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.

Point-wise confidence interval estimation by neural networks: A comparative study based on automotive engine calibration.

In developing neural network techniques for real world applications it is still very rare to see estimates of confidence placed on the neural network predictions. This is a major deficiency, especially in safety-critical systems. In this paper we explore three distinct methods of producing point-wise confidence intervals using neural networks. We compare and contrast Bayesian, Gaussian Process and Predictive error bars evaluated on real data. The problem domain is concerned with the calibration of a real automotive engine management system for both air-fuel ratio determination and on-line ignition timing. This problem requires real-time control and is a good candidate for exploring the use of confidence predictions due to its safety-critical nature.

Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

2000 Mathematics Subject Classification: 62F25, 62F03.

Interval breast cancers in an Australian mammographic screening program

Objective: To determine the incidence of interval cancers which occurred in the first 12 months after mammographic screening at a mammographic screening service. Design: Retrospective analysis of data obtained by crossmatching the screening Service and the New South Wales Central Cancer Registry databases. Setting: The Central & Eastern Sydney Service of BreastScreen NSW. Participants: Women aged 40-69 years at first screen, who attended for their first or second screen between 1 March 1988 and 31 December 1992. Main outcome measures: Interval-cancer rates per 10 000 screens and as a proportion of the underlying incidence of breast cancer (as estimated by the underlying rate in the total NSW population). Results: The 12-month interval-cancer incidence per 10 000 screens was 4.17 for the 40-49 years age group (95% confidence interval [CI], 1.35-9.73) and 4.64 for the 50-69 years age group (95% CI, 2.47-7.94). Proportional incidence rates were 30.1% for the 40-49 years age group (95% CI, 9.8-70.3) and 22% for the 50-69 years age group (95% CI, 11.7-37.7). There was no significant difference between the proportional incidence rate for the 50-69 years age group for the Central & Eastern Sydney Service and those of major successful overseas screening trials. Conclusion: Screening quality was acceptable and should result in a significant mortality reduction in the screened population. Given the small number of cancers involved, comparison of interval-cancer statistics of mammographic screening programs with trials requires age-specific or age-adjusted data, and consideration of confidence intervals of both program and trial data.

Self-Esteem, Confidence, and Relationships in Brazilian Men with Erectile Dysfunction Receiving Sildenafil Citrate: A Randomized, Parallel-Group, Double-Blind, Placebo-Controlled Study in Brazil

Psychosocial manifestations of erectile dysfunction (ED) differ across cultures. Understanding the treatment response to ED medications within cultural groups can aid in resource allocation and in developing treatment strategies. Evaluate the effect of sildenafil treatment on self-esteem, confidence, and sexual relationship satisfaction in Brazilian men with ED. The Self-Esteem and Relationship (SEAR) questionnaire, a validated, 14-question instrument developed to specifically address self-esteem and relationship issues within the context of ED. Men aged 18 years or older with a clinical diagnosis of ED (<= 21 on the Sexual Health Inventory for Men) and in a stable relationship with a partner during the study were eligible. The primary end point was a change from baseline in the self-esteem subscale of the SEAR questionnaire. Thirteen Brazilian sites participated in a randomized, double-blind, placebo-controlled trial of sildenafil treatment for ED. Patients were randomized to receive either 50 mg of sildenafil (adjustable to 25 mg or 100 mg based on patient response) or matching placebo approximately 1 hour before anticipated sexual activity but not more than once a day. At the end of double-blind treatment, 63 and 66 patients in the placebo and sildenafil groups, respectively, from 13 Brazilian sites were assessed for efficacy. Brazilian patients receiving sildenafil had significantly greater improvements in their scores on the SEAR self-esteem subscale (42.9 [95% confidence interval 35.7-50.0]) compared with placebo (21.1 [95% confidence interval 13.7-28.6]; P < 0.0001). Effect sizes ranged from 0.91 to 1.25 for individual SEAR components. The psychosocial parameters in Brazilian men with ED assessed by the SEAR questionnaire showed significant improvements in self-esteem, confidence, and relationships after treatment with sildenafil. Glina S, Damiao R, Abdo C, Afif-Abdo J, Tseng L-J, and Stecher V. Self-esteem, confidence, and relationships in Brazilian men with erectile dysfunction receiving sildenafil citrate: A randomized, parallel-group, double-blind, placebo-controlled study in Brazil. J Sex Med 2009;6:268-275.

