discussion of the two companion articles on the theory and application of “probability estimation with machine learning methods for dichotomous and multicategory outcome” by Kruppa et al. (2014; doi: 10.1002/bimj.201300068 and 10.1002/bimj.201300077). The five discussion papers are Binder (2014; doi: 10.1002/bimj.201300218), Boulesteix and Schmid (2014; doi: 10.1002/bimj.201300226), Shin and Wu (2014; doi: 10.1002/bimj.201300251), Simon (2014; doi: 10.1002/bimj.201300296), and Steyerberg et al. (2014; doi: 10.1002/bimj.201300297).

]]>Diffusion tensor imaging (DTI) is a quantitative magnetic resonance imaging technique that measures the three-dimensional diffusion of water molecules within tissue through the application of multiple diffusion gradients. This technique is rapidly increasing in popularity for studying white matter properties and structural connectivity in the living human brain. One of the major outcomes derived from the DTI process is known as fractional anisotropy, a continuous measure restricted on the interval (0,1). Motivated from a longitudinal DTI study of multiple sclerosis, we use a beta semiparametric-mixed regression model for the neuroimaging data. This work extends the generalized additive model methodology with beta distribution family and random effects. We describe two estimation methods with penalized splines, which are formalized under a Bayesian inferential perspective. The first one is carried out by Markov chain Monte Carlo (MCMC) simulations while the second one uses a relatively new technique called integrated nested Laplace approximation (INLA). Simulations and the neuroimaging data analysis show that the estimates obtained from both approaches are stable and similar, while the INLA method provides an efficient alternative to the computationally expensive MCMC method.

]]>This note is a discussion on the paper “Overview of object oriented data analysis,” by J. Steve Marron and Andrés M. Alonso.

]]>This is a discussion of the following paper: “Overview of object oriented data analysis” by J. Steve Marron and Andrés M. Alonso.

]]>This is a discussion of the paper “Overview of object oriented data analysis” by J. Steve Marron and Andrés M. Alonso.

]]>The area under the receiver operating characteristic (ROC) curve, AUC, is commonly used to assess the ability of a diagnostic test to correctly classify individuals into diseased and nondiseased populations. When there are two diagnostic tests available, it is of interest to evaluate and compare their performances. Based on the difference of two placement values, we propose a two-sample empirical likelihood method for comparing AUCs of two ROC curves. The proposed empirical likelihood ratio statistic converges in distribution to a scaled chi-squared random variable. Simulation results show that the proposed empirical likelihood method has better finite-sample performance than other competitors.

]]>This is a discussion of the following paper: ‘Overview of object oriented data analysis’ by J. Steve Marron and Andrés M. Alonso.

]]>This is a discussion of the following papers: “Probability estimation with machine learning methods for dichotomous and multicategory outcome: Theory” by Jochen Kruppa, Yufeng Liu, Gérard Biau, Michael Kohler, Inke R. König, James D. Malley, and Andreas Ziegler; and “Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications” by Jochen Kruppa, Yufeng Liu, Hans-Christian Diener, Theresa Holste, Christian Weimar, Inke R. König, and Andreas Ziegler.

]]>This is a discussion of the following papers: “Probability estimation with machine learning methods for dichotomous and multicategory outcome: Theory” by Jochen Kruppa, Yufeng Liu, Gérard Biau, Michael Kohler, Inke R. König, James D. Malley, and Andreas Ziegler; and “Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications” by Jochen Kruppa, Yufeng Liu, Hans-Christian Diener, Theresa Holste, Christian Weimar, Inke R. König, and Andreas Ziegler.

]]>I provide a commentary on two papers “Probability estimation with machine learning methods for dichotomous and multicategory outcome: Theory” by Jochen Kruppa, Yufeng Liu, Gérard Biau, Michael Kohler, Inke R. König, James D. Malley, and Andreas Ziegler; and “Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications” by Jochen Kruppa, Yufeng Liu, Hans-Christian Diener, Theresa Holste, Christian Weimar, Inke R. König, and Andreas Ziegler. Those papers provide an up-to-date review of some popular machine learning methods for class probability estimation and compare those methods to logistic regression modeling in real and simulated datasets.

