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.

Relationship between glomerular filtration rate and the adipokines adiponectin, resistin and leptin in coronary patients with predominantly normal or mildly impaired renal function

BACKGROUND: Due to their molecular weight, it is possible that the adipokines adiponectin, resistin and leptin accumulate when glomerular filtration rate (GFR) is decreased. In reduced renal clearance, altered serum concentrations of these proteins might affect cardiovascular risk. The objective of the study was to investigate the relationship between adipokine concentrations and GFR. METHODS: The association between GFR, as determined by the abbreviated MDRD equation, and the concentrations of the adipokines adiponectin, resistin and leptin was assessed in a cohort of coronary patients (n=538; 363 male, 165 female). After calculation of correlations between GFR and adipokine concentrations, the association was further assessed by analysis of covariance following adjustment for age, gender, BMI, presence of type 2 diabetes, presence of hypertension, history of smoking as well as for serum lipid concentrations. RESULTS: Mean GFR in our study population was 68.74+/-15.27 ml/min/1.73 m(2). 74.3% of the patients had a GFR >60 ml/min/1.73 m(2), 24% of the patients had a GFR between 30 and 60 ml/min/1.73 m(2), and 1.7% of the patients had a GFR <30 ml/min/1.73 m(2). There were significant inverse correlations between adiponectin (r=-0.372; p<0.001), resistin (r=-0.227; p<0.001) and leptin (r=-0.151; p=0.009) concentrations and GFR. After multivariate adjustment, the associations remained significant for adiponectin and resistin. Subgroup analysis in patients with GFR >60 ml/min/1.73 m(2) showed a significant correlation between GFR and adiponectin as well as leptin concentrations. However, after adjustment, these associations no longer were significant. CONCLUSIONS: There is an independent association between GFR and the serum concentrations of adiponectin and resistin. However, this association is not present at GFR >60 ml/min/1.73 m(2). This finding suggests that adipokine concentrations in mildly impaired and normal renal function are influenced by factors other than GFR.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

Distribution of amyloid precursor protein and amyloid-beta immunoreactivity in DBA/2J glaucomatous mouse retinas

PURPOSE: Evidence suggests that altered metabolism of amyloid precursor protein (APP) may play a role in the pathophysiology of retinal ganglion cell (RGC) death in the etiology of glaucoma. The authors sought to determine the distribution of APP and amyloid-beta (Abeta) in DBA/2J glaucomatous mouse retinas. METHODS: The retinas of 3- and 15-month-old DBA/2J mice and C57/BL-6 mice (control group) were fixed with 4% paraformaldehyde and processed for immunohistochemistry. Antibodies used included a polyclonal antibody to the C terminus of Abeta 40 and a polyclonal antibody to the APP ectodomain. Immunohistochemically stained tissue was graded using light microscopy. Distribution and semiquantitative expression of APP and Abeta in young and old glaucomatous and normal retinas were determined and compared. RESULTS: Strong APP and Abeta immunoreactivity was found in the RGC layer, optic nerve, and pia/dura of old DBA/2J retinas, with considerably higher intensity found in the old compared with the young DBA/2J mice. In contrast to glaucomatous mice, the control group did not show any notable age-related difference. CONCLUSIONS: Disruption of the homeostatic properties of secreted APP with consecutive Abeta cytotoxicity might be a contributing factor of ganglion cell loss in glaucomatous mouse retinas.

Diagnosis of diabetic autonomic neuropathy: a multivariate approach

In the diagnosis of diabetic autonomic neuropathy (DAN) various autonomic tests are used. We took a novel statistical approach to find a combination of autonomic tests that best separates normal controls from patients with DAN.

Online distribution management framework by incorporating wind generation

In distribution system operations, dispatchers at control center closely monitor system operating limits to ensure system reliability and adequacy. This reliability is partly due to the provision of remote controllable tie and sectionalizing switches. While the stochastic nature of wind generation can impact the level of wind energy penetration in the network, an estimate of the output from wind on hourly basis can be extremely useful. Under any operating conditions, the switching actions require human intervention and can be an extremely stressful task. Currently, handling a set of switching combinations with the uncertainty of distributed wind generation as part of the decision variables has been nonexistent. This thesis proposes a three-fold online management framework: (1) prediction of wind speed, (2) estimation of wind generation capacity, and (3) enumeration of feasible switching combinations. The proposed methodology is evaluated on 29-node test system with 8 remote controllable switches and two wind farms of 18MW and 9MW nameplate capacities respectively for generating the sequence of system reconfiguration states during normal and emergency conditions.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Subcellular distribution of the insulin-like growth factor (IGF) binding proteins (IGFBPs) 2 and 3 in articular chondrocytes

The insulin-like growth factor (IGF) is a major anabolic regulator in articular cartilage. The IGF-binding proteins (IGFBPs) are increased during osteoarthritis (OA), but the function of the later proteins remains unknown. In general, the IGFBPs are pluripotential effectors capable of IGF regulation and of acting on their own to control key cell functions, including survival and proliferation. The independent functions are often associated with their cell location, and therefore this study explores the distribution of IGFBP-2 and IGFBP-3 in articular chondrocytes. Immunohistochemistry was used to localize IGFBP-2 in normal human articular cartilage. Bovine chondrocytes were used for subcellular fractionation (hypotonic cell lysis) under nonreducing conditions and nuclear purification (centrifugation on sucrose cushions). Cell fraction markers and IGFBPs were assayed in the subcellular fractions by Western immunoblot. The IHC results showed association of IGFBP-2 with chondrocytes, but not with the nuclei. Subcellular fractionation of isolated chondrocytes yielded intact nuclei as assessed at the light microscopic level; the nuclear marker histone H1 was exclusively associated with this fraction. More than 90% of the cytoplasmic marker GAPDH and all the detectable IGFBP-2 were in the cytoplasmic fraction. Immunoreactive IGFBP-3 was found in the cytoplasmic and peri-nuclear/nuclear fractions. Chondrocytes contain intracellular IGFBP-2 and IGFBP-3 but only IGFBP-3 is associated with nuclei. This suggests the hypothesis that the actions of these IGFBPs in articular cartilage extend beyond the classic modulation of IGF receptor action.

