Improving the chi-squared approximation for bivariate normal tolerance regions

Let X be a two-dimensional random variable distributed according to N2(mu,Sigma) and let bar-X and S be the respective sample mean and covariance matrix calculated from N observations of X. Given a containment probability beta and a level of confidence gamma, we seek a number c, depending only on N, beta, and gamma such that the ellipsoid R = (x: (x - bar-X)'S(exp -1) (x - bar-X) less than or = c) is a tolerance region of content beta and level gamma; i.e., R has probability gamma of containing at least 100 beta percent of the distribution of X. Various approximations for c exist in the literature, but one of the simplest to compute -- a multiple of the ratio of certain chi-squared percentage points -- is badly biased for small N. For the bivariate normal case, most of the bias can be removed by simple adjustment using a factor A which depends on beta and gamma. This paper provides values of A for various beta and gamma so that the simple approximation for c can be made viable for any reasonable sample size. The methodology provides an illustrative example of how a combination of Monte-Carlo simulation and simple regression modelling can be used to improve an existing approximation

Combining Information on Multiple Detection Techniques to Estimate the Effect of Patent Foramen Ovale on Susceptibility to Decompression Illness

The assembly and the maintenance of the International Space Station is expected to require hundreds of extravehicular excursions (EVA's) in the next 10 years. During an EVA, in order to allow movement and bending of limbs, spacesuit pressures are reduced to about 4.3 psi. as compared with about 14.7 psi. for normal atmospheric pressure at sea level. However, the exposure of astronauts to reduced pressures in spacesuits, is conducive to fonnation and growth of gas bubbles within venous blood or tissues, which could cause decompression illness (DCI), a pathology best known to occur among deep-sea divers when they return to the surface. To reduce the risk of DCI, astronauts adjust to the reduced pressure in stages for a prolonged time known as a "pre-breathe" period prior to their extravehicular activity. Despite the use of pre-breathe protocols, an increased risk of DCI can arise for about 25% of humans who have a small hole, known as a patent foramen ovale (PFO), between two chambers of the heart. The atrial septum's fossa oval is, an embryological remnant of a flap between the septae primum and secundum allows fetal right atrial blood to pass into the left atrium, and usually closes after birth (Hagen, et al,. 1984). If fusion does not occur, a valve-like opening, the foramen ovale persists between the two atria. It has been suggested that astronauts with PFO's might be at greater risk of stroke or other serious neurological DCI because bubbles from a venous site may traverse a PFO, travel to the aorta and then enter the cerebral circulatory system causing a stroke (Figure 1). Astronauts are not now screened for PFO's, however consideration is being given to doing so. Here, we study three main methods abbreviated here as "ITE", "TCD" and "TEE", for detecting PFO's in living subjects. All involve the introduction of bubbles into a vein, immediately after which a sensory probe attempts to detect the bubbles in systemic circulation. Presence of the injected bubbles in the systemic circulation is indicative of a PFO. More detailed descriptions are given after the explanation of PFO's under Figure I. Even if a true PFO affects the risk of DCI, there remains a question of how effective screening would be if the detection method has errors of omission and/or commission. Of the three methods studied here, TEE is the "gold standard", matching autopsy results with near-perfect sensitivity and specificity (Schneider, et al. , 1996). However TEE is also the most difficult method to implement, requiring an internal esophagal probe, and is therefore not widely used. Currently, the easiest to use and most common PFO detection method is TTE, which uses an external chest probe. This method has a specificity of near 100%, but suffers from a low sensitivity rate (about 30%). More recently, TCD has been developed, which uses ultrasound probes to detect the presence of bubbles in cerebral arteries. Studies indicate that TCD is quite effective, having a sensitivity of about 91% and a specificity of about 93% (Droste, et al., 1999) when applied correctly, however implementation is difficult and requires considerable training

Characterizing the Joint Effect of Diverse Test-Statistic Correlation Structures and Effect Size on False Discovery Rates in a Multiple-Comparison Study of Many Outcome Measures

