Inverse correlations for multiple time series and Gaussian random fields and measures of their linear determinism

For a discrete-time vector linear stationary process, {X(t)}, admitting forward and backward autoregressive representations, the variance matrix of an optimal linear interpolator of X(t), based on a knowledge of {X(t-j), j?0}, is known to be given by Ri(0)-1 where Ri(0) denotes the inverse variance of the process. Let A=Is-1Ri(0)?1R(0)?1, where R(0) denotes the variance matrix of {X(t)} and Is an sXs, identity matrix. A measure of linear interpolability of the process, called an index of linear determinism, may be constructed from the determinant Det[Is - A], of Is - A = Ri(0)-1 R(0)-1. An alternative measure is constructed by relating tr[Ri(0)-1] the trace of Ri(0)-1, to tr[R(0)]. The relationship between the matrix A and the corresponding matrix, P, obtained by considering only an optimal one-step linear predictor of X(t) from a knowledge of its infinite past, {X(t-j),j>0}, is also discussed. The possible role the inverse correlation function may have for model specification of a vector ARMA model is explored. Close parallels between the problem of interpolation for a stationary univariate two-dimensional Gaussian random field and time series are examined and an index of linear determinism for the latter class of processes is also defined. An application of this index for model specification and diagnostic testing of a Gaussian Markov Random Field is investigated together with the question of its estimation from observed data. Results are illustrated by a simulation study

Supplementary Material for Model Specification and Selection for Multivariate Time Series

This file gives Supplementary Material for the J Multivariate Analysis paper which has now been accepted for publication. This material will be published online by the Journal

Model specification and selection for multivariate time series

Three major difficulties are identified with an established echelon form approach (see Hannan (1987)) to specifying a Vector Autoregressive Moving Average,V ARMA , model for an observed time series. A family of state space representations, valid for each integer, , is introduced, and collectively referred to as multistep state space representations. This family includes as its special case, with h = 0, a state space representation introduced earlier by Akaike (1974), and, with h = 1, that introduced by Cooper and Wood (1982). Appropriate generalizations of the notions of minimality, McMillan degree, left matrix fraction description and Kronecker indices, as applicable individually to each member of this family, are presented. The reverse echelon form and state space representation corresponding to the Kronecker indices for each h are derived, and the former illustrated with three examples of standard V ARMA processes. The question of how the presence of zero constraints on the coefficients of a reverse echelon form may be detected solely from an inspection of the Kronecker indices is examined. A canonical correlation procedure proposed originally by Akaike (1976) for h is considered for estimating the Kronecker indices with each . The efficacy of the estimation procedure is investigated by a simulation study. A procedure is suggested for implementing the new approach introduced in this paper with an observed time series, and three different applications of this approach are outlined. This approach is also related to some of its alternatives, including the Kronecker invariants of Poskitt (1992) and the scalar component approach of Tiao and Tsay (1989)

Long memory conditional random fields on regular lattices

This paper draws its motivation from applications in geophysics, agricultural, and environmental sciences where empirical evidence of slow decay of correlations have been found for data observed on a regular lattice. Spatial ARFIMA models represent a widely used class of spatial models for analyzing such data. Here, we consider their generalization to conditional autoregressive fractional integrated moving average (CARFIMA) models, a larger class of long memory models which allows a wider range of correlation behavior. For this class we provide detailed descriptions of important representative models, make the necessary comparison with some other existing models, and discuss some important inferential and computational issues on estimation, simulation and long memory process approximation. Results from model fit comparison and predictive performance of CARFIMA models are also discussed through a statistical analysis of satellite land surface temperature data

