Peter X.-K. Song

Multivariate Dispersion Models Generated From Gaussian Copula

In this paper a class of multivariate dispersion models generated from the multivariate Gaussian copula is presented. Being a multivariate extension of Jorgensens (1987a) dispersion models, this class of multivariate models is parametrized by marginal position, dispersion and dependence parameters, producing a large variety of multivariate discrete and continuous models including the multivariate normal as a special case. Properties of the multivariate distributions are investigated, some of which are similar to those of the multivariate normal distribution, which makes these models potentially useful for the analysis of correlated non-normal data in a way analogous to that of multivariate normal data. As an example, we illustrate an application of the models to the regression analysis of longitudinal data, and establish an asymptotic relationship between the likelihood equation and the generalized estimating equation of Liang & Zeger (1986).

Fluid overload at initiation of renal replacement therapy is associated with lack of renal recovery in patients with acute kidney injury

BACKGROUND Patients with acute kidney injury (AKI) requiring initiation of renal replacement therapy (RRT) have poor short- and long-term outcomes, including the development of dialysis dependence. Currently, little is known about what factors may predict renal recovery in this population. METHODS We conducted a single-center, retrospective analysis of 170 hospitalized adult patients with AKI attributed to acute tubular necrosis who required inpatient initiation of RRT. Data collection included patient characteristics, laboratory data, details of hospital course and degree of fluid overload at RRT initiation. The primary outcome was recovery of renal function to dialysis independence. RESULTS Within 1 year of RRT initiation, 35.9% (61/170) of patients reached the primary end point of renal recovery. The median (interquartile range) duration of RRT was 11 (3-33) days and 83.6% (51/61) recovered prior to hospital discharge. Recovering patients had significantly less fluid overload at the time of RRT initiation compared to non-recovering patients (3.5 versus 9.3%, P = 0.004). In multivariate Cox proportional hazard regression analysis, a rise in percent fluid overload at dialysis initiation remained a significant negative predictor of renal recovery (hazard ratio 0.97, 95% confidence interval 0.95-1.00, P = 0.024). CONCLUSIONS In patients with AKI, a higher degree of fluid overload at RRT initiation predicts worse renal recovery at 1 year. Clinical trials are needed to determine whether interventions targeting fluid overload may improve patient and renal outcomes.

Design of the nephrotic syndrome study network (NEPTUNE) to evaluate primary glomerular nephropathy by a multidisciplinary approach

The Nephrotic Syndrome Study Network (NEPTUNE) is a North American multi-center collaborative consortium established to develop a translational research infrastructure for Nephrotic Syndrome. This includes a longitudinal observational cohort study, a pilot and ancillary studies program, a training program, and a patient contact registry. NEPTUNE will enroll 450 adults and children with minimal change disease, focal segmental glomerulosclerosis and membranous nephropathy for detailed clinical, histopathologic, and molecular phenotyping at the time of clinically-indicated renal biopsy. Initial visits will include an extensive clinical history, physical examination, collection of urine, blood and renal tissue samples, and assessments of quality of life and patient-reported outcomes. Follow-up history, physical measures, urine and blood samples, and questionnaires will be obtained every 4 months in the first year and bi-annually, thereafter. Molecular profiles and gene expression data will be linked to phenotypic, genetic, and digitalized histologic data for comprehensive analyses using systems biology approaches. Analytical strategies were designed to transform descriptive information to mechanistic disease classification for Nephrotic Syndrome and to identify clinical, histological, and genomic disease predictors. Thus, understanding the complexity of the disease pathogenesis will guide further investigation for targeted therapeutic strategies.

Joint Regression Analysis of Correlated Data Using Gaussian Copulas

This article concerns a new joint modeling approach for correlated data analysis. Utilizing Gaussian copulas, we present a unified and flexible machinery to integrate separate one-dimensional generalized linear models (GLMs) into a joint regression analysis of continuous, discrete, and mixed correlated outcomes. This essentially leads to a multivariate analogue of the univariate GLM theory and hence an efficiency gain in the estimation of regression coefficients. The availability of joint probability models enables us to develop a full maximum likelihood inference. Numerical illustrations are focused on regression models for discrete correlated data, including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes. In the simulation studies, the proposed copula-based joint model is compared to the popular generalized estimating equations, which is a moment-based estimating equation method to join univariate GLMs. Two real-world data examples are used in the illustration.

Maximization by Parts in Likelihood Inference

This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.

Tissue transcriptome-driven identification of epidermal growth factor as a chronic kidney disease biomarker

Renal and urinary EGF can serve as biomarkers for prediction of outcomes in chronic kidney disease. Urine marker to the rescue Chronic kidney disease is a common medical problem worldwide, but it is difficult to predict which patients are more likely to progress to end-stage disease and need aggressive management. Ju et al. have now drawn on four independent cohorts totaling hundreds of patients from around the world to identify the expression of epidermal growth factor (EGF) in the kidneys as a marker of kidney disease progression. Moreover, the authors demonstrated that the amount of EGF in the urine is just as useful, providing a biomarker that can be easily tracked over time without requiring invasive biopsies. Chronic kidney disease (CKD) affects 8 to 16% people worldwide, with an increasing incidence and prevalence of end-stage kidney disease (ESKD). The effective management of CKD is confounded by the inability to identify patients at high risk of progression while in early stages of CKD. To address this challenge, a renal biopsy transcriptome-driven approach was applied to develop noninvasive prognostic biomarkers for CKD progression. Expression of intrarenal transcripts was correlated with the baseline estimated glomerular filtration rate (eGFR) in 261 patients. Proteins encoded by eGFR-associated transcripts were tested in urine for association with renal tissue injury and baseline eGFR. The ability to predict CKD progression, defined as the composite of ESKD or 40% reduction of baseline eGFR, was then determined in three independent CKD cohorts. A panel of intrarenal transcripts, including epidermal growth factor (EGF), a tubule-specific protein critical for cell differentiation and regeneration, predicted eGFR. The amount of EGF protein in urine (uEGF) showed significant correlation (P < 0.001) with intrarenal EGF mRNA, interstitial fibrosis/tubular atrophy, eGFR, and rate of eGFR loss. Prediction of the composite renal end point by age, gender, eGFR, and albuminuria was significantly (P < 0.001) improved by addition of uEGF, with an increase of the C-statistic from 0.75 to 0.87. Outcome predictions were replicated in two independent CKD cohorts. Our approach identified uEGF as an independent risk predictor of CKD progression. Addition of uEGF to standard clinical parameters improved the prediction of disease events in diverse CKD populations with a wide spectrum of causes and stages.

