Simon J. Sheather

Clinical applications of visual analogue scales: a critical review.

Visual Analogue Scales (VAS) provide a simple technique for measuring subjective experience. They have been established as valid and reliable in a range of clinical and research applications, although there is also evidence of increased error and decreased sensitivity when used with some subject groups. Decisions concerned with the choice of scoring interval, experimental design, and statistical analysis for VAS have in some instances been based on convention, assumption and convenience, highlighting the need for more comprehensive assessment of individual scales if this versatile and sensitive measurement technique is to be used to full advantage.

A Brief Survey of Bandwidth Selection for Density Estimation

Abstract There has been major progress in recent years in data-based bandwidth selection for kernel density estimation. Some “second generation” methods, including plug-in and smoothed bootstrap techniques, have been developed that are far superior to well-known “first generation” methods, such as rules of thumb, least squares cross-validation, and biased cross-validation. We recommend a “solve-the-equation” plug-in bandwidth selector as being most reliable in terms of overall performance. This article is intended to provide easy accessibility to the main ideas for nonexperts.

An Effective Bandwidth Selector for Local Least Squares Regression

Abstract Local least squares kernel regression provides an appealing solution to the nonparametric regression, or “scatterplot smoothing,” problem, as demonstrated by Fan, for example. The practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter. In this article we apply the ideas of plug-in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators. Our results are applicable to odd-degree local polynomial fits and can be extended to other settings, such as derivative estimation and multiple nonparametric regression. An implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice. A by-product of our work is the development of a class of nonparametric variance estimators, based on local least squares ideas, and plug-in rules for their implementation.

Kernel quantile estimators

Abstract For an estimator of quantiles, the efficiency of the sample quantile can be improved by considering linear combinations of order statistics, that is, L estimators. A variety of such methods have appeared in the literature; an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a Guassian kernel, and the bandwidths are identified. It is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal. In addition, the theory of this article suggests a method for choosing the smoothing parameter. How much reliance should be placed on the theoretical results is investigated through a simulation study. Over a variety of distributions little consistent difference is found between various estimators. An important conclusion, made during the theoretical analysis, is that all of these estimators usually provide only modest improvement over the sample quantile. The results indicate that even if one knew the best estimator ...

Daily oral sodium bicarbonate preserves glomerular filtration rate by slowing its decline in early hypertensive nephropathy

In most patients with hypertensive nephropathy and low glomerular filtration rate (GFR), the kidney function progressively declines despite the adequate control of the hypertension with angiotensin-converting enzyme inhibition. Previously we found that 2 years of oral sodium citrate slowed GFR decline in patients whose estimated GFR (eGFR) was very low (mean 33 ml/min). This treatment also slowed GFR decline in an animal model of surgically reduced nephron mass. Here, we tested if daily oral sodium bicarbonate slowed GFR decline in patients with hypertensive nephropathy with reduced but relatively preserved eGFR (mean 75 ml/min) in a 5-year, prospective, randomized, placebo-controlled, and blinded interventional study. Patients matched for age, ethnicity, albuminuria, and eGFR received daily placebo or equimolar sodium chloride or bicarbonate while maintaining antihypertensive regimens (including angiotensin-converting enzyme inhibition) aiming for their recommended blood pressure targets. After 5 years, the rate of eGFR decline, estimated using plasma cystatin C, was slower and eGFR was higher in patients given sodium bicarbonate than in those given placebo or sodium chloride. Thus, our study shows that in hypertensive nephropathy, daily sodium bicarbonate is an effective kidney protective adjunct to blood pressure control along with angiotensin-converting enzyme inhibition.

