Assessing agreement with multiple raters on correlated kappa statistics.

In clinical studies, it is often of interest to see the diagnostic agreement among clinicians on certain symptoms. Previous work has focused on the agreement between two clinicians under two different conditions or the agreement among multiple clinicians under one condition. Few have discussed the agreement study with a design where multiple clinicians examine the same group of patients under two different conditions. In this paper, we use the intraclass kappa statistic for assessing nominal scale agreement with such a design. We derive an explicit variance formula for the difference of correlated kappa statistics and conduct hypothesis testing for the equality of kappa statistics. Simulation studies show that the method performs well with realistic sample sizes and may be superior to a method that did not take into account the measurement dependence structure. The practical utility of the method is illustrated on data from an eosinophilic esophagitis (EoE) study.

NON-HOMOGENEOUS POISSON PROCESS MODEL FOR GENETIC CROSSOVER INTERFERENCE.

The genetic crossover interference is usually modeled with a stationary renewal process to construct the genetic map. We propose two non-homogeneous, also dependent, Poisson process models applied to the known physical map. The crossover process is assumed to start from an origin and to occur sequentially along the chromosome. The increment rate depends on the position of the markers and the number of crossover events occurring between the origin and the markers. We show how to obtain parameter estimates for the process and use simulation studies and real Drosophila data to examine the performance of the proposed models.

A clustering method to identify who benefits most from the treatment group in clinical trials.

In randomized controlled trials (RCTs), the most compelling need is to determine whether the treatment condition was more effective than control. However, it is generally recognized that not all participants in the treatment group of most clinical trials benefit equally. While subgroup analyses are often used to compare treatment effectiveness across pre-determined subgroups categorized by patient characteristics, methods to empirically identify naturally occurring clusters of persons who benefit most from the treatment group have rarely been implemented. This article provides a modeling framework to accomplish this important task. Utilizing information about individuals from the treatment group who had poor outcomes, the present study proposes an a priori clustering strategy that classifies the individuals with initially good outcomes in the treatment group into: (a) group GE (good outcome, effective), the latent subgroup of individuals for whom the treatment is likely to be effective and (b) group GI (good outcome, ineffective), the latent subgroup of individuals for whom the treatment is not likely to be effective. The method is illustrated through a re-analysis of a publically available data set from the National Institute on Drug Abuse. The RCT examines the effectiveness of motivational enhancement therapy from 461 outpatients with substance abuse problems. The proposed method identified latent subgroups GE and GI, and the comparison between the two groups revealed several significantly different and informative characteristics even though both subgroups had good outcomes during the immediate post-therapy period. As a diagnostic means utilizing out-of-sample forecasting performance, the present study compared the relapse rates during the long-term follow-up period for the two subgroups. As expected, group GI, composed of individuals for whom the treatment was hypothesized to be ineffective, had a significantly higher relapse rate than group GE (63% vs. 27%; χ2 = 9.99, p-value = .002).

Robust Analysis of High Throughput Screening (HTS) Assay Data.

Quantitative high throughput screening (qHTS) assays use cells or tissues to screen thousands of compounds in a short period of time. Data generated from qHTS assays are then evaluated using nonlinear regression models, such as the Hill model, and decisions regarding toxicity are made using the estimates of the parameters of the model. For any given compound, the variability in the observed response may either be constant across dose groups (homoscedasticity) or vary with dose (heteroscedasticity). Since thousands of compounds are simultaneously evaluated in a qHTS assay, it is not practically feasible for an investigator to perform residual analysis to determine the variance structure before performing statistical inferences on each compound. Since it is well-known that the variance structure plays an important role in the analysis of linear and nonlinear regression models it is therefore important to have practically useful and easy to interpret methodology which is robust to the variance structure. Furthermore, given the number of chemicals that are investigated in the qHTS assay, outliers and influential observations are not uncommon. In this article we describe preliminary test estimation (PTE) based methodology which is robust to the variance structure as well as any potential outliers and influential observations. Performance of the proposed methodology is evaluated in terms of false discovery rate (FDR) and power using a simulation study mimicking a real qHTS data. Of the two methods currently in use, our simulations studies suggest that one is extremely conservative with very small power in comparison to the proposed PTE based method whereas the other method is very liberal. In contrast, the proposed PTE based methodology achieves a better control of FDR while maintaining good power. The proposed methodology is illustrated using a data set obtained from the National Toxicology Program (NTP). Additional information, simulation results, data and computer code are available online as supplementary materials.