A reassessment of soluble urokinase-type plasminogen activator receptor in glomerular disease

It has been suggested that soluble urokinase receptor (suPAR) is a causative circulating factor for and a biomarker of focal and segmental glomerulosclerosis (FSGS). Here we undertook validation of these assumptions in both mouse and human models. Injection of recombinant suPAR in wild-type mice did not induce proteinuria within 24 hours. Moreover, a disease phenotype was not seen in an inducible transgenic mouse model that maintained elevated suPAR concentrations for 6 weeks. Plasma and urine suPAR concentrations were evaluated as clinical biomarkers in 241 patients with glomerular disease from the prospective, longitudinal multi-center observational NEPTUNE cohort. The serum suPAR concentration at baseline inversely correlated with estimated glomerular filtration rate (eGFR) and the urine suPAR/creatinine ratio positively correlated with the urine protein/creatinine ratio. After adjusting for eGFR and urine protein, neither the serum nor urine suPAR level was an independent predictor of FSGS histopathology. A multivariable mixed-effects model of longitudinal data evaluated the association between the change in serum suPAR concentration from baseline with eGFR. After adjusting for baseline suPAR concentration, age, gender, proteinuria and time, the change in suPAR from baseline was associated with eGFR, but this association was not different for patients with FSGS as compared to other diagnoses. Thus, these results do not support a pathological role for suPAR in FSGS.

Urine Podocyte mRNAs, Proteinuria, and Progression in Human Glomerular Diseases

Model systems demonstrate that progression to ESRD is driven by progressive podocyte depletion (the podocyte depletion hypothesis) and can be noninvasively monitored through measurement of urine pellet podocyte mRNAs. To test these concepts in humans, we analyzed urine pellet mRNAs from 358 adult and pediatric kidney clinic patients and 291 controls (n=1143 samples). Compared with controls, urine podocyte mRNAs increased 79-fold (P<0.001) in patients with biopsy-proven glomerular disease and a 50% decrease in kidney function or progression to ESRD. An independent cohort of patients with Alport syndrome had a 23-fold increase in urinary podocyte mRNAs (P<0.001 compared with controls). Urinary podocyte mRNAs increased during active disease but returned to baseline on disease remission. Furthermore, urine podocyte mRNAs increased in all categories of glomerular disease evaluated, but levels ranged from high to normal, consistent with individual patient variability in the risk for progression. In contrast, urine podocyte mRNAs did not increase in polycystic kidney disease. The association between proteinuria and podocyturia varied markedly by glomerular disease type: a high correlation in minimal-change disease and a low correlation in membranous nephropathy. These data support the podocyte depletion hypothesis as the mechanism driving progression in all human glomerular diseases, suggest that urine pellet podocyte mRNAs could be useful for monitoring risk for progression and response to treatment, and provide novel insights into glomerular disease pathophysiology.

Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data

For high-dimensional data sets with complicated dependency structures, the full likelihood approach often leads to intractable computational complexity. This imposes difficulty on model selection, given that most traditionally used information criteria require evaluation of the full likelihood. We propose a composite likelihood version of the Bayes information criterion (BIC) and establish its consistency property for the selection of the true underlying marginal model. Our proposed BIC is shown to be selection-consistent under some mild regularity conditions, where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size. Simulation studies demonstrate the empirical performance of this new BIC, especially for the scenario where the number of parameters increases with sample size. Technical proofs of our theoretical results are provided in the online supplemental materials.

Clustering categorical data based on distance vectors

We introduce a novel statistical procedure for clustering categorical data based on Hamming distance (HD) vectors. The proposed method is conceptually simple and computationally straightforward, because it does not require any specific statistical models or any convergence criteria. Moreover, unlike most currently existing algorithms that compute the class membership or membership probability for every data point at each iteration, our algorithm sequentially extracts clusters from the given dataset. That is, at each iteration our algorithm strives to identify only one cluster, which will then be deleted from the dataset at the next iteration; this procedure repeats until there are no more significant clusters in the remaining data. Consequently, the number of clusters can be determined automatically by the algorithm. As for the identification and extraction of a cluster, we first locate the cluster center by using a Pearson chi-squared–type statistic on the basis of HD vectors. The partition of the dataset produced by our algorithm is unique and insensitive to the input order of data points. The performance of the proposed algorithm is examined using both simulated and real world datasets. Comparisons with two well-known clustering algorithms, K-modes and AutoClass, show that the proposed algorithm substantially outperforms these competitors, with the classification rate or the information gain typically improved by several orders of magnitude. Computational complexity and run time comparisons are also provided.