In their 2009 Annals of Statistics paper, Gavrilov, Benjamini, and Sarkar report the results of a simulation assessing the robustness of their adaptive step-down procedure (GBS) for controlling the false discovery rate (FDR) when normally distributed test statistics are serially correlated. In this study we extend the investigation to the case of multiple comparisons involving correlated non-central t-statistics, in particular when several treatments or time periods are being compared to a control in a repeated-measures design with many dependent outcome measures. In addition, we consider several dependence structures other than serial correlation and illustrate how the FDR depends on the interaction between effect size and the type of correlation structure as indexed by Foerstner s distance metric from an identity. The relationship between the correlation matrix R of the original dependent variables and R~, the correlation matrix of associated t-statistics is also studied. In general R~ depends not only on R, but also on sample size and the signed effect sizes for the multiple comparisons

Treadmill exercise within lower body negative pressure protects leg lean tissue mass and extensor strength and endurance during bed rest.

Leg muscle mass and strength are decreased during reduced activity and non-weight-bearing conditions such as bed rest (BR) and spaceflight. Supine treadmill exercise within lower body negative pressure (LBNPEX) provides full-body weight loading during BR and may prevent muscle deconditioning. We hypothesized that a 40-min interval exercise protocol performed against LBNPEX 6 days week(-1) would attenuate losses in leg lean mass (LLM), strength, and endurance during 6° head-down tilt BR, with similar benefits for men and women. Fifteen pairs of healthy monozygous twins (8 male and 7 female pairs) completed 30 days of BR with one sibling of each twin pair assigned randomly as the non-exercise control (CON) and the other twin as the exercise subject (EX). Before and after BR, LLM and isokinetic leg strength and endurance were measured. Mean knee and ankle extensor and flexor strength and endurance and LLM decreased from pre- to post-BR in the male CON subjects (P < 0.01), but knee extensor strength and endurance, ankle extensor strength, and LLM were maintained in the male EX subjects. In contrast, no pre- to post-BR changes were significant in the female subjects, either CON or EX, likely due to their lower pre-BR values. Importantly, the LBNPEX countermeasure prevents or attenuates declines in LLM as well as extensor leg strength and endurance. Individuals who are stronger, have higher levels of muscular endurance, and/or have greater LLM are likely to experience greater losses during BR than those who are less fit

Month-to-Month and Year-to-Year Reproducibility of High Frequency QRS ECG signals

High frequency (HF) electrocardiography analyzing the entire QRS complex in the frequency range of 150 to 250 Hz may prove useful in the detection of coronary artery disease, yet the long-term stability of these waveforms has not been fully characterized. We therefore prospectively investigated the reproducibility of the root mean squared (RMS) voltage, kurtosis, and the presence versus absence of reduced amplitude zones (RAzs) in signal averaged 12-lead HF QRS recordings acquired in the supine position one month apart in 16 subjects and one year apart in 27 subjects. Reproducibility of RMS voltage and kurtosis was excellent over these time intervals in the limb leads, and acceptable in the precordial leads using both the V-lead and CR-lead derivations. The relative error of RMS voltage was 12% month-to-month and 16% year-to-year in the serial recordings when averaged over all 12 leads. RAzs were also reproducible at a rate of up to 87% and 8 1 %, respectively, for the month-to-month and year-to-year recordings. We conclude that 12-lead HF QRS electrocardiograms are sufficiently reproducible for clinical use

