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.

Parathyroid hormone venous sampling prior to reoperation for primary hyperparathyroidism

Background: The surgical cure rate for primary hyperparathyroidism is greater than 95%. For those who have recurrent or persistent disease, preoperative localization improves reoperation success rates. Selective parathyroid venous sampling (SPVS) for intact parathyroid hormone is particularly useful when non-invasive localization techniques are negative or inconclusive. Methods: We present all known cases (n = 13) between 1994 and 2002 who had venous sampling for localization at our institution prior to reoperation for recurrent or persistent primary hyperparathyroidism. Comparison was made with non-invasive localization procedures. Results of invasive and non-invasive localization were correlated with surgical findings. Results: Of the nine reoperated cases, eight had positive correlations between SPVS and operative findings and histopathology. SPVS did not reveal the parathyroid hormone source in one case with negative non-invasive localization procedures. Comparisons between SPVS, computerized tomography (CT), and parathyroid scintigraphy (MIBI) as expressed in terms of true positive (TP), false positive (FP) and false negative (FN) were: SPVS - TP 88.8%, FP 0%, FN 11.1%; CT - TP 22.2%, FP 22.2%, FN 55.5%; and MIBI - TP 33.3%, FP 0%, FN 66.6%. At least seven of the nine operated cases have been cured; another remained normocalcaemic 2 weeks after subtotal parathyroidectomy. Conclusion: In our institution SPVS has proven to be a valuable tool in cases with recurrent or persistent primary hyperparathyroidism and negative non-invasive localization procedures.