Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Patients with early diabetic heart disease demonstrate a normal myocardial response to dobutamine

OBJECTIVES We sought to use quantitative markers of the regional left ventricular (LV) response to stress to infer whether diabetic cardiomyopathy is associated with ischemia. BACKGROUND Diabetic cardiomyopathy has been identified in clinical and experimental studies, but its cause remains unclear. METHODS We studied 41 diabetic patients with normal resting LV function and a normal dobutamine echo and 41 control subjects with a low probability of coronary disease. Peak myocardial systolic velocity (Sm) and early diastolic velocity (Em) in each segment were averaged, and mean Sm and Em were compared between diabetic patients and controls and among different stages of dobutamine stress. RESULTS Both Sm and Em progressively increased from rest to peak dobutamine stress. In the diabetic group, Sm was significantly lower than in control subjects at baseline (4.2 +/- 0.9 cm/s vs. 4.7 +/- 0.9 cm/s, p = 0.012). However, Sin at a low dose (6.0 +/- 1.3), before peak (8.4 +/- 1.8), and at peak stress (8.9 +/- 1.8) in diabetic patients was not significantly different from that of controls (6.3 +/- 1.4, 8.9 +/- 1.6, and 9.6 +/- 2.1 cm/s, respectively). The Em (cm/s) in the diabetic group (rest: 4.2 +/- 1.2; low dose: 5.0 +/- 1.4; pre-peak: 5.3 +/- 1.1; peak: 5.9 +/- 1.5) was significantly lower than that of controls (rest: 5.8 +/- 1.5; low dose: 6.6 +/- 1.5; pre-peak: 6.9 +/- 1.3; peak: 7.3 +/- 1.7; all p < 0.001). However, the absolute and relative increases in Sm or Em from rest to peak stress were similar in diabetic and control groups. CONCLUSIONS Subtle LV dysfunction is present in diabetic patients without overt cardiac disease. The normal response to stress suggests that ischemia due to small-vessel disease may not be important in early diabetic heart muscle disease. (C) 2003 by the American College of Cardiology Foundation.