Bootstrap Statistical Method Research Articles

Optimal sampling designs for estimation of Plasmodium falciparum clearance rates in patients treated with artemisinin derivatives

BackgroundThe emergence of Plasmodium falciparum resistance to artemisinins in Southeast Asia threatens the control of malaria worldwide. The pharmacodynamic hallmark of artemisinin derivatives is rapid parasite clearance (a short parasite half-life), therefore, the in vivo phenotype of slow clearance defines the reduced susceptibility to the drug. Measurement of parasite counts every six hours during the first three days after treatment have been recommended to measure the parasite clearance half-life, but it remains unclear whether simpler sampling intervals and frequencies might also be sufficient to reliably estimate this parameter.MethodsA total of 2,746 parasite density-time profiles were selected from 13 clinical trials in Thailand, Cambodia, Mali, Vietnam, and Kenya. In these studies, parasite densities were measured every six hours until negative after treatment with an artemisinin derivative (alone or in combination with a partner drug). The WWARN Parasite Clearance Estimator (PCE) tool was used to estimate “reference” half-lives from these six-hourly measurements. The effect of four alternative sampling schedules on half-life estimation was investigated, and compared to the reference half-life (time zero, 6, 12, 24 (A1); zero, 6, 18, 24 (A2); zero, 12, 18, 24 (A3) or zero, 12, 24 (A4) hours and then every 12 hours). Statistical bootstrap methods were used to estimate the sampling distribution of half-lives for parasite populations with different geometric mean half-lives. A simulation study was performed to investigate a suite of 16 potential alternative schedules and half-life estimates generated by each of the schedules were compared to the “true” half-life. The candidate schedules in the simulation study included (among others) six-hourly sampling, schedule A1, schedule A4, and a convenience sampling schedule at six, seven, 24, 25, 48 and 49 hours.ResultsThe median (range) parasite half-life for all clinical studies combined was 3.1 (0.7-12.9) hours. Schedule A1 consistently performed the best, and schedule A4 the worst, both for the individual patient estimates and for the populations generated with the bootstrapping algorithm. In both cases, the differences between the reference and alternative schedules decreased as half-life increased. In the simulation study, 24-hourly sampling performed the worst, and six-hourly sampling the best. The simulation study confirmed that more dense parasite sampling schedules are required to accurately estimate half-life for profiles with short half-life (≤three hours) and/or low initial parasite density (≤10,000 per μL). Among schedules in the simulation study with six or fewer measurements in the first 48 hours, a schedule with measurements at times (time windows) of 0 (0–2), 6 (4–8), 12 (10–14), 24 (22–26), 36 (34–36) and 48 (46–50) hours, or at times 6, 7 (two samples in time window 5–8), 24, 25 (two samples during time 23–26), and 48, 49 (two samples during time 47–50) hours, until negative most accurately estimated the “true” half-life. For a given schedule, continuing sampling after two days had little effect on the estimation of half-life, provided that adequate sampling was performed in the first two days and the half-life was less than three hours. If the measured parasitaemia at two days exceeded 1,000 per μL, continued sampling for at least once a day was needed for accurate half-life estimates.ConclusionsThis study has revealed important insights on sampling schedules for accurate and reliable estimation of Plasmodium falciparum half-life following treatment with an artemisinin derivative (alone or in combination with a partner drug). Accurate measurement of short half-lives (rapid clearance) requires more dense sampling schedules (with more than twice daily sampling). A more intensive sampling schedule is, therefore, recommended in locations where P. falciparum susceptibility to artemisinins is not known and the necessary resources are available. Counting parasite density at six hours is important, and less frequent sampling is satisfactory for estimating long parasite half-lives in areas where artemisinin resistance is present.

Investigating the need of triggering the acquisition for infant diffusion MRI: A quantitative study including bootstrap statistics

