Modeling sensitivity and specificity with a time-varying reference standard within a longitudinal setting

Diagnostic tests are used in a wide range of behavioral, medical, psychosocial, and healthcare-related research. Test sensitivity and specificity are the most popular measures of accuracy for diagnostic tests. Available methods for analyzing longitudinal study designs assume fixed gold or reference standards and as such do not apply to studies with dynamically changing reference standards, which are especially popular in psychosocial research. In this article, we develop a novel approach to address missing data and other related issues for modeling sensitivity and specificity within such a time-varying reference standard setting. The approach is illustrated with real as well as simulated data.     

Bayesian Analysis of a Queueing System with a Long-Tailed Arrival Process

Internet traffic data is characterized by some unusual statistical properties, in particular, the presence of heavy-tailed variables. A typical model for heavy-tailed distributions is the Pareto distribution although this is not adequate in many cases. In this article, we consider a mixture of two-parameter Pareto distributions as a model for heavy-tailed data and use a Bayesian approach based on the birth-death Markov chain Monte Carlo algorithm to fit this model. We estimate some measures of interest related to the queueing system k-Par/M/1 where k-Par denotes a mixture of k Pareto distributions. Heavy-tailed variables are difficult to model in such queueing systems because of the lack of a simple expression for the Laplace Transform (LT). We use a procedure based on recent LT approximating results for the Pareto/M/1 system. We illustrate our approach with both simulated and real data.     

Post-stratification based direct adjustment approach to a missing data problem in clinical trials

In clinical trials we always expect some missing data. If data are missing completely at random, then missing data can be ignored for the purpose of statistical inference. In most situation, however, ignoring missing data will introduce bias. Adjustment is possible for missing data if the missing mechanism is known, which is rare in real problems. Our approach is to estimate directly the mean outcome of each treatment group in the presence of missing data. To this end, we post-stratify all the subjects by the expected value of outcome (or by a variable predictive of the outcome) so that subjects within a stratum may be considered homogeneous with respect to the expected outcome, and assume that subjects within a stratum are missing at random. We apply this post-stratification approach to a recently concluded clinical trial where a high proportion of data are missing and the missingness depends on the same factors affecting the outcome variable. A simulation study shows that the post-stratification approach reduces the bias substantially compared to the naive approach where only non-missing subjects are analyzed.     

Nonparametric Random Variate Generation Using a Piecewise-Linear Cumulative Distribution Function

The standard approach to solving the interpolation problem for a trace-driven simulation involving a continuous random variable is to construct a piecewise-linear cdf that fills in the gaps between the data values. Some probabilistic properties of this estimator are derived, and three extensions to the standard approach (matching moments, weighted values, and right-censored data) are presented, along with associated random variate generation algorithms. The algorithm is a nonparametric blackbox variate generator requiring only observed data from the user.     

On inference for Kendall's τ within a longitudinal data setting

Kendall's τ is a non-parametric measure of correlation based on ranks and is used in a wide range of research disciplines. Although methods are available for making inference about Kendall's τ, none has been extended to modeling multiple Kendall's τs arising in longitudinal data analysis. Compounding this problem is the pervasive issue of missing data in such study designs. In this article, we develop a novel approach to provide inference about Kendall's τ within a longitudinal study setting under both complete and missing data. The proposed approach is illustrated with simulated data and applied to an HIV prevention study.     

Forecasting interstate migration with limited data: a demographic-economic approach

"The limitations of available migration data preclude a time-series approach of modeling interstate migration [in the United States]. The method presented here combines aspects of the demographic and economic approaches to forecasting migration in a manner compatible with existing data. Migration rates are modeled to change in response to changes in economic conditions. When applied to resently constructed data on migration based on income tax returns and then compared to standard demographic projections, the demographic-economic approach has a 20% lower total error in forecasting net migration by state for cohorts of labor-force age."     

