Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Introduction to Discounted Cash Flow Analysis and Financial Functions in Excel

The financial and economic analysis of investment projects is typically carried out using the technique of discounted cash flow (DCF) analysis. This module introduces concepts of discounting and DCF analysis for the derivation of project performance criteria such as net present value (NPV), internal rate of return (IRR) and benefit to cost (B/C) ratios. These concepts and criteria are introduced with respect to a simple example, for which calculations using MicroSoft Excel are demonstrated.

Molecular clocks in reptiles: Life history influences rate of molecular evolution

Life history has been implicated as a determinant of variation in rate of molecular evolution amongst vertebrate species because of a negative correlation between bode size and substitution rate for many Molecular data sets. Both the generality and the cause of the negative bode size trend have been debated, and the validity of key studies has been questioned (particularly concerning the failure to account for phylogenetic bias). In this study, a comparative method has been used to test for an association between a range of life-history variables-such as body size age at maturity, and clutch size-and DNA substitution rate for three genes (NADH4, cytochrome b, and c-mos). A negative relationship between body size and rate of molecular evolution was found for phylogenetically independent pairs of reptile species spanning turtles. lizards. snakes, crocodile, and tuatara. Although this Study was limited by the number of comparisons for which both sequence and lite-history data were available, the results, suggest that a negative bode size trend in rate of molecular evloution may be a general feature of reptile molecular evolution. consistent with similar studies of mammals and birds. This observation has important implications for uncovering the mechanisms of molecular evolution and warns against assuming that related lineages will share the same substitution rate (a local molecular clock) in order to date evolutionary divergences from DNA sequences.

On the robustness of short-term interest rate models

This paper investigates the robustness of a range of short–term interest rate models. We examine the robustness of these models over different data sets, time periods, sampling frequencies, and estimation techniques. We examine a range of popular one–factor models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that parameter estimates are highly sensitive to all of these factors in the eight countries that we examine. Since parameter estimates are not robust, these models should be used with caution in practice.

In vivo and in vitro models demonstrate a role for caveolin-1 in the pathogenesis of ischaemic acute renal failure

Caveolae and their proteins, the caveolins, transport macromolecules; compartmentalize signalling molecules; and are involved in various repair processes. There is little information regarding their role in the pathogenesis of significant renal syndromes such as acute renal failure (ARF). In this study, an in vivo rat model of 30 min bilateral renal ischaemia followed by reperfusion times from 4 h to 1 week was used to map the temporal and spatial association between caveolin-1 and tubular epithelial damage (desquamation, apoptosis, necrosis). An in vitro model of ischaemic ARF was also studied, where cultured renal tubular epithelial cells or arterial endothelial cells were subjected to injury initiators modelled on ischaemia-reperfusion (hypoxia, serum deprivation, free radical damage or hypoxia-hyperoxia). Expression of caveolin proteins was investigated using immunohistochemistry, immunoelectron microscopy, and immunoblots of whole cell, membrane or cytosol protein extracts. In vivo, healthy kidney had abundant caveolin-1 in vascular endothelial cells and also some expression in membrane surfaces of distal tubular epithelium. In the kidneys of ARF animals, punctate cytoplasmic localization of caveolin-1 was identified, with high intensity expression in injured proximal tubules that were losing basement membrane adhesion or were apoptotic, 24 h to 4 days after ischaemia-reperfusion. Western immunoblots indicated a marked increase in caveolin-1 expression in the cortex where some proximal tubular injury was located. In vitro, the main treatment-induced change in both cell types was translocation of caveolin-1 from the original plasma membrane site into membrane-associated sites in the cytoplasm. Overall, expression levels did not alter for whole cell extracts and the protein remained membrane-bound, as indicated by cell fractionation analyses. Caveolin-1 was also found to localize intensely within apoptotic cells. The results are indicative of a role for caveolin-1 in ARF-induced renal injury. Whether it functions for cell repair or death remains to be elucidated. Copyright (C) 2003 John Wiley Sons, Ltd.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Expression of the HPV16E7 oncoprotein by thymic epithelium is accompanied by disrupted T cell maturation and a failure of the thymus to involute with age