Diffusion weighted magnetic resonance imaging is increasingly being used for neonatal and young pediatric subjects. Our purpose was to investigate a) whether cardiac triggering was needed to reduce variability of diffusion (tensor) imaging data, b) how pulsation artifacts affect the fitted diffusion tensor when triggering is not used and c) the feasibility of triggered data acquisition in neonates and young children.Data were collected from 11 infants and 7 adults. In seven infants and seven adults, diffusion encoding was applied solely along the z gradient direction with and without cardiac triggering. Non-parametric bootstrap statistical methods were applied to investigate the dependence of variance on triggering. One infant and all adults served as test–retest controls. From the remaining three infants diffusion tensor imaging data were acquired with and without triggering.Our findings that used the repeated measurements in a single diffusion-encoding direction indicated that without triggering the variability in the data was increased significantly both in infants and adults. When collecting diffusion tensor data in infants, this increased variability results in erroneous fractional anisotropy values and artifactual fiber direction estimates. Contrary to previous reports but supported by our findings involving adults, pulsation artifacts were present in a larger extent of the brain in the infant population.In conclusion, triggering is feasible in young subjects and is preferred when acquiring diffusion MRI data. In doing so, the amount of erroneous estimations due to image artifacts will be minimized, which in turn will lead to more specific and less ambiguous interpretations. Although fitting the pulse-monitoring device requires additional set-up time, the total imaging time is usually shorter than acquiring multiple data sets to compile a single, artifact-free set.

Adverse drug reactions in Germany: direct costs of internal medicine hospitalizations

German hospital reimbursement modalities changed as a result of the introduction of Diagnosis Related Groups (DRG) in 2004. Therefore, no data on the direct costs of adverse drug reactions (ADRs) resulting in admissions to departments of internal medicine are available. The objective was to quantify the ADR-related economic burden (direct costs) of hospitalizations in internal medicine wards in Germany. Record-based study analyzing the patient records of about 57,000 hospitalizations between 2006 and 2007 of the Net of Regional Pharmacovigilance Centers (Germany). All ADRs were evaluated by a team of experts in pharmacovigilance for severity, causality, and preventability. The calculation of accurate person-related costs for ADRs relied on the German DRG system (G-DRG 2009). Descriptive and bootstrap statistical methods were applied for data analysis. The incidence of hospitalization due to at least 'possible' serious outpatient ADRs was estimated to be approximately 3.25%. Mean age of the 1834 patients was 71.0 years (SD 14.7). Most frequent ADRs were gastrointestinal hemorrhage (n = 336) and drug-induced hypoglycemia (n = 270). Average inpatient length-of-stay was 9.3 days (SD 7.1). Average treatment costs of a single ADR were estimated to be approximately €2250. The total costs sum to €434 million per year for Germany. Considering the proportion of preventable cases (20.1%), this equals a saving potential of €87 million per year. Preventing ADRs is advisable in order to realize significant nationwide savings potential. Our cost estimates provide a reliable benchmark as they were calculated based on an intensified ADR surveillance and an accurate person-related cost application.

Global optical model potential forA=3projectiles

A global optical model potential (GDP08) for $^{3}\mathrm{He}$ projectiles has been obtained by simultaneously fitting the elastic scattering data of $^{3}\mathrm{He}$ from targets of $40\ensuremath{\leqslant}{A}_{T}\ensuremath{\leqslant}209$ at incident energies of $30\ensuremath{\leqslant}{E}_{\mathrm{inc}}\ensuremath{\leqslant}217$ MeV. Uncertainties and correlation coefficients between the global potential parameters were obtained by using the bootstrap statistical method. GDP08 was found to satisfactorily account for the elastic scattering of $^{3}\mathrm{H}$ as well, which makes it a global optical potential for the $A=3$ nuclei. Optical model calculations using the GDP08 global potential are compared with the experimental angular distributions of differential cross sections for $^{3}\mathrm{He}$-nucleus and $^{3}\mathrm{H}$-nucleus scattering from different targets of $6\ensuremath{\leqslant}{A}_{T}\ensuremath{\leqslant}232$ at incident energies of $4\ensuremath{\leqslant}{E}_{\mathrm{inc}}\ensuremath{\leqslant}450$ MeV. The optical potential for the doubly-magic nucleus $^{40}\mathrm{Ca}$, the low-energy correction to the real potential for nuclei with $58\ensuremath{\lesssim}{A}_{T}\ensuremath{\lesssim}120$ at ${E}_{\mathrm{inc}}<30$ MeV, the comparison with double-folding model calculations and the CH89 potential, and the spin-orbit potential parameters are discussed.