Amelioration of metabolic acidosis in patients with low GFR reduced kidney endothelin production and kidney injury, and better preserved GFR

Metabolic acidosis often accompanies low glomerular filtration rate and induces secretion of endothelin, which in turn might mediate kidney injury. Here we tested whether treatment of metabolic acidosis in patients with low glomerular filtration rate reduced the progression of kidney disease. Fifty-nine patients with hypertensive nephropathy and metabolic acidosis had their blood pressure reduced with regimens that included angiotensin-converting enzyme inhibition. Thirty patients were then prescribed sodium citrate, and the remaining 29, unable or unwilling to take sodium citrate, served as controls. All were followed for 24 months with maintenance of their blood pressure reduction. Urine endothelin-1 excretion, a surrogate of kidney endothelin production, and N-acetyl-beta-D-glucosaminidase, a marker of kidney tubulointerstitial injury, were each significantly lower, while the rate of estimated glomerular filtration rate decline was significantly slower. The estimated glomerular filtration rate was statistically higher after 24 months of sodium citrate treatment compared to the control group. Hence it appears that sodium citrate is an effective kidney-protective adjunct to blood pressure reduction and angiotensin-converting enzyme inhibition.

Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives

Improved kernel-based estimates of integrated squared density derivatives are obtained by reinstating non-stochastic terms that have previously been omitted, and using the bandwidth to (approximately) cancel these positive quantities with the leading smoothing bias terms which are negative. Such estimators have exhibited great practical merit in the context of data-based selection of the bandwidth in kernel density estimation, a motivating application of this work discussed elsewhere.

Acid retention accompanies reduced GFR in humans and increases plasma levels of endothelin and aldosterone

Dietary alkali slows GFR decline in humans with a moderately reduced glomerular filtration rate (GFR) despite the absence of metabolic acidosis. Similarly, dietary alkali slows GFR decline in animals with 2/3 nephrectomy (Nx), a chronic kidney disease (CKD) model without metabolic acidosis in which GFR decline is mediated by acid (H(+)) retention through endothelin (ET) and mineralocorticoid receptors. To gain insight as to whether this mechanism might mediate GFR decline in humans, we explored whether macroalbuminuric subjects with moderately reduced (CKD stage 2 = 60-90 ml/min; CKD 2) compared with normal estimated GFR (> 90 ml/min; CKD 1), each without metabolic acidosis, have H(+) retention that increases plasma levels of ET-1 and aldosterone. Baseline plasma ET and aldosterone concentrations were each higher in CKD 2 than CKD 1. Baseline dietary H(+) and urine net acid excretion (NAE) were not different between groups, but an acute oral NaHCO₃ bolus reduced urine NAE less (i.e., postbolus urine NAE was higher) in CKD 2 than CKD 1, consistent with greater H(+) retention in CKD 2 subjects. Thirty days of oral NaHCO₃ reduced H(+) retention in CKD 2 but not CKD 1 subjects and reduced plasma ET and aldosterone in both groups but to levels that remained higher in CKD 2 for each. Subjects with CKD stage 2 eGFR and no metabolic acidosis nevertheless have H(+) retention that increases plasma ET and aldosterone levels, factors that might mediate subsequent GFR decline and other untoward vascular effects.

A Cautionary Note on the Method of Least Median Squares

Abstract This article describes and illustrates a local instability that may arise when using the method of least median squares (LMS) to fit models to data. This idea is contrary to the generally held belief that the method is highly resistant to perturbations in the data. In fact, slight changes in centrally located data can cause the LMS estimate to change by a large amount. The LMS method uses a criterion function that is calculated on half samples. If there are two or more half-samples with roughly the same value of the criterion function, then by slight changes in some of the data the LMS solution can be made to jump from one half sample to the other. An example of a data set from a standard text that exhibits this feature is presented. This suggests that some caution should be exercised when using this method. It does not automatically guarantee complete robustness to misspecifications in the data.

Kernel density estimation with binned data

Continuous data are often measured or used in binned or rounded form. In this paper we follow up on Halls work analyzing the effect of using equally-spaced binned data in a kernel density estimator. It is shown that a surprisingly large amount of binning does not adversely affect the integrated mean squared error of a kernel estimate.