Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Efficiency of arthroscopic lysis and lavage for internal derangement of the temporomandibular joint correlated with Wilkes classification

OBJECTIVES: To compare the outcome of arthroscopic lysis and lavage of TMJ with internal derangement of Wilkes stages II, III, IV, and V. STUDY DESIGN: Arthroscopic lysis and lavage was performed in 45 TMJ of 39 patients with internal derangement. The cases were divided into 4 groups corresponding to Wilkes stages II, III, IV, and V. Two parameters were compared pre- and postoperatively: pain and mouth opening. Statistical significance was determined using the chi(2) test. RESULTS: Overall success rate was 86.7% (Wilkes stage II 90.9%, Wilkes stage III 92.3%, Wilkes stage IV 84.6%, Wilkes stage V 75%). There were no statistically significant differences between the success rates for Wilkes stages II, III, IV, and V. CONCLUSION: Arthroscopic lysis and lavage should be performed as a standard operation for internal derangement of the TMJ after failure of conservative treatment in all Wilkes stages.

Losses of chromosome arms 4q, 8p, 13q and gain of 8q are correlated with increasing chromosomal instability in hepatocellular carcinoma

OBJECTIVE: Chromosomal instability is a key feature in hepatocellular carcinoma (HCC). Array comparative genomic hybridization (aCGH) revealed recurring structural aberrations, whereas fluorescence in situ hybridization (FISH) indicated an increasing number of numerical aberrations in dedifferentiating HCC. Therefore, we examined whether there was a correlation between structural and numerical aberrations of chromosomal instability in HCC. METHODS AND RESULTS: 27 HCC (5 well, 10 moderately, 12 lower differentiated) already cytogenetically characterized by aCGH were analyzed. FISH analysis using probes for chromosomes 1, 3, 7, 8 and 17 revealed 1.46-4.24 signals/nucleus, which correlated with the histological grade (well vs. moderately,p < 0.0003; moderately vs. lower, p < 0.004). The number of chromosomes to each other was stable with exceptions only seen for chromosome 8. Loss of 4q and 13q, respectively, were correlated with the number of aberrations detected by aCGH (p < 0.001, p < 0.005; Mann-Whitney test). Loss of 4q and gain of 8q were correlated with an increasing number of numerical aberrations detected by FISH (p < 0.020, p < 0.031). Loss of 8p was correlated with the number of structural imbalances seen in aCGH (p < 0.048), but not with the number of numerical changes seen in FISH. CONCLUSION: We found that losses of 4q, 8p and 13q were closely correlated with an increasing number of aberrations detected by aCGH, whereas a loss of 4q and a gain of 8q were also observed in the context of polyploidization, the cytogenetic correlate of morphological dedifferentiation.

Fading pdf of free-space optical communication system with pointing error

A free-space optical (FSO) laser communication system with perfect fast-tracking experiences random power fading due to atmospheric turbulence. For a FSO communication system without fast-tracking or with imperfect fast-tracking, the fading probability density function (pdf) is also affected by the pointing error. In this thesis, the overall fading pdfs of FSO communication system with pointing errors are calculated using an analytical method based on the fast-tracked on-axis and off-axis fading pdfs and the fast-tracked beam profile of a turbulence channel. The overall fading pdf is firstly studied for the FSO communication system with collimated laser beam. Large-scale numerical wave-optics simulations are performed to verify the analytically calculated fading pdf with collimated beam under various turbulence channels and pointing errors. The calculated overall fading pdfs are almost identical to the directly simulated fading pdfs. The calculated overall fading pdfs are also compared with the gamma-gamma (GG) and the log-normal (LN) fading pdf models. They fit better than both the GG and LN fading pdf models under different receiver aperture sizes in all the studied cases. Further, the analytical method is expanded to the FSO communication system with beam diverging angle case. It is shown that the gamma pdf model is still valid for the fast-tracked on-axis and off-axis fading pdfs with point-like receiver aperture when the laser beam is propagated with beam diverging angle. Large-scale numerical wave-optics simulations prove that the analytically calculated fading pdfs perfectly fit the overall fading pdfs for both focused and diverged beam cases. The influence of the fast-tracked on-axis and off-axis fading pdfs, the fast-tracked beam profile, and the pointing error on the overall fading pdf is also discussed. At last, the analytical method is compared with the previous heuristic fading pdf models proposed since 1970s. Although some of previously proposed fading pdf models provide close fit to the experiment and simulation data, these close fits only exist under particular conditions. Only analytical method shows accurate fit to the directly simulated fading pdfs under different turbulence strength, propagation distances, receiver aperture sizes and pointing errors.

