Bayesian borrowing from historical control data in a vaccine efficacy trial

In the context of vaccine efficacy trial where the incidence rate is very low and a very large sample size is usually expected, incorporating historical data into a new trial is extremely attractive to reduce sample size and increase estimation precision. Nevertheless, for some infectious diseases, seasonal change in incidence rates poses a huge challenge in borrowing historical data and a critical question is how to properly take advantage of historical data borrowing with acceptable tolerance to between-trials heterogeneity commonly from seasonal disease transmission. In this article, we extend a probability-based power prior which determines the amount of information to be borrowed based on the agreement between the historical and current data, to make it applicable for either a single or multiple historical trials available, with constraint on the amount of historical information to be borrowed. Simulations are conducted to compare the performance of the proposed method with other methods including modified power prior (MPP), meta-analytic-predictive (MAP) prior and the commensurate prior methods. Furthermore, we illustrate the application of the proposed method for trial design in a practical setting.     

Algebraic exact inference for rater agreement models

In recent years, a method for sampling from conditional distributions for categorical data has been presented by Diaconis and Sturmfels. Their algorithm is based on the algebraic theory of toric ideals which are used to create so called “Markov Bases”. The Diaconis-Sturmfels algorithm leads to a non-asymptotic Monte Carlo Markov Chain algorithm for exact inference on some classes of models, such as log-linear models. In this paper we apply the Diaconis-Sturmfels algorithm to a set of models arising from the rater agreement problem with special attention to the multi-rater case. The relevant Markov bases are explicitly computed and some results for simplify the computation are presented. An extended example on a real data set shows the wide applicability of this methodology. Partially supported by MIUR Cofin03 (G. Consonni) and by INdAM projectAlgebraic Statistics.     

Regression modelling of weighted κ by using generalized estimating equations

In many clinical studies more than one observer may be rating a characteristic measured on an ordinal scale. For example, a study may involve a group of physicians rating a feature seen on a pathology specimen or a computer tomography scan. In clinical studies of this kind, the weighted κ coefficient is a popular measure of agreement for ordinally scaled ratings. Our research stems from a study in which the severity of inflammatory skin disease was rated. The investigators wished to determine and evaluate the strength of agreement between a variable number of observers taking into account patient-specific (age and gender) as well as rater-specific (whether board certified in dermatology) characteristics. This suggested modelling κ as a function of these covariates. We propose the use of generalized estimating equations to estimate the weighted κ coefficient. This approach also accommodates unbalanced data which arise when some subjects are not judged by the same set of observers. Currently an estimate of overall κ for a simple unbalanced data set without covariates involving more than two observers is unavailable. In the inflammatory skin disease study none of the covariates were significantly associated with κ, thus enabling the calculation of an overall weighted κ for this unbalanced data set. In the second motivating example (multiple sclerosis), geographic location was significantly associated with κ. In addition we also compared the results of our method with current methods of testing for heterogeneity of weighted κ coefficients across strata (geographic location) that are available for balanced data sets.     

Differential equation model of carbon dioxide emission using functional linear regression

Carbon dioxide is one of the major contributors to Global Warming. In the present study, we develop a differential equation to model the carbon dioxide emission data in the atmosphere using functional linear regression approach. In the proposed method, a differential operator is defined as data smoother and we use the penalized least square fitting criteria to smooth the data. The profile error sum of squares is optimized to estimate the differential operators using functional regression. The solution of the developed differential equation estimates and predicts the rate of change of carbon dioxide in the atmosphere at a particular time. We apply the proposed model to fit the emission of carbon dioxide data in the continental United States. Numerical simulations of a number of test cases depict a satisfactory agreement with real data.     

Temporal disaggregation and restricted forecasting of multiple population time series

This article presents some applications of time-series procedures to solve two typical problems that arise when analyzing demographic information in developing countries: (1) unavailability of annual time series of population growth rates (PGRs) and their corresponding population time series and (2) inappropriately defined population growth goals in official population programs. These problems are considered as situations that require combining information of population time series. Firstly, we suggest the use of temporal disaggregation techniques to combine census data with vital statistics information in order to estimate annual PGRs. Secondly, we apply multiple restricted forecasting to combine the official targets on future PGRs with the disaggregated series. Then, we propose a mechanism to evaluate the compatibility of the demographic goals with the annual data. We apply the aforementioned procedures to data of the Mexico City Metropolitan Zone divided by concentric rings and conclude that the targets established in the official program are not feasible. Hence, we derive future PGRs that are both in line with the official targets and with the historical demographic behavior. We conclude that growth population programs should be based on this kind of analysis to be supported empirically. So, through specialized multivariate time-series techniques, we propose to obtain first an optimal estimate of a disaggregate vector of population time series and then, produce restricted forecasts in agreement with some data-based population policies here derived.     