Analytical modeling of gravity changes and crustal deformation at volcanoes: The Long Valley caldera, California, case study

Joint measurements of ground deformation and micro-gravity changes are an indispensable component for any volcano monitoring strategy. A number of analytical mathematical models are available in the literature that can be used to fit geodetic data and infer source location, depth and density. Bootstrap statistical methods allow estimations of the range of the inferred parameters. Although analytical models often assume that the crust is elastic, homogenous and isotropic, they can take into account different source geometries, the influence of topography, and gravity background noise. The careful use of analytical models, together with high quality data sets, can produce valuable insights into the nature of the deformation/gravity source. Here we present a review of various modeling methods, and use the historical unrest at Long Valley caldera (California) from 1982 to 1999 to illustrate the practical application of analytical modeling and bootstrap to constrain the source of unrest. A key question is whether the unrest at Long Valley since the late 1970s can be explained without calling upon an intrusion of magma. The answer, apparently, is no. Our modeling indicates that the inflation source is a slightly tilted prolate ellipsoid (dip angle between 91° and 105°) at a depth of 6.5 to 7.9 km beneath the caldera resurgent dome with an aspect ratio between 0.44 and 0.60, a volume change from 0.161 to 0.173 km 3 and a density of 1241 to 2093 kg/m 3. The larger uncertainty of the density estimate reflects the higher noise of gravity measurements. These results are consistent with the intrusion of silicic magma with a significant amount of volatiles beneath the caldera resurgent dome.

DYNAMICS OF COGNITIVE FUNCTIONING IN HEALTHY CONTROLS AND PATIENTS WITH SCHIZOPHRENIA

We have developed a toolbox and graphic user interface, EEGLAB, running under the crossplatform MATLAB environment (The Mathworks, Inc.) for processing collections of single-trial and/or averaged EEG data of any number of channels. Available functions include EEG data, channel and event information importing, data visualization (scrolling, scalp map and dipole model plotting, plus multi-trial ERP-image plots), preprocessing (including artifact rejection, filtering, epoch selection, and averaging), independent component analysis (ICA) and time/frequency decompositions including channel and component cross-coherence supported by bootstrap statistical methods based on data resampling. EEGLAB functions are organized into three layers. Top-layer functions allow users to interact with the data through the graphic interface without needing to use MATLAB syntax. Menu options allow users to tune the behavior of EEGLAB to available memory. Middle-layer functions allow users to customize data processing using command history and interactive ‘pop’ functions. Experienced MATLAB users can use EEGLAB data structures and stand-alone signal processing functions to write custom and/or batch analysis scripts. Extensive function help and tutorial information are included. A ‘plug-in’ facility allows easy incorporation of new EEG modules into the main menu. EEGLAB is freely available (http://www.sccn.ucsd.edu/eeglab/) under the GNU public license for noncommercial use and open source development, together with sample data, user tutorial and extensive documentation.

Bootstrap method for the estimation of measurement uncertainty in spotted dual-color DNA microarrays

DNA microarrays permit the measurement of gene expression across the entire genome of an organism, but the quality of the thousands of measurements is highly variable. For spotted dual-color microarrays the situation is complicated by the use of ratio measurements. Studies have shown that measurement errors can be described by multiplicative and additive terms, with the latter dominating for low-intensity measurements. In this work, a measurement-error model is presented that partitions the variance into general experimental sources and sources associated with the calculation of the ratio from noisy pixel data. The former is described by a proportional (multiplicative) structure, while the latter is estimated using a statistical bootstrap method. The model is validated using simulations and three experimental data sets. Monte-Carlo fits of the model to data from duplicate experiments are excellent, but suggest that the bootstrap estimates, while proportionately correct, may be underestimated. The bootstrap standard error estimates are particularly useful in determining the reliability of individual microarray spots without the need for replicate spotting. This information can be used in screening or weighting the measurements.

Abstracts of the XLV International Symposium of ISCEV—Hyderabad, India, 25–29 August 2007

Introduction: Most commonly, the estimation of transient evoked potentials such as the ERG, PERG and VEP is by simple ensemble averaging, synchronized by the stimulation signal. This requires three assumptions: (i) the signal to be recovered is stationary; (ii) the noise (or ‘incoherent’ signal component) is stationary with zero mean; (iii) the number of epochs sampled is sufficient to statistically represent the signal of interest within acceptable confidence limits. Whilst ensemble averaging still forms the cornerstone of transient evoked potential measurement, it does not exploit modern statistical signal processing techniques and the potential for extracting more statistical information from the recorded signals. Purpose: To describe a statistical bootstrap method that provides an estimate of the probability that the response obtained is due to random variation in the data rather than a physiological response (viz., the null hypothesis). This method can be applied to (almost) any signal parameter (e.g., power, amplitude range, estimates of signal-to-noise ratio) and is based on randomly re-sampling (with replacement) of the continuously recorded data. Method: The proposed method was developed and tested initially on simulated data with realistic autoregressive moving average (ARMA) noise. This was extended to a series of clinical PERG recordings. Results: The bootstrap model was able to detect the presence of PERG responses at user-defined significance levels in both artificial and clinical recordings. Conclusion: The bootstrap re-sampling technique is simple to implement, very flexible in terms of the signal features that can be statistically analysed, and provides a novel means of objectively testing signal recovery. It thus holds the potential to optimize the acquisition process, and to determine the shortest recording time required, based on a clearly defined statistical criterion.