Hepatobiliary and pancreatic tuberculosis: A two decade experience

<p>Abstract</p> <p>Background</p> <p>Isolated hepatobiliary or pancreatic tuberculosis (TB) is rare and preoperative diagnosis is difficult. We reviewed our experience over a period two decades with this rare site of abdominal tuberculosis.</p> <p>Methods</p> <p>The records of 18 patients with proven histological diagnosis of hepatobiliary and pancreatic tuberculosis were reviewed retrospectively. The demographic features, sign and symptoms, imaging, cytology/histopathology, procedures performed, outcome and follow up data were obtained from the departmental records. The diagnosis of tuberculosis was based on granuloma with caseation necrosis on histopathology or presence of acid fast bacilli.</p> <p>Results</p> <p>Of 18 patients (11 men), 11 had hepatobiliary TB while 7 had pancreatic TB. Two-thirds of the patients were < 40 years (mean: 42 yrs; range 19–70 yrs). The duration of the symptoms varied between 2 weeks to 104 weeks (mean: 20 weeks). The most common symptom was pain in the abdomen (n = 13), followed by jaundice (n = 10), fever, anorexia and weight loss (n = 9). Five patients (28%) had associated extra-abdominal TB which helped in preoperative diagnosis in 3 patients. Imaging demonstrated extrahepatic bile duct obstruction in the patients with jaundice and in addition picked up liver, gallbladder and pancreatic masses with or without lymphadenopathy (peripancreatic/periportal). Preoperative diagnosis was made in 4 patients and the other 14 were diagnosed after surgery. Two patients developed significant postoperative complications (pancreaticojejunostomy leak <abbrgrp><abbr bid="B1">1</abbr></abbrgrp> intraabdominal abscess <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>) and 3 developed ATT induced hepatotoxicity. No patient died. The median follow up period was 12 months (9 – 96 months).</p> <p>Conclusion</p> <p>Tuberculosis should be considered as a differential diagnosis, particularly in young patients, with atypical signs and symptoms coming from areas where tuberculosis is endemic and preoperative tissue and/or cytological diagnosis should be attempted before labeling them as hepatobiliary and pancreatic malignancy.</p

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015

SummaryBackground The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. Methods We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors—the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). Findings Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6–58·8) of global deaths and 41·2% (39·8–42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. Interpretation Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. Funding Bill & Melinda Gates Foundation

Common Variants of Inflammatory Cytokine Genes Are Associated with Risk of Nephropathy in Type 2 Diabetes among Asian Indians

BACKGROUND: Inflammatory cytokine genes have been proposed as good candidate genes for conferring susceptibility to diabetic nephropathy. In the present study, we examined the combined effect of multiple alleles of pro inflammatory cytokine genes for determining the risk of nephropathy in type 2 diabetic patients. METHODOLOGY/PRINCIPAL FINDINGS: Eight single nucleotide polymorphisms (SNPs) of pro-inflammatory cytokine genes (CCL2, TGFB1, IL8, CCR5, and MMP9) were genotyped in two independently ascertained type 2 diabetic cohorts with (DN) and without nephropathy (DM); consisting of patients from North India (n = 495) and South India (n = 188). Genotyping was carried out using PCR, allele specific oligonucleotide-PCR (ASO-PCR), PCR-RFLP and TaqMan allelic discrimination assays and the gene-gene interaction among genetic variants were determined by multi dimensional reduction (MDR) software. Serum high sensitive CRP (hs-CRP) levels were measured by ELISA. The hs-CRP levels were significantly higher in DN as compared to the DM group (p<0.05). The CCL2, IL8, CCR5 and MMP9 polymorphisms were found to be associated with the risk of diabetic nephropathy. Frequency of CCL2 II, IL8 -251AA, CCR5 59029AA and MMP9 279Gln/Gln genotypes were significantly higher in DN than in DM group (p<0.05) and associated with an increased risk of nephropathy in both North and South Indian cohorts. CCR5 DD and IL8 -251AA genotypes were more prevalent in North Indian DN group only. The co-occurrence of risk associated genotypes (II, -2518GG (CCL2), DD (CCR5) and 279Gln/Gln (MMP9) conferred a tenfold increased risk of nephropathy among type 2 diabetics (p<0.0002). CONCLUSION: The present study highlights that common variants of inflammatory cytokine genes exert a modest effect on risk of DN and a combination of risk alleles confer a substantial increased risk of nephropathy in type 2 diabetes among Asian Indians

Effects of alirocumab on types of myocardial infarction: insights from the ODYSSEY OUTCOMES trial