Substitution of (R,S)-methadone by (R)-methadone: Impact on QTc interval.

Methadone is administered as a chiral mixture of (R,S)-methadone. The opioid effect is mainly mediated by (R)-methadone, whereas (S)-methadone blocks the human ether-à-go-go-related gene (hERG) voltage-gated potassium channel more potently, which can cause drug-induced long QT syndrome, leading to potentially lethal ventricular tachyarrhythmias. To investigate whether substitution of (R,S)-methadone by (R)-methadone could reduce the corrected QT (QTc) interval, (R,S)-methadone was replaced by (R)-methadone (half-dose) in 39 opioid-dependent patients receiving maintenance treatment for 14 days. (R)-methadone was then replaced by the initial dose of (R,S)-methadone for 14 days (n = 29). Trough (R)-methadone and (S)-methadone plasma levels and electrocardiogram measurements were taken. The Fridericia-corrected QT (QTcF) interval decreased when (R,S)-methadone was replaced by a half-dose of (R)-methadone; the median (interquartile range [IQR]) values were 423 (398-440) milliseconds (ms) and 412 (395-431) ms (P = .06) at days 0 and 14, respectively. Using a univariate mixed-effect linear model, the QTcF value decreased by a mean of -3.9 ms (95% confidence interval [CI], -7.7 to -0.2) per week (P = .04). The QTcF value increased when (R)-methadone was replaced by the initial dose of (R,S)-methadone for 14 days; median (IQR) values were 424 (398-436) ms and 424 (412-443) ms (P = .01) at days 14 and 28, respectively. The univariate model showed that the QTcF value increased by a mean of 4.7 ms (95% CI, 1.3-8.1) per week (P = .006). Substitution of (R,S)-methadone by (R)-methadone reduces the QTc interval value. A safer cardiac profile of (R)-methadone is in agreement with previous in vitro and pharmacogenetic studies. If the present results are confirmed by larger studies, (R)-methadone should be prescribed instead of (R,S)-methadone to reduce the risk of cardiac toxic effects and sudden death.

Stereoselective block of hERG channel by (S)-methadone and QT interval prolongation in CYP2B6 slow metabolizers.

Methadone inhibits the cardiac potassium channel hERG and can cause a prolonged QT interval. Methadone is chiral but its therapeutic activity is mainly due to (R)-methadone. Whole-cell patch-clamp experiments using cells expressing hERG showed that (S)-methadone blocked the hERG current 3.5-fold more potently than (R)-methadone (IC50s (half-maximal inhibitory concentrations) at 37 degrees C: 2 and 7 microM). As CYP2B6 slow metabolizer (SM) status results in a reduced ability to metabolize (S)-methadone, electrocardiograms, CYP2B6 genotypes, and (R)- and (S)-methadone plasma concentrations were obtained for 179 patients receiving (R,S)-methadone. The mean heart-rate-corrected QT (QTc) was higher in CYP2B6 SMs (*6/*6 genotype; 439+/-25 ms; n=11) than in extensive metabolizers (non *6/*6; 421+/-25 ms; n=168; P=0.017). CYP2B6 SM status was associated with an increased risk of prolonged QTc (odds ratio=4.5, 95% confidence interval=1.2-17.7; P=0.03). This study reports the first genetic factor implicated in methadone metabolism that may increase the risk of cardiac arrhythmias and sudden death. This risk could be reduced by the administration of (R)-methadone.

QT interval in healthy dogs: which method of correcting the QT interval in dogs is appropriate for use in small animal clinics?