Empirical Bayes spatial prediction using a Monte Carlo EM algorithm

This paper deals with an empirical Bayes approach for spatial prediction of a Gaussian random field. In fact, we estimate the hyperparameters of the prior distribution by using the maximum likelihood method. In order to maximize the marginal distribution of the data, the EM algorithm is used. Since this algorithm requires the evaluation of analytically intractable and high dimensionally integrals, a Monte Carlo method based on discretizing parameter space, is proposed to estimate the relevant integrals. Then, the approach is illustrated by its application to a spatial data set. Finally, we compare the predictive performance of this approach with the reference prior method.     

Universal codes as a basis for time series testing

We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the distribution law of the codeword lengths is not known. We apply this approach to the following four problems: goodness-of-fit testing (or identity testing), testing for independence, testing of serial independence and homogeneity testing and suggest nonparametric statistical tests for these problems. It is important to note that practically used so-called archivers can be used for suggested testing.     

The impact of missing data on the results of a schizophrenia study

Missing data pose a serious challenge to the integrity of randomized clinical trials, especially of treatments for prolonged illnesses such as schizophrenia, in which long‐term impact assessment is of great importance, but the follow‐up rates are often no more than 50%. Sensitivity analysis using Bayesian modeling for missing data offers a systematic approach to assessing the sensitivity of the inferences made on the basis of observed data. This paper uses data from an 18‐month study of veterans with schizophrenia to demonstrate this approach. Data were obtained from a randomized clinical trial involving 369 patients diagnosed with schizophrenia that compared long‐acting injectable risperidone with a psychiatrist's choice of oral treatment. Bayesian analysis utilizing a pattern‐mixture modeling approach was used to validate the reported results by detecting bias due to non‐random patterns of missing data. The analysis was applied to several outcomes including standard measures of schizophrenia symptoms, quality of life, alcohol use, and global mental status. The original study results for several measures were confirmed against a wide range of patterns of non‐random missingness. Robustness of the conclusions was assessed using sensitivity parameters. The missing data in the trial did not likely threaten the validity of previously reported results. Copyright © 2014 John Wiley & Sons, Ltd.     

Joint models with multiple longitudinal outcomes and a time-to-event outcome: a corrected two-stage approach

Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also available for their implementation. Although mathematically straightforward, the inclusion of multiple longitudinal outcomes in the joint model remains computationally difficult due to the large number of random effects required, which hampers the practical application of this extension. We present a novel approach that enables the fitting of such models with more realistic computational times. The idea behind the approach is to split the estimation of the joint model in two steps: estimating a multivariate mixed model for the longitudinal outcomes and then using the output from this model to fit the survival submodel. So-called two-stage approaches have previously been proposed and shown to be biased. Our approach differs from the standard version, in that we additionally propose the application of a correction factor, adjusting the estimates obtained such that they more closely resemble those we would expect to find with the multivariate joint model. This correction is based on importance sampling ideas. Simulation studies show that this corrected two-stage approach works satisfactorily, eliminating the bias while maintaining substantial improvement in computational time, even in more difficult settings.

     

A semi‐parametric approach to fitting a nonlinear mixed PK/PD model with an effect compartment using SAS

Modelling of the relationship between concentration (PK) and response (PD) plays an important role in drug development. The modelling becomes complicated when the drug concentration and response measurements are not taken simultaneously and/or hysteresis occurs between the response and the concentration. A model‐based approach fits a joint pharmacokinetic (PK) and concentration–response (PK/PD) model, including an effect compartment if necessary, to concentration and response data. However, this approach relies on the PK data being well described by a common PK model. We propose an algorithm for a semi‐parametric approach to fitting nonlinear mixed PK/PD models including an effect compartment using linear interpolation and extrapolation for concentration data. This approach is independent of the PK model, and the algorithm can easily be implemented using SAS PROC NLMIXED. Practical issues in programming and computing are also discussed. The properties of this approach are examined using simulations. This approach is used to analyse data from a study of the PK/PD relationship between insulin and glucose levels. Copyright © 2005 John Wiley & Sons, Ltd.     