Comparing the methods of measuring multi-rater agreement on an ordinal rating scale: a simulation study with an application to real data

Agreement among raters is an important issue in medicine, as well as in education and psychology. The agreement among two raters on a nominal or ordinal rating scale has been investigated in many articles. The multi-rater case with normally distributed ratings has also been explored at length. However, there is a lack of research on multiple raters using an ordinal rating scale. In this simulation study, several methods were compared with analyze rater agreement. The special case that was focused on was the multi-rater case using a bounded ordinal rating scale. The proposed methods for agreement were compared within different settings. Three main ordinal data simulation settings were used (normal, skewed and shifted data). In addition, the proposed methods were applied to a real data set from dermatology. The simulation results showed that the Kendall's W and mean gamma highly overestimated the agreement in data sets with shifts in data. ICC₄ for bounded data should be avoided in agreement studies with rating scales<5, where this method highly overestimated the simulated agreement. The difference in bias for all methods under study, except the mean gamma and Kendall's W, decreased as the rating scale increased. The bias of ICC₃ was consistent and small for nearly all simulation settings except the low agreement setting in the shifted data set. Researchers should be careful in selecting agreement methods, especially if shifts in ratings between raters exist and may apply more than one method before any conclusions are made.     

A simple method for estimating a regression model for κ between a pair of raters

Agreement studies commonly occur in medical research, for example, in the review of X-rays by radiologists, blood tests by a panel of pathologists and the evaluation of psychopathology by a panel of raters. In these studies, often two observers rate the same subject for some characteristic with a discrete number of levels. The κ-coefficient is a popular measure of agreement between the two raters. The κ-coefficient may depend on covariates, i.e. characteristics of the raters and/or the subjects being rated. Our research was motivated by two agreement problems. The first is a study of agreement between a pastor and a co-ordinator of Christian education on whether they feel that the congregation puts enough emphasis on encouraging members to work for social justice (yes versus no). We wish to model the κ-coefficient as a function of covariates such as political orientation (liberal versus conservative) of the pastor and co-ordinator. The second example is a spousal education study, in which we wish to model the κ-coefficient as a function of covariates such as the highest degree of the father of the wife and the father of the husband. We propose a simple method to estimate the regression model for the κ-coefficient, which consists of two logistic (or multinomial logistic) regressions and one linear regression for binary data. The estimates can be easily obtained in any generalized linear model software program.     

Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis–Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.     

The iterative proportional fitting algorithm for adjusted agreement in a non‐inferiority diagnostic clinical trial

In this paper, we describe a method of comparing agreement between two diagnostic contingency tables after adjustment to more clinically relevant marginal distributions using the iterative proportional fitting algorithm. When the categories of a contingency table represent mild, moderate, and severe outcomes, the majority of patients often are in the mild category. Because it is often of more interest to evaluate agreement when patients are uniformly distributed among categories, we present the primary results of two clinical trials with adjustment to this structure. We also describe the relationship between the sponsor's pre‐specified agreement measure for the observed contingency table and kappa for the adjusted table; and by either criterion, we then show that the agreement of the new diagnostic tool with the standard diagnostic tool is comparably non‐inferior to the agreement of the standard diagnostic tool with itself. Copyright © 2014 John Wiley & Sons, Ltd.     

Algorithms for Point Processes Analysis

A time point process can be defined either by the statistical properties of the time intervals between successive points or by those of the number of points in arbitrary time intervals. There are mathematical expressions to link up these two points of view, but they are in many cases too complicated to be used in practice. In this article, we present an algorithmic procedure to obtain the number of points of a stationary point process recorded in some time intervals by processing the values of the distances between successive points. We present some results concerning the statistical analysis of these numbers of points and when analytical calculations are possible the experimental results obtained with our algorithms are in excellent agreement with those predicted by the theory. Some properties of point processes in which theoretical calculations are almost impossible are also presented.     

Homogeneity test for functional data

In the context of functional data analysis, we propose new sample tests for homogeneity. Based on some well-known depth measures, we construct four different statistics in order to measure distance between the two samples. A simulation study is performed to check the efficiency of the tests when confronted with shape and magnitude perturbation. Finally, we apply these tools to measure the homogeneity in some samples of real data, and we obtain good results using this new method.     

False discovery rates for large-scale model checking under certain dependence

In many scientific fields, it is interesting and important to determine whether an observed data stream comes from a prespecified model or not, particularly when the number of data streams is of large scale, where multiple hypotheses testing is necessary. In this article, we consider large-scale model checking under certain dependence among different data streams observed at the same time. We propose a false discovery rate (FDR) control procedure to check those unusual data streams. Specifically, we derive an approximation of false discovery and construct a point estimate of FDR. Theoretical results show that, under some mild assumptions, our proposed estimate of FDR is simultaneously conservatively consistent with the true FDR, and hence it is an asymptotically strong control procedure. Simulation comparisons with some competing procedures show that our proposed FDR procedure behaves better in general settings. Application of our proposed FDR procedure is illustrated by the StarPlus fMRI data.     