On the mean oxygen isotope composition of the Solar System

Since the first discovery of extraordinary oxygen isotope compositions in carbonaceous meteorites by Clayton et al. [Clayton, R.N., Grossman, L., Mayeda, T.K., 1973. Science 182, 485–488], numerous studies have been done to explain the unusual mass-independent isotope fractionation, but the problem is still unresolved to this day. Clayton's latest interpretation [Clayton, R.N., 2002. Nature 415, 860–861] sheds new light on the problem, and possible hypotheses now seem to be fairly well defined. A key issue is to resolve whether the oxygen isotopes in the Solar System represented by the Sun (solar oxygen) are the same as oxygen isotopes in planetary objects such as bulk meteorites, Mars, Earth, and Moon, or whether the solar oxygen is more similar to the lightest oxygen isotopes observed in CAIs (Calcium Aluminum-rich Inclusions) in primitive meteorites. Here, we examined the problem using oxygen isotope analytical data of about 400 bulk meteorite samples of various classes or types (data compiled by K. Lodders). We used in our discussion exclusively the parameter ΔO17, a direct measure of the degree of mass-independent isotope fractionation of oxygen isotopes. When ΔO17 is arranged according to a characteristic size of their host planetary object, it shows a systematic trend: (1) ΔO17 values scatter around zero; (2) the scatter from the mean (ΔO17=0) decreases with increasing representative size of the respective host planetary object. This systematic trend is easily understood on the basis of a hierarchical scenario of planetary formation, that is, larger planetary objects have formed by progressive accretion of planetesimals by random sampling over a wide spectrum of proto-solar materials. If this progressive random sampling of planetesimals were the essential process of planetary formation, the isotopic composition of planetary oxygen should approach that of the solar oxygen. To test this random sampling hypothesis, we applied a multiscale, multistep bootstrap statistical method [Shimodaira, H., 2004. Ann. Statist. 32, 2616–2641] to the meteorite oxygen isotope data, and deduced a σ–N relation, where σ is the standard deviation of ΔO17, and N is the representative size of a host planetary object. If we assign 200 and 500 km as a representative sizes of the chondrite and achondrite parent bodies, the observed σ of ΔO17 agree well with the values predicted by the σ–N relation. A common mean value of ΔO17=0 for all planetary objects also agrees with the progressive random sampling process. Therefore, we conclude that the solar oxygen is the same as planetary oxygen, but differs from CAI oxygen. The conclusion implies that a massive enrichment in 17O and 18O resulting from CO self-shielding, a current influential interpretation of CAI-O, did not occur.

African‐American race is a predictor of prostate cancer detection: incorporation into a pre‐biopsy nomogram

To construct a pre-biopsy predictive model incorporating several clinical variables, including African-American (AA) or Caucasian race, to predict the risk of prostate cancer detection on prostate biopsy, as traditionally AA men have had a higher incidence of prostate cancer than Caucasian men, but previous predictive tools for prostate cancer have not incorporated the effect of race. We evaluated 9473 patients undergoing initial prostate biopsy at three equal-access healthcare institutes from 1993 to 2003. At each biopsy session, patient age, race, serum prostate-specific antigen level (PSA), digital rectal examination (DRE) findings, number of biopsy cores taken, year of biopsy, and pathological findings were recorded. A logistic regression model was constructed to evaluate predictors of cancer detection based on pre-biopsy variables. The model was internally validated using the bootstrap statistical method, and a nomogram was constructed. Prostate cancer was diagnosed in 1895 (33%) AA men and 991 (26%) Caucasians. AA men had a significantly higher mean serum PSA level than Caucasians, at 13.0 and 8.5 ng/mL, respectively (P < 0.001). The mean ages were similar between AA and Caucasian men (P = 0.23), but Caucasian men had a higher incidence of an abnormal DRE (P < 0.001). On multivariate analysis, age, race, year of biopsy, PSA level, DRE, and number of cores taken were all statistically significant (P < 0.001). Hazard ratios were (controlling for year of biopsy); age (1.30), Caucasian race (0.74), PSA level (1.47), DRE (1.75), and number of cores taken (1.19). The predicted model had a boot-strapped concordance index of 0.75. AA race remains an independent predictor of prostate cancer detection in men undergoing initial prostate biopsy. This nomogram is the first to individualise the risk by AA or Caucasian race in a predictive model for counselling men on their probability of having cancer at the time of their first biopsy.