Comparison of Two Alternate Methods for Tracking Toe Clearance

Analyses of toe clearance during the swing phase of locomotion has often been utilized in determining a subject s propensity to trip while either walking or stepping over an obstacle. In the literature, toe clearance has been studied using a marker on the superior aspect of the second toe (rtoe), a marker on the lateral aspect of the fifth metatarsal head (mth5), or a virtual marker positioned at the anterior tip of the toe (vtoe). The purpose of this study was to compute toe clearance and associated parameters using a fifth metatarsal marker and a virtual toe marker, and compare the results with those of the standard toe marker. Subjects walked on a motorized treadmill at five different speeds while performing a visual acuity task at two separate target distances (ten 60-second trials). The minimum vertical height (TCl) was determined for each stride, along with its point of occurence in the gait cycle, and the angles of the foot and ankle at that time. A regression analysis was performed on the vtoe and mth5 results versus rtoe individually. For all TCl parameters, the mth5 marker did not correlate well with rtoe; the vtoe marker showed better agreement. Most importantly, the mth5 marker predicted a later occurence of TCl than rtoe and vtoe - thereby missing the most dangerous point in swing phase for a trip. From this analysis, the vtoe marker proved to be a better analog to rtoe than mth5, especially for determining a subject s propensity to trip

Statistical Challenges in Biomedical Research

Potentially debilitating effects of spaceflight environment include: a) Bone Demineralization - Osteoporosis. b)Impaired Fracture Healing - Non-Union. c) Renal Stone Formation & Soft Tissue Calcification. d) Orthostatic Intolerance (on return to gravity). e) Cardiac Arrhythmias. f) Dehydration (on return to gravity). g) Decreased Aerobic Capacity. h) Impaired Coordination. i) Muscle Atrophy (Loss of Strength). j) Radiation Sickness. k) Increased Cancer Risk. l) Impaired Immune Function. m) Behavioral Changes & Performance Decrements n) Altitude Decompression Sickness during EVA

Evaluations of Risks from the Lunar and Mars Radiation Environments

Protecting astronauts from the space radiation environments requires accurate projections of radiation in future space missions. Characterization of the ionizing radiation environment is challenging because the interplanetary plasma and radiation fields are modulated by solar disturbances and the radiation doses received by astronauts in interplanetary space are likewise influenced. The galactic cosmic radiation (GCR) flux for the next solar cycle was estimated as a function of interplanetary deceleration potential, which has been derived from GCR flux and Climax neutron monitor rate measurements over the last 4 decades. For the chaotic nature of solar particle event (SPE) occurrence, the mean frequency of SPE at any given proton fluence threshold during a defined mission duration was obtained from a Poisson process model using proton fluence measurements of SPEs during the past 5 solar cycles (19-23). Analytic energy spectra of 34 historically large SPEs were constructed over broad energy ranges extending to GeV. Using an integrated space radiation model (which includes the transport codes HZETRN [1] and BRYNTRN [2], and the quantum nuclear interaction model QMSFRG[3]), the propagation and interaction properties of the energetic nucleons through various media were predicted. Risk assessment from GCR and SPE was evaluated at the specific organs inside a typical spacecraft using CAM [4] model. The representative risk level at each event size and their standard deviation were obtained from the analysis of 34 SPEs. Risks from different event sizes and their frequency of occurrences in a specified mission period were evaluated for the concern of acute health effects especially during extra-vehicular activities (EVA). The results will be useful for the development of an integrated strategy of optimizing radiation protection on the lunar and Mars missions. Keywords: Space Radiation Environments; Galactic Cosmic Radiation; Solar Particle Event; Radiation Risk; Risk Analysis; Radiation Protection

Evaluation of the Danish Aerospace Corporation Portable Pulmonary Function System