Bayesian analysis of multivariate threshold autoregressive models with missing data

In some fields, we are forced to work with missing data in multivariate time series. Unfortunately, the data analysis in this context cannot be carried out in the same way as in the case of complete data. To deal with this problem, a Bayesian analysis of multivariate threshold autoregressive models with exogenous inputs and missing data is carried out. In this paper, Markov chain Monte Carlo methods are used to obtain samples from the involved posterior distributions, including threshold values and missing data. In order to identify autoregressive orders, we adapt the Bayesian variable selection method in this class of multivariate process. The number of regimes is estimated using marginal likelihood or product parameter-space strategies.     

Default Bayesian goodness-of-fit tests for the skew-normal model

In this paper we propose a series of goodness-of-fit tests for the family of skew-normal models when all parameters are unknown. As the null distributions of the considered test statistics depend only on asymmetry parameter, we used a default and proper prior on skewness parameter leading to the prior predictive p-value advocated by G. Box. Goodness-of-fit tests, here proposed, depend only on sample size and exhibit full agreement between nominal and actual size. They also have good power against local alternative models which also account for asymmetry in the data.     

TESTING THE AGREEMENT OF TWO QUANTITATIVE ASSAYS IN INDIVIDUAL MEANS

ABSTRACT

Existing approaches for the statistical evaluation of the agreement of two quantitative assays in terms of individual means are either based on a linear model and some stringent assumptions or comparisons of averages of individual means. Furthermore, the related statistical tests for some of these approaches are not valid in the sense that the sizes of these tests are not exactly the same as the nominal size even asymptotically. In this paper we propose a new method, which produces exact statistical tests that are easy to compute. When independent replicates are available, the proposed method requires very little or no assumption on the individual error variances. Simulation results show that the proposed tests perform better than some existing tests. Some examples are presented for illustration.     

Empirical likelihood inference for general transformation models with right censored data

In this work, we consider empirical likelihood inference for general transformation models with right censored data. The models are a class of flexible semiparametric survival models and include many popular survival models as their special cases. Based on the marginal likelihood function, we define an empirical likelihood ratio statistic. Under some regularity conditions, we show that the empirical likelihood ratio statistic asymptotically follows a standard chi-squared distribution. Through some simulation studies and a real data application, we show that our proposed procedure can work fairly well even for relatively small sample size and high censoring.     

Unbiased estimation of income inequality

In a previous paper Gastwirth shows that a broad family of measures of inequality can be accurately estimated when the tax data are known in groups (more precisely, when we know the number of returns in each of several class intervals and their corresponding average income). In the present paper we show that some measures of the preceding family can be unbiasedly estimated when the tax data are individually known for a sample from the population. Specifically, we construct unbiased estimators of a particular measure of inequality in the samplings with and without replacement, and in the stratified samplings with and without replacement.     

Detection of concordance for extreme ranks

When analysing ranking data from one or more groups of judges one may wish to allow for the possibility that the judges have paid more attention to the allocation of the extreme ranks, rather than to the intermediate ranks. In some cases they may have only worried about assigning the top ranks (1 and 2, say) while randomly allocating the remaining ones.

In another context, the analystmay wish to only take account of the agreement among judges with respect to extreme ranks (top or bottom, or both),

In such situations an analysis of concordance within, and between groups, if appropriate, should be able to deal with extreme ranks specifically. We propose a data analyticapproach, related to an analysis of diversity,which actyally permits an analysis of concordance for each rank separately.     

Bayesian univariate space-time hierarchical model for mapping pollutant concentrations in the municipal area of Taranto

An analysis of air quality data is provided for the municipal area of Taranto (Italy) characterized by high environmental risks as decreed by the Italian government in the 1990s. In the context of an agreement between Dipartimento di Scienze Statistiche—Università degli Studi di Bari and the local regional environmental protection agency air quality, data were provided concerning six monitoring stations and covering years from 2005 to 2007. In this paper we analyze the daily concentrations of three pollutants highly relevant in such an industrial area, namely SO₂, NO₂ and PM₁₀, with the aim of reconstructing daily pollutants concentration surfaces for the town area. Taking into account the large amount of sparse missing data and the non normality affecting pollutants’ concentrations, we propose a full Bayesian separable space-time hierarchical model for each pollutant concentration series. The proposed model allows to embed missing data imputation and prediction of pollutant concentration. We critically discuss the results, highlighting advantages and disadvantages of the proposed methodology.