Utilization of treatment effect on a surrogate endpoint for planning a study to evaluate treatment effect on a final endpoint

To design a phase III study with a final endpoint and calculate the required sample size for the desired probability of success, we need a good estimate of the treatment effect on the endpoint. It is prudent to fully utilize all available information including the historical and phase II information of the treatment as well as external data of the other treatments. It is not uncommon that a phase II study may use a surrogate endpoint as the primary endpoint and has no or limited data for the final endpoint. On the other hand, external information from the other studies for the other treatments on the surrogate and final endpoints may be available to establish a relationship between the treatment effects on the two endpoints. Through this relationship, making full use of the surrogate information may enhance the estimate of the treatment effect on the final endpoint. In this research, we propose a bivariate Bayesian analysis approach to comprehensively deal with the problem. A dynamic borrowing approach is considered to regulate the amount of historical data and surrogate information borrowing based on the level of consistency. A much simpler frequentist method is also discussed. Simulations are conducted to compare the performances of different approaches. An example is used to illustrate the applications of the methods.     

Generalised quasi‐likelihood inference in a semi‐parametric binary dynamic mixed logit model

There exists a recent study where dynamic mixed‐effects regression models for count data have been extended to a semi‐parametric context. However, when one deals with other discrete data such as binary responses, the results based on count data models are not directly applicable. In this paper, we therefore begin with existing binary dynamic mixed models and generalise them to the semi‐parametric context. For inference, we use a new semi‐parametric conditional quasi‐likelihood (SCQL) approach for the estimation of the non‐parametric function involved in the semi‐parametric model, and a semi‐parametric generalised quasi‐likelihood (SGQL) approach for the estimation of the main regression, dynamic dependence and random effects variance parameters. A semi‐parametric maximum likelihood (SML) approach is also used as a comparison to the SGQL approach. The properties of the estimators are examined both asymptotically and empirically. More specifically, the consistency of the estimators is established and finite sample performances of the estimators are examined through an intensive simulation study.     

Quantile regression based on a weighted approach under semi-competing risks data

In this article, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. Due to the dependent censoring, the estimation of quantile regression coefficients on the non-terminal event becomes difficult. In order to handle this problem, we assume Archimedean Copula to specify the dependence of the non-terminal event and the terminal event. Portnoy [Censored regression quantiles. J Amer Statist Assoc. 2003;98:1001–1012] considered the quantile regression model under right-censoring data. We extend his approach to construct a weight function, and then impose the weight function to estimate the quantile regression parameter for the non-terminal event under semi-competing risks data. We also prove the consistency and asymptotic properties for the proposed estimator. According to the simulation studies, the performance of our proposed method is good. We also apply our suggested approach to analyse a real data.     

A Bayesian approach to inference about a change point model with application to DNA copy number experimental data

In this paper, we study the change-point inference problem motivated by the genomic data that were collected for the purpose of monitoring DNA copy number changes. DNA copy number changes or copy number variations (CNVs) correspond to chromosomal aberrations and signify abnormality of a cell. Cancer development or other related diseases are usually relevant to DNA copy number changes on the genome. There are inherited random noises in such data, therefore, there is a need to employ an appropriate statistical model for identifying statistically significant DNA copy number changes. This type of statistical inference is evidently crucial in cancer researches, clinical diagnostic applications, and other related genomic researches. For the high-throughput genomic data resulting from DNA copy number experiments, a mean and variance change point model (MVCM) for detecting the CNVs is appropriate. We propose to use a Bayesian approach to study the MVCM for the cases of one change and propose to use a sliding window to search for all CNVs on a given chromosome. We carry out simulation studies to evaluate the estimate of the locus of the DNA copy number change using the derived posterior probability. These simulation results show that the approach is suitable for identifying copy number changes. The approach is also illustrated on several chromosomes from nine fibroblast cancer cell line data (array-based comparative genomic hybridization data). All DNA copy number aberrations that have been identified and verified by karyotyping are detected by our approach on these cell lines.     