]]>Globalization and increased mobility of individuals enable person-to-person transmitted infectious diseases to spread faster to distant places around the world, making good models for the spread increasingly important. We study the spatiotemporal pattern of spread in the remotely located and sparsely populated region of North Norway in various models with fixed, seasonal, and random effects. The models are applied to influenza A counts using data from positive microbiology laboratory tests as proxy for the underlying disease incidence. Human travel patterns with local air, road, and sea traffic data are incorporated as well as power law approximations thereof, both with quasi-Poisson regression and based on the adjacency structure of the relevant municipalities. We investigate model extensions using information about the proportion of positive laboratory tests, data on immigration from outside North Norway and by connecting population to the movement network. Furthermore, we perform two separate analyses for nonadults and adults as children are an important driver for influenza A. Comparisons of one-step-ahead predictions generally yield better or comparable results using power law approximations.

]]>Current cancer mortality data are available with a delay of roughly three years due to the administrative procedure necessary to create the registries. Therefore, health agencies rely on forecast cancer deaths. In this context, statistical procedures providing mortality/incidence risk predictions for different regions or health areas are very useful. These predictions are essential for defining priorities for cancer prevention and treatment. The main objective of this work is to evaluate the predictive performance of alternative spatio-temporal models for short-term cancer risk/counts prediction in small areas. All the models analyzed here are presented under a general-mixed model framework, providing a unified structure of presentation and facilitating the use of similar tools for computing the prediction mean squared error. Prostate cancer mortality data are used to illustrate the behavior of the different models in Spanish provinces.

]]>Stomach cancer belongs to the most common malignant tumors in Portugal. Main causal factors are age, dietary habits, smoking, and *Helicobacter pylori* infections. As these factors do not only operate on different time dimensions, such as age, period, or birth cohort, but may also vary along space, it is of utmost interest to model temporal and spatial trends jointly. In this paper, we analyze incidence of stomach cancer in Southern Portugal between 1998 and 2006 for females and males jointly using a spatial multivariate age-period-cohort model. Thus, we avoid age aggregation and allow the exploration of heterogeneous time trends between males and females across age, period, birth cohort, and space. Model estimation is performed within a Bayesian setting assuming (gender specific) smoothing priors. Our results show that the posterior expected rate of stomach cancer is decreasing for all counties in Southern Portugal and that males around 70 have a two times higher risk of getting stomach cancer compared with their female counterparts. We further found that, except for some few counties, the spatial influence is almost constant over time and negligible in the southern counties of Southern Portugal.

Breast cancer risk is believed to be associated with several reproductive factors, such as early menarche and late menopause. This study is based on the registries of the first time a woman enters the screening program, and presents a spatio-temporal analysis of the variables age of menarche and age of menopause along with other reproductive and socioeconomic factors. The database was provided by the Portuguese Cancer League (LPCC), a private nonprofit organization dealing with multiple issues related to oncology of which the Breast Cancer Screening Program is one of its main activities. The registry consists of 259,652 records of women who entered the screening program for the first time between 1990 and 2007 (45–69-year age group). Structured Additive Regression (STAR) models were used to explore spatial and temporal correlations with a wide range of covariates. These models are flexible enough to deal with a variety of complex datasets, allowing us to reveal possible relationships among the variables considered in this study. The analysis shows that early menarche occurs in younger women and in municipalities located in the interior of central Portugal. Women living in inland municipalities register later ages for menopause, and those born in central Portugal after 1933 show a decreasing trend in the age of menopause. Younger ages of menarche and late menopause are observed in municipalities with a higher purchasing power index. The analysis performed in this study portrays the time evolution of the age of menarche and age of menopause and their spatial characterization, adding to the identification of factors that could be of the utmost importance in future breast cancer incidence research.

]]>The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space–time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space–time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space–time disease spread. Specifically, it was applied to obtain a space–time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space–time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time.

]]>Over/underdispersed count data arise in many biostatistical practices in which a number of different treatment groups are compared in an experiment. In the analysis of several treatment groups of such count data, a very common statistical inference problem is to test whether these data come from the same population. The usual practice for testing homogeneity of several treatment groups in terms of means and dispersions is first to test the equality of dispersions and then to test the equality of the means based on the result of the test for equality of dispersions. Previous studies reported test procedures for testing the homogeneity of the means of several treatment groups with an assumption of equal or unequal dispersions. This article develops test procedures for testing the validity of the equal or unequal dispersions assumption of several treatment groups in the analysis of over/underdispersed count data. We consider the test based on the maximum likelihood (ML) method using the negative binomial model as well as the three other tests based on the method of moments, extended quasi-likelihood, and double extended quasi-likelihood using the models specified by the first two moments of counts. Monte Carlo simulations are then used to study the comparative behavior of these tests along with the likelihood ratio test in terms of size and power. The simulation results demonstrate that all four statistics hold the nominal level reasonably well in most of the data situations studied here, and the test based on ML shows some edge in power over the other three tests. Finally, applications to biostatistical practices are analyzed.