Transgenic mice expressing the E7 protein of HPV16 from the keratin 14 promoter demonstrate increasing thymic hypertrophy with age. This hypertrophy is associated with increased absolute numbers of all thymocyte types, and with increased cortical and medullary cellularity. In the thymic medulla, increased compartmentalization of the major thymic stromal cell types and expansion of thymic epithelial cell population is observed. Neither an increased rate of immature thymocyte division nor a decreased rate of immature thymocyte death was able to account for the observed hypertrophy. Thymocytes with reduced levels of expression of CD4 and/or CD8 were more abundant in transgenic (tg) mice and became increasingly more so with age. These thymic SP and DP populations with reduced levels of CD4 and/or CD8 markers had a lower rate of apoptosis in the tg than in the non-tg mice. The rate of export of mature thymocytes to peripheral lymphoid organs was less in tg animals relative to the pool of available mature cells, particularly for the increasingly abundant CD4lo population. We therefore suggest that mature thymocytes that would normally die in the thymus gradually accumulated in E7 transgenic animals, perhaps as a consequence of exposure to a hypertrophied E7-expressing thymic epithelium or to factors secreted by this expanded thymic stromal cell population. The K14E7 transgenic mouse thus provides a unique model to study effects of the thymic epithelial cell compartment on thymus development and involution.

Improved slope adjustment functions for soil erosion prediction

Numerous studies in the last 60 years have investigated the relationship between land slope and soil erosion rates. However, relatively few of these have investigated slope gradient responses: ( a) for steep slopes, (b) for specific erosion processes, and ( c) as a function of soil properties. Simulated rainfall was applied in the laboratory on 16 soils and 16 overburdens at 100 mm/h to 3 replicates of unconsolidated flume plots 3 m long by 0.8 m wide and 0.15 m deep at slopes of 20, 5, 10, 15, and 30% slope in that order. Sediment delivery at each slope was measured to determine the relationship between slope steepness and erosion rate. Data from this study were evaluated alongside data and existing slope adjustment functions from more than 55 other studies from the literature. Data and the literature strongly support a logistic slope adjustment function of the form S = A + B/[1 + exp (C - D sin theta)] where S is the slope adjustment factor and A, B, C, and D are coefficients that depend on the dominant detachment and transport processes. Average coefficient values when interill-only processes are active are A - 1.50, B 6.51, C 0.94, and D 5.30 (r(2) = 0.99). When rill erosion is also potentially active, the average slope response is greater and coefficient values are A - 1.12, B 16.05, C 2.61, and D 8.32 (r(2) = 0.93). The interill-only function predicts increases in sediment delivery rates from 5 to 30% slope that are approximately double the predictions based on existing published interill functions. The rill + interill function is similar to a previously reported value. The above relationships represent a mean slope response for all soils, yet the response of individual soils varied substantially from a 2.5-fold to a 50-fold increase over the range of slopes studied. The magnitude of the slope response was found to be inversely related ( log - log linear) to the dispersed silt and clay content of the soil, and 3 slope adjustment equations are proposed that provide a better estimate of slope response when this soil property is known. Evaluation of the slope adjustment equations proposed in this paper using independent datasets showed that the new equations can improve soil erosion predictions.

Effect of aldosterone antagonism on myocardial dysfunction in hypertensive patients with diastolic heart failure