The Clustering of Categorical Data: A Comparison of a Model-based and a Distance-based Approach

For clustering multivariate categorical data, a latent class model-based approach (LCC) with local independence is compared with a distance-based approach, namely partitioning around medoids (PAM). A comprehensive simulation study was evaluated by both a model-based as well as a distance-based criterion. LCC was better according to the model-based criterion and PAM was sometimes better according to the distance-based criterion. However, LCC had an overall good and sometimes better distance-based performance as PAM, although this was not the case in a real data set on tribal art items.     

Semi-parametric segmentation of multiple series using a DP-Lasso strategy

We consider a semi-parametric approach to perform the joint segmentation of multiple series sharing a common functional part. We propose an iterative procedure based on Dynamic Programming for the segmentation part and Lasso estimators for the functional part. Our Lasso procedure, based on the dictionary approach, allows us to both estimate smooth functions and functions with local irregularity, which permits more flexibility than previous proposed methods. This yields to a better estimation of the functional part and improvements in the segmentation. The performance of our method is assessed using simulated data and real data from agriculture and geodetic studies. Our estimation procedure results to be a reliable tool to detect changes and to obtain an interpretable estimation of the functional part of the model in terms of known functions.     

Statistical analysis of rank data from a visual matching of colored textures

Nowadays, sensory properties of materials are subject to growing attention both in an hedonic point of view and in an utilitarian one. Hence, the formulation of the foundations of an instrumental metrological approach that will allow for the characterization of visual similarities between textures belonging to the same type becomes a challenge of the research activities in the domain of perception. In this paper, our specific objective is to link an instrumental approach of metrology of the assessment of visual textures with a metrology approach based on a softcopy experiment performed by human judges. The experiment consisted in ranking of isochromatic colored textures according to the visual contrast. A fixed effects additive model is considered for the analysis of the rank data collected from the softcopy experiment. The model is fitted to the data using a least-squares criterion. The resulting data analysis gives rise to a sensory scale that shows a non-linear correlation and a monotonic functional relationship with the physical attribute on which the ranking experiment is based. Furthermore, the capacity of the judges to discriminate the textures according to the visual contrast varies according to the color ranges and the textures types.     

Detection of biomass change in a Norwegian mountain forest area using small footprint airborne laser scanner data

Different approaches for estimation of change in biomass between two points in time by means of airborne laser scanner data were tested. Both field and laser data were collected at two occasions on 52 sample plots in a mountain forest in southeastern Norway. In the first approach, biomass change was estimated as the difference between predicted biomass for the two measurement occasions. Joint models for the biomass at both occasions were fitted using different height and density variables from laser data as explanatory variables. The second approach modelled the observed change directly using the change in different variables extracted from the laser data as explanatory variables. In the third approach we modelled the relative change in biomass. The explanatory variables were also expressed as relative change between measurement occasions. In all approaches we allowed spline terms to be entered. We also investigated the aptness of models for which the residual variance was modeled by allowing it to be proportional to the area of the plot on which biomass was assessed. All alternative models were initially assessed by AIC. All models were also evaluated by estimating biomass change on the model development data. This evaluation indicated that the two direct approaches (approach 2 and 3) were better than relying on modeling biomass at both occasions and taking change as the difference between biomass estimates. Approach 2 seemed to be slightly better than approach 3 based on assessments of bias in the evaluation.     

Data disaggregation procedures within a maximum entropy framework

The aim of this paper is to formulate an analytical–informational–theoretical approach which, given the incomplete nature of the available micro-level data, can be used to provide disaggregated values of a given variable. A functional relationship between the variable to be disaggregated and the available variables/indicators at the area level is specified through a combination of different macro- and micro-data sources. Data disaggregation is accomplished by considering two different cases. In the first case, sub-area level information on the variable of interest is available, and a generalized maximum entropy approach is employed to estimate the optimal disaggregate model. In the second case, we assume that the sub-area level information is partial and/or incomplete, and we estimate the model on a smaller scale by developing a generalized cross-entropy-based formulation. The proposed spatial-disaggregation approach is used in relation to an Italian data set in order to compute the value-added per manufacturing sector of local labour systems within the Umbria region, by combining the available micro/macro-level data and by formulating a suitable set of constraints for the optimization problem in the presence of errors in micro-aggregates.