Identification of pathogen and host-response markers correlated with periodontal disease

BACKGROUND: Periodontitis is the major cause of tooth loss in adults and is linked to systemic illnesses, such as cardiovascular disease and stroke. The development of rapid point-of-care (POC) chairside diagnostics has the potential for the early detection of periodontal infection and progression to identify incipient disease and reduce health care costs. However, validation of effective diagnostics requires the identification and verification of biomarkers correlated with disease progression. This clinical study sought to determine the ability of putative host- and microbially derived biomarkers to identify periodontal disease status from whole saliva and plaque biofilm. METHODS: One hundred human subjects were equally recruited into a healthy/gingivitis group or a periodontitis population. Whole saliva was collected from all subjects and analyzed using antibody arrays to measure the levels of multiple proinflammatory cytokines and bone resorptive/turnover markers. RESULTS: Salivary biomarker data were correlated to comprehensive clinical, radiographic, and microbial plaque biofilm levels measured by quantitative polymerase chain reaction (qPCR) for the generation of models for periodontal disease identification. Significantly elevated levels of matrix metalloproteinase (MMP)-8 and -9 were found in subjects with advanced periodontitis with Random Forest importance scores of 7.1 and 5.1, respectively. The generation of receiver operating characteristic curves demonstrated that permutations of salivary biomarkers and pathogen biofilm values augmented the prediction of disease category. Multiple combinations of salivary biomarkers (especially MMP-8 and -9 and osteoprotegerin) combined with red-complex anaerobic periodontal pathogens (such as Porphyromonas gingivalis or Treponema denticola) provided highly accurate predictions of periodontal disease category. Elevated salivary MMP-8 and T. denticola biofilm levels displayed robust combinatorial characteristics in predicting periodontal disease severity (area under the curve = 0.88; odds ratio = 24.6; 95% confidence interval: 5.2 to 116.5). CONCLUSIONS: Using qPCR and sensitive immunoassays, we identified host- and bacterially derived biomarkers correlated with periodontal disease. This approach offers significant potential for the discovery of biomarker signatures useful in the development of rapid POC chairside diagnostics for oral and systemic diseases. Studies are ongoing to apply this approach to the longitudinal predictions of disease activity.

Approximate decoding approaches for network coded correlated data

This paper considers a framework where data from correlated sources are transmitted with the help of network coding in ad hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth variations. We show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples showing how the proposed algorithm can be deployed in sensor networks and distributed imaging applications.

Evaluation of the accuracy of multilevel analysis parameter estimates for intra-cluster correlation in correlated binary data

Many studies in biostatistics deal with binary data. Some of these studies involve correlated observations, which can complicate the analysis of the resulting data. Studies of this kind typically arise when a high degree of commonality exists between test subjects. If there exists a natural hierarchy in the data, multilevel analysis is an appropriate tool for the analysis. Two examples are the measurements on identical twins, or the study of symmetrical organs or appendages such as in the case of ophthalmic studies. Although this type of matching appears ideal for the purposes of comparison, analysis of the resulting data while ignoring the effect of intra-cluster correlation has been shown to produce biased results.^ This paper will explore the use of multilevel modeling of simulated binary data with predetermined levels of correlation. Data will be generated using the Beta-Binomial method with varying degrees of correlation between the lower level observations. The data will be analyzed using the multilevel software package MlwiN (Woodhouse, et al, 1995). Comparisons between the specified intra-cluster correlation of these data and the estimated correlations, using multilevel analysis, will be used to examine the accuracy of this technique in analyzing this type of data. ^

A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^