A HIERARCHICAL FUNCTIONAL DATA ANALYTIC APPROACH FOR ANALYZING PHYSIOLOGICALLY BASED PHARMACOKINETIC MODELS.

Ordinary differential equation (ODE) based models find application in a wide variety of biological and physiological phenomena. For instance, they arise in the description of gene regulatory networks, study of viral dynamics and other infectious diseases, etc. In the field of toxicology, they are used in physiologically based pharmacokinetic (PBPK) models for describing absorption, distribution, metabolism and excretion (ADME) of a chemical in-vivo. Knowledge about the model parameters is important for understanding the mechanism of action of a chemical and are often estimated using non-linear least squares methodology. However, there are several challenges associated with the usual methodology. Using functional data analytic methodology, in this article we develop a general framework for drawing inferences on parameters in models described by a system of differential equations. The proposed methodology takes into account variability between and within experimental units. The performance of the proposed methodology is evaluated using a simulation study and data obtained from a benzene inhalation study. We also describe a R-based software developed towards this purpose.

Robust nonlinear regression in applications.

Robust statistical methods, such as M-estimators, are needed for nonlinear regression models because of the presence of outliers/influential observations and heteroscedasticity. Outliers and influential observations are commonly observed in many applications, especially in toxicology and agricultural experiments. For example, dose response studies, which are routinely conducted in toxicology and agriculture, sometimes result in potential outliers, especially in the high dose groups. This is because response to high doses often varies among experimental units (e.g., animals). Consequently, this may result in outliers (i.e., very low values) in that group. Unlike the linear models, in nonlinear models the outliers not only impact the point estimates of the model parameters but can also severely impact the estimate of the information matrix. Note that, the information matrix in a nonlinear model is a function of the model parameters. This is not the case in linear models. In addition to outliers, heteroscedasticity is a major concern when dealing with nonlinear models. Ignoring heteroscedasticity may lead to inaccurate coverage probabilities and Type I error rates. Robustness to outliers/influential observations and to heteroscedasticity is even more important when dealing with thousands of nonlinear regression models in quantitative high throughput screening assays. Recently, these issues have been studied very extensively in the literature (references are provided in this paper), where the proposed estimator is robust to outliers/influential observations as well as to heteroscedasticity. The focus of this paper is to provide the theoretical underpinnings of robust procedures developed recently.

Accounting for Uncertainty in Heteroscedasticity in Nonlinear Regression.

Toxicologists and pharmacologists often describe toxicity of a chemical using parameters of a nonlinear regression model. Thus estimation of parameters of a nonlinear regression model is an important problem. The estimates of the parameters and their uncertainty estimates depend upon the underlying error variance structure in the model. Typically, a priori the researcher would know if the error variances are homoscedastic (i.e., constant across dose) or if they are heteroscedastic (i.e., the variance is a function of dose). Motivated by this concern, in this article we introduce an estimation procedure based on preliminary test which selects an appropriate estimation procedure accounting for the underlying error variance structure. Since outliers and influential observations are common in toxicological data, the proposed methodology uses M-estimators. The asymptotic properties of the preliminary test estimator are investigated; in particular its asymptotic covariance matrix is derived. The performance of the proposed estimator is compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using a data set obtained from the National Toxicology Program.

Multiple Hypothesis Testing for Experimental Gingivitis Based on Wilcoxon Signed Rank Statistics.

Dental research often involves repeated multivariate outcomes on a small number of subjects for which there is interest in identifying outcomes that exhibit change in their levels over time as well as to characterize the nature of that change. In particular, periodontal research often involves the analysis of molecular mediators of inflammation for which multivariate parametric methods are highly sensitive to outliers and deviations from Gaussian assumptions. In such settings, nonparametric methods may be favored over parametric ones. Additionally, there is a need for statistical methods that control an overall error rate for multiple hypothesis testing. We review univariate and multivariate nonparametric hypothesis tests and apply them to longitudinal data to assess changes over time in 31 biomarkers measured from the gingival crevicular fluid in 22 subjects whereby gingivitis was induced by temporarily withholding tooth brushing. To identify biomarkers that can be induced to change, multivariate Wilcoxon signed rank tests for a set of four summary measures based upon area under the curve are applied for each biomarker and compared to their univariate counterparts. Multiple hypothesis testing methods with choice of control of the false discovery rate or strong control of the family-wise error rate are examined.

A linear exponent AR(1) family of correlation structures.