Background - Specific treatments targeting the pathophysiology of hypertensive heart disease are lacking. As aldosterone has been implicated in the genesis of myocardial fibrosis, hypertrophy, and dysfunction, we sought to determine the effects of aldosterone antagonism on myocardial function in hypertensive patients with suspected diastolic heart failure by using sensitive quantitative echocardiographic techniques in a randomized, double-blinded, placebo-controlled study. Methods and Results - Thirty medically treated ambulatory hypertensive patients (19 women, age 62 +/- 6 years) with exertional dyspnea, ejection fraction >50%, and diastolic dysfunction (E/A 250m/sec) and without ischemia were randomized to spironolactone 25 mg/d or placebo for 6 months. Patients were overweight (31 +/- 5 kg/m(2)) with reduced treadmill exercise capacity (6.7 +/- 2.1 METS). Long-axis strain rate (SR), peak systolic strain, and cyclic variation of integrated backscatter (CVIB) were averaged from 6 walls in 3 standard apical views. Mean 24-hour ambulatory blood pressure at baseline (133 +/- 17/80 +/- 7mm Hg) did not change in either group. Values for SR, peak systolic strain, and CVIB were similar between groups at baseline and remained unchanged with placebo. Spironolactone therapy was associated with increases in SR (baseline: -1.57 +/- 0.46 s(-1) versus 6-months: -1.91 +/- 0.36 s(-1), P < 0.01), peak systolic strain (-20.3 &PLUSMN; 5.0% versus -26.9 &PLUSMN; 4.3%, P < 0.001), and CVIB (7.4 +/- 1.7dB versus 8.6 +/- 1.7 dB, P = 0.08). Each parameter was significantly greater in the spironolactone group compared with placebo at 6 months (P = 0.05, P = 0.02, and P = 0.02, respectively), and the increases remained significant after adjusting for baseline differences. The increase in strain was independent of changes in blood pressure with intervention. The spironolactone group also exhibited reduction in posterior wall thickness (P = 0.04) and a trend to reduced left atrial area (P = 0.09). Conclusions - Aldosterone antagonism improves myocardial function in hypertensive heart disease.

Response of B-type natriuretic pepticle to exercise in hypertensive patients with suspected diastolic heart failure: Correlation with cardiac function, hemodynamics, and workload

Background Diastolic heart failure (DHF) is characterized by dyspnea due to increased left ventricular (LV) filling pressures during stress. We sought the relationship of exercise-induced increases in B-type natriuretic peptide (BNP) to LV filling pressures and parameters of cardiovascular performance in suspected DHF. Methods Twenty-six treated hypertensive patients with suspected DHF (exertional dyspnea, LV ejection fraction >50%, and diastolic dysfunction) underwent maximal exercise echocardiography using the Bruce protocol. BNP, transmitral Doppler, and tissue Doppler for systolic (So) and early (Ea) and late (Aa) diastolic mitral annular velocities were obtained at rest and peak stress. LV filling pressures were estimated with E/Ea ratios. Results Resting BNP correlated with resting pulse pressure (r=0.45, P=0.02). Maximal exercise performance (4.6 +/- 2.5min) was limited by dyspnea. Blood pressure increased with exercise (from 143 +/- 19/88 +/- 8 to 191 +/- 22/90 +/- 10 mm Hg); 13 patients (50%) had a hypertensive response. Peak exercise BNP correlated with peak transmitral E velocity (r = 0.41, P <.05) and peak heart rate (r = -0.40, P <.05). BNP increased with exercise (from 48 57 to 74 97 pg/mL, P =.007), and the increment of BNP with exercise was associated with maximal workload and peak exercise So, Ea, and Aa (P <.01 for all). Filling pressures, approximated by lateral E/Ea ratio, increased with exercise (7.7 +/- 2.0 to 10.0 +/- 4.8, P <.01). BNP was higher in patients with possibly elevated filling pressures at peak exercise (E/Ea >10) compared to those with normal pressures (123 +/- 124 vs 45 +/- 71 pg/mL, P =.027). Conclusions Augmentation of BNP with exercise in hypertensive patients with suspected DHF is associated with better exercise capacity, LV systolic and diastolic function, and left atrial function. Peak exercise BNP levels may identify exercise-induced elevation of filling pressures in DHF.

National survey of the prevalence, incidence, primary care burden, and treatment of heart failure in Scotland

Objective: To examine the epidemiology, primary care burden, and treatment of heart failure in Scotland, UK. Design: Cross sectional data from primary care practices participating in the Scottish continuous morbidity recording scheme between 1 April 1999 and 31 March 2000. Setting: 53 primary care practices ( 307 741 patients). Subjects: 2186 adult patients with heart failure. Results: The prevalence of heart failure in Scotland was 7.1 in 1000, increasing with age to 90.1 in 1000 among patients greater than or equal to 85 years. The incidence of heart failure was 2.0 in 1000, increasing with age to 22.4 in 1000 among patients greater than or equal to 85 years. For older patients, consultation rates for heart failure equalled or exceeded those for angina and hypertension. Respiratory tract infection was the most common comorbidity leading to consultation. Among men, 23% were prescribed a beta blocker, 11% spironolactone, and 46% an angiotensin converting enzyme inhibitor. The corresponding figures for women were 20% (p = 0.29 versus men), 7% (p = 0.02), and 34% (p < 0.001). Among patients, 75 years 26% were prescribed a β blocker, 11% spironolactone, and 50% an angiotensin converting enzyme inhibitor. The corresponding figures for patients &GE; 75 years were 19% (p = 0.04 versus patients < 75), 7% (p = 0.04), and 33% (p < 0.001). Conclusions: Heart failure is a common condition, especially with advancing age. In the elderly, the community burden of heart failure is at least as great as that of angina or hypertension. The high rate of concomitant respiratory tract infection emphasises the need for strategies to immunise patients with heart failure against influenza and pneumococcal infection. Drugs proven to improve survival in heart failure are used less frequently for elderly patients and women.

