Condence Intervals Research Articles

Approximating Moments by Nonlinear Transformations

We derive expansions of E(x) in terms of the moments of a transformation of x, in a more general context than Taylor expansions. Apart from the intrinsic interest in such a fundamental relation that links the moments of a variate and its nonlinear transformations, our results can be used in practice to approximate E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). We generalize the approach of bounding the terms in expansions of characteristic functions, and use it to derive an explicit and accurate bound for the remainder in the moment expansion. We illustrate one of the implications of our method by providing accurate bootstrap con dence intervals for the mean of a fat-tailed distribution with an infinite variance, in which case currently-available bootstrap methods are either asymptotically invalid or unreliable in finite sample.

Upper Limb Neural Tension and Seated Slump Tests: The False Positive Rate among Healthy Young Adults without Cervical or Lumbar Symptoms

This study examined the false positive rate of the upper limb neural tension test (ULNTT) and seated slump test (SST) among healthy young adults with no history of cervical, lumbar, or peripheral symptoms. Eighty-four subjects (27 men and 57 women) with a mean age of 22.9 years participated in the investigation. All participants completed a screening questionnaire designed to exclude subjects with a history of cervical or lumbar spine pain or injury, or upper or lower extremity neurological symptoms. e ULNTT and the SST were performed on the le upper and lower extremity of each participant. Of the 84 participants tested, 73 (86.9%) were found to have a positive ULNTT at some point in the available range of elbow extension. Twenty-eight (33.3%) of the 84 subjects had a positive SST at some point in the available range of knee extension. e mean knee extension angle for those subjects with a positive SST was 15.1° with a 95% con dence interval (CI) of 12.3 and 19.7°. e mean elbow extension angle for those with a positive ULNTT was 49.4° with a 95% CI of 44.8 and 54.0°. e number of positive tests for both the ULNTT and the SST was found to be high in this sample of asymptomatic healthy young adults. Based on the re- sults of this investigation, the authors suggest that the current criteria for determining a positive test for both the ULNTT and the SST should be examined using the proposed range of motion cut-o scores.

The impact of atypical antipsychotic medications on long-term memory dysfunction in schizophrenia spectrum disorder: a quantitative review

This meta-analytic review examines the efficacy of antipsychotic medications in ameliorating schizophrenia-related long-term memory (LTM) impairments. Twenty-three studies were reviewed that compared schizophrenia spectrum patients treated (a) with atypical versus typical antipsychotic medications, or (b) with various atypical treatments. In 17 atypical versus typical trials aggregating 939 participants, superior overall (verbal and nonverbal) LTM was detected in patients assigned to atypical trials. However, this difference was small (effect size estimate (ES) 0.17; 95% Confidence Interval (CI) 0.04 to 0.31) and specific to certain atypical treatments. Relative to typical antipsychotic trials, LTM superiority was marginally significant for risperidone trials (ES 0.20; 95% CI -0.03 to 0.44) and significant for olanzapine trials (ES 0.29; 95% CI 0.08 to 0.49). In contrast, clozapine trials did not produce a LTM advantage over typical trials (ES -0.06; 95% CI -0.35 to 0.23). Due to the lack of available studies, the effect of quetiapine was indeterminate. Direct comparison between atypical trials revealed a similar effect pattern. A marginally significant superiority in overall LTM was detected for risperidone and olanzapine compared to clozapine (ES 0.28; 95% CI -0.04 to 0.59), which reached significance for verbal LTM (ES 0.36; 95% CI 0.04 to 0.67). Finally, the beneficial impact of antipsychotic medications emerged as a function of differences in the anticholinergic properties of the treatment arms being compared.

The genetics of allergic contact hypersensitivity to nickel.