In repeated measures settings, modeling the correlation pattern of the data can be immensely important for proper analyses. Accurate inference requires proper choice of the correlation model. Optimal efficiency of the estimation procedure demands a parsimonious parameterization of the correlation structure, with sufficient sensitivity to detect the range of correlation patterns that may occur. Many repeated measures settings have within-subject correlation decreasing exponentially in time or space. Among the variety of correlation patterns available for this context, the continuous-time first-order autoregressive correlation structure, denoted AR(1), sees the most utilization. Despite its wide use, the AR(1) structure often poorly gauges within-subject correlations that decay at a slower or faster rate than required by the AR(1) model. To address this deficiency we propose a two-parameter generalization of the continuous-time AR(1) model, termed the linear exponent autoregressive (LEAR) correlation structure, which accommodates much slower and much faster decay patterns. Special cases of the LEAR family include the AR(1), compound symmetry, and first-order moving average correlation structures. Excellent analytic, numerical, and statistical properties help make the LEAR structure a valuable addition to the suite of parsimonious correlation models for repeated measures data. Both medical imaging data concerning neonate neurological development and longitudinal data concerning diet and hypertension [DASH (Dietary Approaches to Stop Hypertension) study] exemplify the utility of the LEAR correlation structure.

A semi-Markov multistate model for estimation of the mean quality-adjusted survival for non-progressive processes.

We discuss the estimation of the expected value of the quality-adjusted survival, based on multistate models. We generalize an earlier work, considering the sojourn times in health states are not identically distributed, for a given vector of covariates. Approaches based on semiparametric and parametric (exponential and Weibull distributions) methodologies are considered. A simulation study is conducted to evaluate the performance of the proposed estimator and the jackknife resampling method is used to estimate the variance of such estimator. An application to a real data set is also included.

A Robust QTL Mapping Procedure.

In quantitative-trait linkage studies using experimental crosses, the conventional normal location-shift model or other parameterizations may be unnecessarily restrictive. We generalize the mapping problem to a genuine nonparametric setup and provide a robust estimation procedure for the situation where the underlying phenotype distributions are completely unspecified. Classical Wilcoxon-Mann-Whitney statistics are employed for point and interval estimation of QTL positions and effects.

Exterior exposure estimation using a one-compartment toxicokinetic model with blood sample measurements.

Exposure assessment of individuals exposed to certain chemicals plays an important role in the analysis of occupational-as well as environmental-health problems. Biological monitoring, as an alternative to direct environmental measurements, may be applied to relate the exterior exposure with the amount of individual intake. In this paper, we estimate individuals' (inhalation) exposure retrospectively from their blood concentrations via a simplified one-compartment toxicokinetic model. Considering stochastic variations to the toxicokinetic model, the solution to the resultant stochastic differential equation (SDE), together with measurement error, is transformed into a dynamic linear state-space model. The unknown model parameters and the mean inhalation concentration are then estimated via Markov Chain Monte Carlo (MCMC) simulations. The proposed method is used in the analysis of the styrene data (Wang et al. in Occup Environ Med 53:601-605, 1996) to backward estimate the inhalation concentration, assuming it is unknown. The data analysis showed that the internal stochastic variations, often ignored in toxicokinetic model analysis, outweighed in standard deviation almost twice that of the measurement error. Also, the simulation results showed that the method performed relatively well to the approach considering measurement error only.

Association of leukocyte count with progression of aortic atheroma in stroke/transient ischemic attack patients.

BACKGROUND AND PURPOSE: Leukocyte count is an independent predictor of stroke. We investigated the association between leukocyte count and progression of aortic atheroma over 12 months in stroke/transient ischemic attack (TIA) patients. METHODS: Consecutive ischemic stroke and transient ischemic attack patients underwent 12-month sequential transesophageal echocardiography and were assessed for total and differential leukocyte counts on admission. Paired aortic plaque images were assessed for several parameters, including changes in grade, intimal-medial thickness (IMT), and cross-sectional area. Multivariate linear and logistic regressions were used to calculate the effect of leukocyte count on the change in aortic atheromas over 12 months. RESULTS: Of the 115 participants (mean+/-SD age, 64.6+/-11.9 years; 53.1% men; 73.4% white, 24.2% black, and 2.3% Asian), 45 (35%) showed clinically significant progression of aortic atheromas (maximal change in IMT >0.70 mm over 12 months). The mean admission leukocyte count was higher in the progression group compared with the no-progression group (8.6+/-2.2 vs 7.3+/-2.2 x 10(9)/L respectively, P=0.002). Each unit increase in leukocyte count was associated with a 0.26-mm increase in aortic arch IMT over 12 months (P=0.006). After adjustment for other atherosclerosis risk factors, the relation persisted (mean increase in aortic arch IMT per unit increase in leukocyte count=0.27 mm, P=0.007). Each unit increase in leukocyte count was associated with an increased risk of significant progression of aortic atheromas (adjusted odds ratio=1.33; 95% CI, 1.09 to 1.61). CONCLUSIONS: In stroke/transient ischemic attack patients, leukocyte count is independently associated with the progression of aortic atheroma over 12 months (>0.70 mm), which is associated with cardiovascular risk.