Caveolins in the repair phase of acute renal failure after oxidative stress

Ischaemia-reperfusion and toxic injury are leading causes of acute renal failure (ARF). Both of these injury initiators use secondary mediators of damage in oxygen-derived free radicals. Several recent publications about ischaemia-reperfusion and toxin-induced ARF have indicated that plasma membrane structures called caveolae, and their proteins, the caveolins, are potential participants in protecting or repairing renal tissues. Caveolae and caveolins have previously been ascribed many functions, a number of which may mediate cell death or survival of injured renal cells. This review proposes possible pathophysiological mechanisms by which altered caveolin-1 expression and localization may affect renal cell survival following oxidative stress.

Effects of a nurse-led, clinic and home-based intervention on recurrent hospital use in chronic heart failure

Background: Few studies have examined the potential benefits of specialist nurse-led programs of care involving home and clinic-based follow-up to optimise the post-discharge management of chronic heart failure (CHF). Objective: To determine the effectiveness of a hybrid program of clinic plus home-based intervention (C+HBI) in reducing recurrent hospitalisation in CHF patients. Methods: CHF patients with evidence of left ventricular systolic dysfunction admitted to two hospitals in Northern England were assigned to a C+HBI lasting 6 months post-discharge (n=58) or to usual, post-discharge care (UC: n=48) via a cluster randomization protocol. The co-primary endpoints were death or unplanned readmission (event-free survival) and rate of recurrent, all-cause readmission within 6 months of hospital discharge. Results: During study follow-up, more UC patients had an unplanned readmission for any cause (44% vs. 22%: P=0.0191 OR 1.95 95% CI 1.10-3.48) whilst 7 (15%) versus 5 (9%) UC and C+HBI patients, respectively, died (P=NS). Overall, 15 (26%) C+HBI versus 21 (44%) UC patients experienced a primary endpoint. C+HBI was associated with a non-significant, 45% reduction in the risk of death or readmission when adjusting for potential confounders (RR 0.55, 95% CI 0.28-1.08: P=0.08). Overall, C+HBI patients accumulated significantly fewer unplanned readmissions (15 vs. 45: P

Is mortality from heart failure increasing in Australia? An analysis of official data on mortality for 1997-2003

Objective To assess whether trends in mortality from heart failure(HF) in Australia are due to a change in awareness of the condition or real changes in its epidemiology. Methods We carried out a retrospective analysis of official data on national mortality data between 1997 and 2003. A death was attributed to HF if the death certificate mentioned HF as either the underlying cause of death (UCD) or among the contributory factors. Findings From a total of 907 242 deaths, heart failure was coded as the UCD for 29 341 (3.2%) and was mentioned anywhere on the death certificate in 135 268 (14.9%). Between 1997 and 2003, there were decreases in the absolute numbers of deaths and in the age-specific and age-standardized mortality rates for HF either as UCD or mentioned anywhere for both sexes. HF was mentioned for 24.6% and 17.8% of deaths attributed to ischaemic heart disease and circulatory disease, respectively, and these proportions remained unchanged over the period of study. In addition, HF as UCD accounted for 8.3% of deaths attributed to circulatory disease and this did not change materially from 1997 to 2003. Conclusion The decline in mortality from HF measured as either number of deaths or rate probably reflects a real change in the epidemiology of HF. Population-based studies are required to determine accurately the contributions of changes in incidence, survival and demographic factors to the evolving epidemiology of HF.