The electrocardiography (ECG) QT interval is influenced by fluctuations in heart rate (HR) what may lead to misinterpretation of its length. Considering that alterations in QT interval length reflect abnormalities of the ventricular repolarisation which predispose to occurrence of arrhythmias, this variable must be properly evaluated. The aim of this work is to determine which method of correcting the QT interval is the most appropriate for dogs regarding different ranges of normal HR (different breeds). Healthy adult dogs (n=130; German Shepherd, Boxer, Pit Bull Terrier, and Poodle) were submitted to ECG examination and QT intervals were determined in triplicates from the bipolar limb II lead and corrected for the effects of HR through the application of three published formulae involving quadratic, cubic or linear regression. The mean corrected QT values (QTc) obtained using the diverse formulae were significantly different (ρ<0.05), while those derived according to the equation QTcV = QT + 0.087(1- RR) were the most consistent (linear regression). QTcV values were strongly correlated (r=0.83) with the QT interval and showed a coefficient of variation of 8.37% and a 95% confidence interval of 0.22-0.23 s. Owing to its simplicity and reliability, the QTcV was considered the most appropriate to be used for the correction of QT interval in dogs.

Point estimates and confidence regions for sequential trials involving selection

A number of authors have proposed clinical trial designs involving the comparison of several experimental treatments with a control treatment in two or more stages. At the end of the first stage, the most promising experimental treatment is selected, and all other experimental treatments are dropped from the trial. Provided it is good enough, the selected experimental treatment is then compared with the control treatment in one or more subsequent stages. The analysis of data from such a trial is problematic because of the treatment selection and the possibility of stopping at interim analyses. These aspects lead to bias in the maximum-likelihood estimate of the advantage of the selected experimental treatment over the control and to inaccurate coverage for the associated confidence interval. In this paper, we evaluate the bias of the maximum-likelihood estimate and propose a bias-adjusted estimate. We also propose an approach to the construction of a confidence region for the vector of advantages of the experimental treatments over the control based on an ordering of the sample space. These regions are shown to have accurate coverage, although they are also shown to be necessarily unbounded. Confidence intervals for the advantage of the selected treatment are obtained from the confidence regions and are shown to have more accurate coverage than the standard confidence interval based upon the maximum-likelihood estimate and its asymptotic standard error.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Electrocardiographic PR interval and adverse outcomes in older adults: the Health, Aging, and Body Composition study

BACKGROUND The electrocardiographic PR interval increases with aging, differs by race, and is associated with atrial fibrillation (AF), pacemaker implantation, and all-cause mortality. We sought to determine the associations between PR interval and heart failure, AF, and mortality in a biracial cohort of older adults. METHODS AND RESULTS The Health, Aging, and Body Composition (Health ABC) Study is a prospective, biracial cohort. We used multivariable Cox proportional hazards models to examine PR interval (hazard ratios expressed per SD increase) and 10-year risks of heart failure, AF, and all-cause mortality. Multivariable models included demographic, anthropometric, and clinical variables in addition to established cardiovascular risk factors. We examined 2722 Health ABC participants (aged 74±3 years, 51.9% women, and 41% black). We did not identify significant effect modification by race for the outcomes studied. After multivariable adjustment, every SD increase (29 ms) in PR interval was associated with a 13% greater 10-year risk of heart failure (95% confidence interval, 1.02-1.25) and a 13% increased risk of incident AF (95% confidence interval, 1.04-1.23). PR interval >200 ms was associated with a 46% increased risk of incident heart failure (95% confidence interval, 1.11-1.93). PR interval was not associated with increased all-cause mortality. CONCLUSIONS We identified significant relationships of PR interval to heart failure and AF in older adults. Our findings extend prior investigations by examining PR interval and associations with adverse outcomes in a biracial cohort of older men and women.

Small sample confidence intervals for the mean of a positively skewed distribution

This thesis proposes some confidence intervals for the mean of a positively skewed distribution. The following confidence intervals are considered: Student-t, Johnson-t, median-t, mad-t, bootstrap-t, BCA, T1 , T3 and six new confidence intervals, the median bootstrap-t, mad bootstrap-t, median T1, mad T1 , median T3 and the mad T3. A simulation study has been conducted and average widths, coefficient of variation of widths, and coverage probabilities were recorded and compared across confidence intervals. To compare confidence intervals, the width and coverage probabilities were compared so that smaller widths indicated a better confidence interval when coverage probabilities were the same. Results showed that the median T1 and median T3 outperformed other confidence intervals in terms of coverage probability and the mad bootstrap-t, mad-t, and mad T3 outperformed others in terms of width. Some real life data are considered to illustrate the findings of the thesis.