Aims  The third Universal Definition of Myocardial Infarction (MI) Task Force classified MIs into five types: Type 1, spontaneous; Type 2, related to oxygen supply/demand imbalance; Type 3, fatal without ascertainment of cardiac biomarkers; Type 4, related to percutaneous coronary intervention; and Type 5, related to coronary artery bypass surgery. Low-density lipoprotein cholesterol (LDL-C) reduction with statins and proprotein convertase subtilisin–kexin Type 9 (PCSK9) inhibitors reduces risk of MI, but less is known about effects on types of MI. ODYSSEY OUTCOMES compared the PCSK9 inhibitor alirocumab with placebo in 18 924 patients with recent acute coronary syndrome (ACS) and elevated LDL-C (≥1.8 mmol/L) despite intensive statin therapy. In a pre-specified analysis, we assessed the effects of alirocumab on types of MI. Methods and results  Median follow-up was 2.8 years. Myocardial infarction types were prospectively adjudicated and classified. Of 1860 total MIs, 1223 (65.8%) were adjudicated as Type 1, 386 (20.8%) as Type 2, and 244 (13.1%) as Type 4. Few events were Type 3 (n = 2) or Type 5 (n = 5). Alirocumab reduced first MIs [hazard ratio (HR) 0.85, 95% confidence interval (CI) 0.77–0.95; P = 0.003], with reductions in both Type 1 (HR 0.87, 95% CI 0.77–0.99; P = 0.032) and Type 2 (0.77, 0.61–0.97; P = 0.025), but not Type 4 MI. Conclusion  After ACS, alirocumab added to intensive statin therapy favourably impacted on Type 1 and 2 MIs. The data indicate for the first time that a lipid-lowering therapy can attenuate the risk of Type 2 MI. Low-density lipoprotein cholesterol reduction below levels achievable with statins is an effective preventive strategy for both MI types.For complete list of authors see http://dx.doi.org/10.1093/eurheartj/ehz299</p

Effect of alirocumab on mortality after acute coronary syndromes. An analysis of the ODYSSEY OUTCOMES randomized clinical trial

Background: Previous trials of PCSK9 (proprotein convertase subtilisin-kexin type 9) inhibitors demonstrated reductions in major adverse cardiovascular events, but not death. We assessed the effects of alirocumab on death after index acute coronary syndrome. Methods: ODYSSEY OUTCOMES (Evaluation of Cardiovascular Outcomes After an Acute Coronary Syndrome During Treatment With Alirocumab) was a double-blind, randomized comparison of alirocumab or placebo in 18 924 patients who had an ACS 1 to 12 months previously and elevated atherogenic lipoproteins despite intensive statin therapy. Alirocumab dose was blindly titrated to target achieved low-density lipoprotein cholesterol (LDL-C) between 25 and 50 mg/dL. We examined the effects of treatment on all-cause death and its components, cardiovascular and noncardiovascular death, with log-rank testing. Joint semiparametric models tested associations between nonfatal cardiovascular events and cardiovascular or noncardiovascular death. Results: Median follow-up was 2.8 years. Death occurred in 334 (3.5%) and 392 (4.1%) patients, respectively, in the alirocumab and placebo groups (hazard ratio [HR], 0.85; 95% CI, 0.73 to 0.98; P=0.03, nominal P value). This resulted from nonsignificantly fewer cardiovascular (240 [2.5%] vs 271 [2.9%]; HR, 0.88; 95% CI, 0.74 to 1.05; P=0.15) and noncardiovascular (94 [1.0%] vs 121 [1.3%]; HR, 0.77; 95% CI, 0.59 to 1.01; P=0.06) deaths with alirocumab. In a prespecified analysis of 8242 patients eligible for ≥3 years follow-up, alirocumab reduced death (HR, 0.78; 95% CI, 0.65 to 0.94; P=0.01). Patients with nonfatal cardiovascular events were at increased risk for cardiovascular and noncardiovascular deaths (P<0.0001 for the associations). Alirocumab reduced total nonfatal cardiovascular events (P<0.001) and thereby may have attenuated the number of cardiovascular and noncardiovascular deaths. A post hoc analysis found that, compared to patients with lower LDL-C, patients with baseline LDL-C ≥100 mg/dL (2.59 mmol/L) had a greater absolute risk of death and a larger mortality benefit from alirocumab (HR, 0.71; 95% CI, 0.56 to 0.90; Pinteraction=0.007). In the alirocumab group, all-cause death declined wit h achieved LDL-C at 4 months of treatment, to a level of approximately 30 mg/dL (adjusted P=0.017 for linear trend). Conclusions: Alirocumab added to intensive statin therapy has the potential to reduce death after acute coronary syndrome, particularly if treatment is maintained for ≥3 years, if baseline LDL-C is ≥100 mg/dL, or if achieved LDL-C is low. Clinical Trial Registration: URL: https://www.clinicaltrials.gov. Unique identifier: NCT01663402