A research project designed to investigate changes in maximal oxygen consumption (VO2max) during and following long duration flight on the International Space Station (ISS) has recently been completed. The device used to measure VO2 on board ISS, the Portable Pulmonary Function System (PPFS) manufactured by the Danish Aerospace Corporation (DAC), is based on previous-generation devices manufactured by DAC, but the PPFS has not been validated for analyzing metabolic gases or measuring cardiac output (Qc). The purpose of the present evaluation is to compare PPFS metabolic gas analysis measurements to measurements obtained using a clinically-validated system (ParvoMedics TrueOne(c) 2400 system; Parvo). In addition, Qc data collected with the PPFS were compared to Qc measurements from echocardiography. METHODS: Ten subjects completed three cycle exercise tests to maximal exertion. The first test was conducted to determine each subject's VO2max and set the work rates for the second and third (comparison) tests. The protocol for the two comparison tests consisted of three 5-minute stages designed to elicit 25%, 50%, and 75% VO2max (based upon results from the initial test), followed by 1-minute stages of increasing work rate (25 watt/minute) until the subject reached maximal effort. During one of the two comparison tests, metabolic gases and Qc were assessed with the PPFS; metabolic gases and Qc were assessed with the Parvo and by echocardiography, respectively, during the other test. The order of the comparison tests was counterbalanced. VO2max and maximal work rate during the comparison tests were compared using t tests. Mixed-effects regression modeling was used to analyze submaximal data. RESULTS: All of the data were within normal physiological ranges. The PPFS-measured values for VO2max were 6% lower than values obtained with the Parvo (PPFS: 3.11 +/- 0.75 L/min; Parvo: 3.32 +/- 0.87 L/min; mean +/- standard deviation; P = 0.02); this difference is probably due to flow restriction imposed by the PPFS Qc accessories. Submaximal VO2 values were slightly lower when measured with the PPFS, although differences were not physiologically relevant. The PPFS-measured values of submaximal carbon dioxide production (VCO2) were lower than the data obtained from Parvo, which could be attributed to lower fractions of expired carbon dioxide measured by the PPFS. The PPFS Qc values tended to be lower than echocardiography-derived values. CONCLUSIONS: The results of the present study indicate a need to further examine the PPFS and to better quantify its reproducibility; however, none of the findings of the current evaluation indicate that the PPFS needs to be replaced or modified

Orthostatic Hypotension After Long-Duration Space Flight: NASA's Experiences from the International Space Station

Our laboratory previously reported that the incidence of orthostatic hypotension (OH) was greater after long- than short-duration spaceflight in astronauts who participated in Mir Space Station and Space Shuttle missions. To confirm and extend these findings, we retrospectively examined tilt test data from International Space Station (ISS) and Shuttle astronauts. We anticipated that the proportion of ISS astronauts experiencing OH would be high on landing day and the number of days to recover greater after long- than short-duration missions. Methods: Twenty ISS and 66 Shuttle astronauts participated in 10-min 80? head-up tilt tests 10 d before launch (L-10), on landing day (R+0) or 1 d after landing (R+1). Data from 5 ISS astronauts tested on R+0 or R+1 who used non-standard countermeasures were excluded. Many astronauts repeated the test 3 d (R+3) after landing. Fisher?s Exact Test was used to compare the ability of ISS and Shuttle astronauts to complete the tilt test on R+0. Cox regression was used to identify cardiovascular parameters that were associated with test completion across all tests, and mixed model analysis was used to compare the change and recovery rates between ISS and Shuttle astronauts. In these analyses, ISS data from R+0 and R+1 were pooled to provide sufficient statistical power. Results: The proportion of astronauts who completed the tilt test on R+0 without OH was less in ISS than in Shuttle astronauts (p=0.03). On R+0, only 2 of 6 ISS astronauts completed the test compared to 53 of 66 (80%) Shuttle astronauts. However, 8 of 9 ISS astronauts completed the test on R+1. On R+3, 13 of 15 (87%) of the ISS and 19 of 19 (100%) of the Shuttle astronauts completed the 10-min test. An index comprised of stroke volume and diastolic blood pressure provided a very good prediction of overall tilt survival. This index was altered by spaceflight similarly for both groups soon after landing (pooled R+0 and R+ 1), but ISS astronauts did not recover at the same rate as Shuttle astronauts (p=0.007). Conclusions: The proportion of ISS astronauts who could not complete the tilt test on R+0 due to OH (4 of 6) is similar to that reported in astronauts who flew on Mir (5 of 6). Further, cardiovascular parameters most closely associated with OH recover more slowly after long- compared to short-duration spaceflight