The Burden Of Eclampsia: Results From A Multicenter Study On Surveillance Of Severe Maternal Morbidity In Brazil.

Maternal mortality (MM) is a core indicator of disparities in women's rights. The study of Near Miss cases is strategic to identifying the breakdowns in obstetrical care. In absolute numbers, both MM and occurrence of eclampsia are rare events. We aim to assess the obstetric care indicators and main predictors for severe maternal outcome from eclampsia (SMO: maternal death plus maternal near miss). Secondary analysis of a multicenter, cross-sectional study, including 27 centers from all geographic regions of Brazil, from 2009 to 2010. 426 cases of eclampsia were identified and classified according to the outcomes: SMO and non-SMO. We classified facilities as coming from low- and high-income regions and calculated the WHO's obstetric health indicators. SPSS and Stata softwares were used to calculate the prevalence ratios (PR) and respective 95% confidence interval (CI) to assess maternal characteristics, clinical and obstetrical history, and access to health services as predictors for SMO, subsequently correlating them with the corresponding perinatal outcomes, also applying multiple regression analysis (adjusted for cluster effect). Prevalence of and mortality indexes for eclampsia in higher and lower income regions were 0.2%/0.8% and 8.1%/22%, respectively. Difficulties in access to health care showed that ICU admission (adjPR 3.61; 95% CI 1.77-7.35) and inadequate monitoring (adjPR 2.31; 95% CI 1.48-3.59) were associated with SMO. Morbidity and mortality associated with eclampsia were high in Brazil, especially in lower income regions. Promoting quality maternal health care and improving the availability of obstetric emergency care are essential actions to relieve the burden of eclampsia.

Genetic Predictors Of Long-term Response To Growth Hormone (gh) Therapy In Children With Gh Deficiency And Turner Syndrome: The Influence Of A Socs2 Polymorphism.

There is great interindividual variability in the response to GH therapy. Ascertaining genetic factors can improve the accuracy of growth response predictions. Suppressor of cytokine signaling (SOCS)-2 is an intracellular negative regulator of GH receptor (GHR) signaling. The objective of the study was to assess the influence of a SOCS2 polymorphism (rs3782415) and its interactive effect with GHR exon 3 and -202 A/C IGFBP3 (rs2854744) polymorphisms on adult height of patients treated with recombinant human GH (rhGH). Genotypes were correlated with adult height data of 65 Turner syndrome (TS) and 47 GH deficiency (GHD) patients treated with rhGH, by multiple linear regressions. Generalized multifactor dimensionality reduction was used to evaluate gene-gene interactions. Baseline clinical data were indistinguishable among patients with different genotypes. Adult height SD scores of patients with at least one SOCS2 single-nucleotide polymorphism rs3782415-C were 0.7 higher than those homozygous for the T allele (P < .001). SOCS2 (P = .003), GHR-exon 3 (P= .016) and -202 A/C IGFBP3 (P = .013) polymorphisms, together with clinical factors accounted for 58% of the variability in adult height and 82% of the total height SD score gain. Patients harboring any two negative genotypes in these three different loci (homozygosity for SOCS2 T allele; the GHR exon 3 full-length allele and/or the -202C-IGFBP3 allele) were more likely to achieve an adult height at the lower quartile (odds ratio of 13.3; 95% confidence interval of 3.2-54.2, P = .0001). The SOCS2 polymorphism (rs3782415) has an influence on the adult height of children with TS and GHD after long-term rhGH therapy. Polymorphisms located in GHR, IGFBP3, and SOCS2 loci have an influence on the growth outcomes of TS and GHD patients treated with rhGH. The use of these genetic markers could identify among rhGH-treated patients those who are genetically predisposed to have less favorable outcomes.