]]>Generalized estimating equations (GEE) are commonly used for the marginal analysis of correlated data, although the quadratic inference function (QIF) approach is an alternative that is increasing in popularity. This method optimally combines distinct sets of unbiased estimating equations that are based upon a working correlation structure, therefore asymptotically increasing or maintaining estimation efficiency relative to GEE. However, in finite samples, additional estimation variability arises when combining these sets of estimating equations, and therefore the QIF approach is not guaranteed to work as well as GEE. Furthermore, estimation efficiency can be improved for both analysis methods by accurate modeling of the correlation structure. Our goal is to improve parameter estimation, relative to existing methods, by simultaneously selecting a working correlation structure and choosing between GEE and two versions of the QIF approach. To do this, we propose the use of a criterion based upon the trace of the empirical covariance matrix (TECM). To make GEE and both QIF versions directly comparable for any given working correlation structure, the proposed TECM utilizes a penalty to account for the finite-sample variance inflation that can occur with either version of the QIF approach. Via a simulation study and in application to a longitudinal study, we show that penalizing the variance inflation that occurs with the QIF approach is necessary and that the proposed criterion works very well.

]]>This paper presents an efficient algorithm based on the combination of Newton Raphson and Gradient Ascent, for using the fused lasso regression method to construct a genome-based classifier. The characteristic structure of copy number data suggests that feature selection should take genomic location into account for producing more interpretable results for genome-based classifiers. The fused lasso penalty, an extension of the lasso penalty, encourages sparsity of the coefficients and their differences by penalizing the L1-norm for both of them at the same time, thus using genomic location. The major advantage of the algorithm over other existing fused lasso optimization techniques is its ability to predict binomial as well as survival response efficiently. We apply our algorithm to two publicly available datasets in order to predict survival and binary outcomes.

]]>Dose-response studies are performed to investigate the potency of a compound. EC50 is the concentration of the compound that gives half-maximal response. Dose-response data are typically evaluated by using a log-logistic model that includes EC50 as one of the model parameters. Often, more than one experiment is carried out to determine the EC50 value for a compound, requiring summarization of EC50 estimates from a series of experiments. In this context, mixed-effects models are designed to estimate the average behavior of EC50 values over all experiments by considering the variabilities within and among experiments simultaneously. However, fitting nonlinear mixed-effects models is more complicated than in a linear situation, and convergence problems are often encountered. An alternative strategy is the application of a meta-analysis approach, which combines EC50 estimates obtained from separate log-logistic model fitting. These two proposed strategies to summarize EC50 estimates from multiple experiments are compared in a simulation study and real data example. We conclude that the meta-analysis strategy is a simple and robust method to summarize EC50 estimates from multiple experiments, especially suited in the case of a small number of experiments.

]]>The Vaccine Safety Datalink project captures electronic health record data including vaccinations and medically attended adverse events on 8.8 million enrollees annually from participating managed care organizations in the United States. While the automated vaccination data are generally of high quality, a presumptive adverse event based on diagnosis codes in automated health care data may not be true (misclassification). Consequently, analyses using automated health care data can generate false positive results, where an association between the vaccine and outcome is incorrectly identified, as well as false negative findings, where a true association or signal is missed. We developed novel conditional Poisson regression models and fixed effects models that accommodate misclassification of adverse event outcome for self-controlled case series design. We conducted simulation studies to evaluate their performance in signal detection in vaccine safety hypotheses generating (screening) studies. We also reanalyzed four previously identified signals in a recent vaccine safety study using the newly proposed models. Our simulation studies demonstrated that (i) outcome misclassification resulted in both false positive and false negative signals in screening studies; (ii) the newly proposed models reduced both the rates of false positive and false negative signals. In reanalyses of four previously identified signals using the novel statistical models, the incidence rate ratio estimates and statistical significances were similar to those using conventional models and including only medical record review confirmed cases.

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