Aortic arch atheroma progression and recurrent vascular events in patients with stroke or transient ischemic attack.

BACKGROUND: It is not known whether progression of aortic arch (AA) atheroma is associated with vascular events in patients with stroke or transient ischemic attack (TIA). METHODS AND RESULTS: AA atheroma was detected on baseline transesophageal echocardiogram in 167 consecutive patients who had prevalent stroke or TIA. Of these, 125 consented to a follow-up transesophageal echocardiogram at 12 months. Adequate paired AA images were obtained in 117 (78 with strokes, 39 with TIAs), which allowed detailed measurements of plaques. On admission for their index stroke or TIA, patients were assessed for stroke risk factors, stroke subtypes, baseline AA plaque characteristics, and laboratory parameters. Progression of AA atheroma was observed in 33 patients (28%) on 12-month follow-up transesophageal echocardiogram. It was determined that the progression group had significantly higher adjusted homocysteine levels (P<0.0001) and neutrophil counts (P<0.0001) than the no-progression group. These patients were followed up for a median of 1.7 years from the index stroke/TIA (range 0.5 to 4.5 years) for vascular events including stroke, TIA, myocardial infarction, and death due to vascular causes. Kaplan-Meier curves showed fewer patients with AA atheroma progression remained free of the composite vascular end point (49% compared with 89% in the no-progression group; P<0.0001). AA atheroma progression was associated with composite vascular events (hazard ratio 5.8, 95% confidence interval 2.3 to 14.5, P=0.0002) after adjustment for a propensity score based on confounders. CONCLUSIONS: In this preliminary study of stroke/TIA patients with AA atheroma on transesophageal echocardiogram, AA atheroma progression was associated with recurrent vascular events.

Making inferences about projected completors in longitudinal studies.

In this article, we present methodology for making inferences about projected completors in the presence of attrition. The approach is motivated by a clinical trial that investigates a treatment for disability among individuals who sustain severe head injuries. Although most studies attempt to make inferences about the entire study population, our application poses important scientific questions targeting individuals who are likely to complete the study or to remain on protocol for a specified time period. We propose using measures of each individual's dropout inclination to identify projected completors and then building a stratified response model based on projected completion status. We present several prediction measures along with procedures for evaluating accuracy with respect to observed dropout. Estimation of model parameters proceeds using maximum likelihood and restricted maximum likelihood methods. We illustrate the utility of our proposed analysis by using the motivating disability data example.

Estimating correlation by using a general linear mixed model: evaluation of the relationship between the concentration of HIV-1 RNA in blood and semen.

Estimating the correlation coefficient between two outcome variables is one of the most important aspects of epidemiological and clinical research. A simple Pearson's correlation coefficient method is usually employed when there are complete independent data points for both outcome variables. However, researchers often deal with correlated observations in a longitudinal setting with missing values where a simple Pearson's correlation coefficient method cannot be used. General linear mixed models (GLMM) techniques were used to estimate correlation coefficients in a longitudinal data set with missing values. A random regression mixed model with unstructured covariance matrix was employed to estimate correlation coefficients between concentrations of HIV-1 RNA in blood and seminal plasma. The effects of CD4 count and antiretroviral therapy were also examined. We used data sets from three different centres (650 samples from 238 patients) where blood and seminal plasma HIV-1 RNA concentrations were collected from patients; 137 samples from 90 different patients without antiviral therapy and 513 samples from 148 patients receiving therapy were considered for analysis. We found no significant correlation between blood and semen HIV-1 RNA concentration in the absence of antiviral therapy. However, a moderate correlation between blood and semen HIV-1 RNA was observed among subjects with lower CD4 counts receiving therapy. Our findings confirm and extend the idea that the concentrations of HIV-1 in semen often differ from the HIV-1 concentration in blood. Antiretroviral therapy administered to subjects with low CD4 counts result in sufficient concomitant reduction of HIV-1 in blood and semen so as to improve the correlation between these compartments. These results have important implications for studies related to the sexual transmission of HIV, and development of HIV prevention strategies.