We have examined evidence for familial disposition to nickel allergic contact dermatitis (Ni ACD). 258 patients attending for routine patch testing were recruited prospectively. 39 patients were diagnosed with Ni ACD. 31 of 209 1st-degree relatives (15%) of probands had a history of nickel hypersensitivity. 84 patients with no history of nickel hypersensitivity and negative patch tests to nickel were used as controls. 24 of 458 1st degree relatives of controls (5.2%) had a history of Ni ACD. The risk ratio for 1st degree relatives of a patient with Ni ACD is 2.83 (95% confidence intervals are 2.45, 3.27). This is the 1st study to present a statistic to represent risk to relatives of developing ACD. Relatives of patients with Ni ACD have an increased risk of developing the condition, but the genetic basis for this is not yet known. With currently available techniques, this value of relative risk makes a positional cloning approach to gene identification impractical.

Reverse successive weighting.

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Enhanced Monte Carlo Estimates for American Option Prices

A simulation-based methodology to price American options with nite exercise opportunities has recently been introduced by Broadie and Glasserman [1995a]. This method simulates the evolution of underlying assets via random trees that branch at each of the possible earlyexercise dates. From these trees, two consistent and asymptotically unbiased price estimates, one biased high and one biased low, are obtained. These two estimates can be used to give a conservative condence interval for the option price. In this paper, we develop several enhancements to improve the eciency of the two estimates so that the resulting condence interval is small. Since branching can be computationally very expensive, we suggest \pruning the trees by eliminating branching whenever possible, thus cutting down the simulation time and allowing for faster convergence of the estimates. In particular, it is shown that branching at the penultimate exercise point is certainly not required whenever a formula for pricing the corresponding European option is available. Next, in order to further improve the estimators, we forego the idea of generating branches from independent samples. Indeed, we demonstrate that if half of the branches at a node are generated using the antithetic variates of the other half, both bias and variance are reduced signicantly. Further enhancement is possible by combining pruning with this technique. It is also shown that by selecting the branches from Latin hypercube samples, better results are obtained. We conclude by showing that an option with innite exercise opportunities can be well approximated by extrapolating a series of options with nitely many exercise points.

Prognostic value of heart rate adjustment of exercise-induced ST segment depression in the multiple risk factor intervention trial

Objectives.We sought to assess the effect of heart rate adjustment of ST segment depression on risk stratification for the prediction of death from coronary artery disease.Background.Standard analysis of the ST segment response to exercise based on a fixed magnitude of horizontal or downsloping ST segment depression has demonstrated only limited diagnostic sensitivity for the detection of coronary artery disease and has variable test performance in predicting coronary artery disease mortality. Heart rate adjustment of the magnitude of ST segment depression has been proposed as an alternative approach to increase the diagnostic and prognostic accuracy of the exercise electrocardiogram (ECG).Methods.Exercise ECGs were performed in 5,940 men from the Usual Care Group of the Multiple Risk Factor Intervention Trial at entry into the study. An abnormal ST segment response to exercise was defined according to standard criteria as ≥ 100 μV of additional horizontal or downsloping ST segment depression at peak exercise. The ST segment/heart rate index was calculated by dividing the change in ST segment depression from rest to peak exercise by the exercise-induced change in heart rate. An abnormal ST segment/heart rate index was defined as >1.60 μV/beats per min.Results.After a mean follow-up of 7 years there were 109 coronary artery disease deaths. Using a Cox proportional hazards model, a positive exercise ECG by standard criteria was not predictive of coronary mortality (age-adjusted relative risk [RR] 1.5,95% condence interval [CI] 0.6 to 3.6, p = 0.39). In contrast, an abnormal ST segment/heart rate index significantly increased the risk of death from coronary artery disease (age-adjusted RR 4.1, 95% CI 2.7 to 6.0, p < 0.0001). Excess risk of death was confined to the highest quintile of ST segment/heart rate index values, and within this quintile, risk was directly related to the magnitude of test abnormality. After multivariate adjustment for age, diastolic blood pressure, serum cholesterol and cigarettes smoked per day, the ST segment/heart rate index remained a significant independent predictor of coronary death (RR 3.6, 95% CI 2.4 to 5.4, p < 0.001).Conclusions.Simple heart rate adjustment of the magnitude of ST segment depression improves the prediction of death from coronary artery disease in relatively high risk, asymptomatic men. These findings strongly support the use of heart rate-adjusted indexes of ST segment depression to improve the predictive value of the exercise ECG.