Bone mineral density at distal tibia using dual-energy X-ray absorptiometry in normal women and in patients with vertebral osteoporosis or primary hyperparathyroidism

To assess the effect of age and disease on mineral distribution at the distal third of the tibia, bone mineral content (BMC) and bone mineral density (BMD) were measured at lumbar spine (spine), femoral neck (neck), and diaphysis (Dia) and distal epiphysis (Epi) of the tibia in 89 healthy control women of different age groups (20-29, n = 12; 30-39, n = 11; 40-44, n = 12; 45-49, n = 12; 50-54, n = 12; 55-59, n = 10; 60-69, n = 11; 70-79, n = 9), in 25 women with untreated vertebral osteoporosis (VOP), and in 19 women with primary hyperparathyroidism (PHPT) using dual-energy x-ray absorptiometry (DXA; Hologic QDR 1000 and standard spine software). A soft tissue simulator was used to compensate for heterogeneity of soft tissue thickness around the leg. Tibia was scanned over a length of 130 mm from the ankle joint, fibula being excluded from analysis. For BMC and BMD, 10 sections 13 mm each were analyzed separately and then pooled to define the epiphysis (Epi 13-52 mm) and diaphysis area (Dia 91-130 mm). Precision after repositioning was 1.9 and 2.1% for Epi and Dia, respectively. In the control group, at any site there was no significant difference between age groups 20-29 and 30-39, which thus were pooled to define the peak bone mass (PBM).(ABSTRACT TRUNCATED AT 250 WORDS)

Osteopontin (OPN) and neoplastic disease: Circulating levels and tissue distribution

OPN is a secreted phosphate containing protein which is expressed by osteoblasts and a variety of other cells in vivo. Data from in vitro studies has accumulated which relates OPN to cellular transformation. We hypothesize that OPN expression is associated with neoplastic disease in humans as suggested by cell culture models. The overall objective of the current study was to determine the tissue distribution of OPN in human malignancy and to determine whether or not a correlation exists between OPN serum levels and malignancy. At the inception of this project, no study had been made demonstrating the relevance of OPN expression with naturally occurring neoplastic disease in humans. To date, few studies have reported OPN distribution in human neoplasia and are limited by either the number of specimens analyzed or the technique used in analysis. In this dissertation study, OPN was purified from human milk and $\alpha$-OPN antiserum developed and characterized. Following antibody development, the distribution and prevalence of OPN in human oral squamous cell carcinoma and human prostate carcinoma was evaluated using immunohistochemical localization. OPN immunolocalization was found in a high percentage of oral epithelial dysplasia and oral squamous cell carcinoma in humans. One oral squamous cell carcinoma cells line, UMSCC-1, was found to express OPN mRNA using Northern blotting. OPN localized to a high percentage of primary prostate adenocarcinomas. OPN localized to 52% of androgen dependent cases and 100% of androgen independent cases. Androgen dependent cell lines such as LNCap and NbE showed minimal OPN mRNA expression while the androgen independent lines C4-2 and PC3 produced ample OPN mRNA. An OPN sandwich assay was developed and used to determine the serum level of OPN in normal males, patients with BPH (benign prostate hypertrophy), and patients with prostate carcinoma. No statistically significant difference was found in OPN serum levels among the three groups. However, a trend of increasing OPN in the serum was noted in patients with BPH and prostate cancer. ^

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Extent and distribution of calcification of both the aortic annulus and the left ventricular outflow tract predict aortic regurgitation after transcatheter aortic valve replacement

Aims: We sought to analyse local distribution of aortic annulus and left ventricular outflow tract (LVOT) calcification in patients undergoing transcatheter aortic valve replacement (TAVR) and its impact on aortic regurgitation (AR) immediately after device placement. Methods and results: A group of 177 patients with severe aortic stenosis undergoing multislice computed tomography of the aortic root followed by TAVR were enrolled in this single-centre study. Annular and LVOT calcifications were assessed per cusp using a semi-quantitative grading system (0: none; 1 [mild]: small, non-protruding calcifications; 2 [moderate]: protruding [>1 mm] or extensive [>50% of cusp sector] calcifications; 3 [severe]: protruding and extensive calcifications). Any calcification of the annulus or LVOT was present in 107 (61%) and 63 (36%) patients, respectively. Prevalence of annulus/LVOT calcifications in the left coronary cusp was 42% and 25%, respectively, in the non-coronary cusp 28% and 13%, in the right coronary cusp 13% and 5%. AR grade 2 to 4 assessed by the method of Sellers immediately after TAVR device implantation was observed in 55 patients (31%). Multivariate regression analysis revealed that the overall annulus calcification (OR [95% CI] 1.48 [1.10-2.00]; p=0.0106), the overall LVOT calcification (1.93 [1.26-2.96]; p=0.0026), any moderate or severe LVOT calcification (5.37 [1.52-18.99]; p=0.0092), and asymmetric LVOT calcification were independent predictors of AR. Conclusions: Calcifications of the aortic annulus and LVOT are frequent in patients undergoing TAVR, and both the distribution and the severity of calcifications appear to be independent predictors of aortic regurgitation after device implantation. - See more at: http://www.pcronline.com/eurointervention/77th_issue/126/#sthash.Hzodgju5.dpuf