The Retail Price Index and the Cost-of-Living Index: testing for consistency in theory and practice

This paper tests the published section-level price and weight data used in the compilation of the UK retail price index (RPI) for consistency with the theory of the cost-of-living index. We use a non-parametric test of theoretical consistency and bootstrap statistical methods to estimate the probability of consistency.

EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis

We have developed a toolbox and graphic user interface, EEGLAB, running under the crossplatform MATLAB environment (The Mathworks, Inc.) for processing collections of single-trial and/or averaged EEG data of any number of channels. Available functions include EEG data, channel and event information importing, data visualization (scrolling, scalp map and dipole model plotting, plus multi-trial ERP-image plots), preprocessing (including artifact rejection, filtering, epoch selection, and averaging), independent component analysis (ICA) and time/frequency decompositions including channel and component cross-coherence supported by bootstrap statistical methods based on data resampling. EEGLAB functions are organized into three layers. Top-layer functions allow users to interact with the data through the graphic interface without needing to use MATLAB syntax. Menu options allow users to tune the behavior of EEGLAB to available memory. Middle-layer functions allow users to customize data processing using command history and interactive ‘pop’ functions. Experienced MATLAB users can use EEGLAB data structures and stand-alone signal processing functions to write custom and/or batch analysis scripts. Extensive function help and tutorial information are included. A ‘plug-in’ facility allows easy incorporation of new EEG modules into the main menu. EEGLAB is freely available ( http://www.sccn.ucsd.edu/eeglab/) under the GNU public license for noncommercial use and open source development, together with sample data, user tutorial and extensive documentation.

A New Approach to Predict the Pit Depth Extreme Value of a Localized Corrosion Process

Depth of pits that propagate during a pitting corrosion process is an important characteristic of the damage of steels; the greater the depth, the more dramatic the damage. For evident reasons of safety and reliability of industrial installations, statistical procedures must be constructed to assess the maximum pit depth to perform proper maintenance from limited inspection data. This paper outlines a new methodology to predict accurately the pit depth extreme value related to a localized corrosion process independently of the nature of the unknown parent distribution of the experimental data. Based on computer calculations and simulations, this methodology combines the Generalized Lambda Distribution (GLD) and the Bootstrap statistical methods. The GLD method was used in this study to determine a modeled distribution that fits the experimental frequency distribution of pit depths produced on a ferritic stainless steel sample during an accelerated corrosion test. This modeled distribution was used to generate, thanks to the Computer-Based Bootstrap Method (CBBM), simulated distributions of corrosion pit depths equivalent to the experimental one. An estimation of the mean with a 90% confidence interval of the maximum pit depth can be finally deduced not only for these simulated samples of equivalent surface size than the experimental one but also for a large scale installation.

An unscaled parameter to measure the order of surfaces: a new surface elaboration to increase cells adhesion

We present a new parameter to quantify the order of a surface. This parameter is scale-independent and can be used to compare the organization of a surface at different scales of range and amplitude. To test the accuracy of this roughness parameter versus a hundred existing ones, we created an original statistical bootstrap method. In order to assess the physical relevance of this new parameter, we elaborated a great number of surfaces with various roughness amplitudes on titanium and titanium-based alloys using different physical processes. Then we studied the influence of the roughness amplitude on in vitro adhesion and proliferation of human osteoblasts. It was then shown that our new parameter best discriminates among the cell adhesion phenomena than others' parameters (Average roughness (Ra…)): cells adhere better on isotropic surfaces with a low order, provided this order is quantified on a scale that is more important than that of the cells. Additionally, on these low ordered metallic surfaces, the shape of the cells presents the same morphological aspect as that we can see on the human bone trabeculae. The method used to prepare these isotropic surfaces (electroerosion) could be undoubtedly and easily applied to prepare most biomaterials with complex geometries and to improve bone implant integration. Moreover, the new order parameter we developed may be particularly useful for the fundamental understanding of the mechanism of bone cell installation on a relief and of the formation of bone cell–material interface.

Molecular characterization of genomic AML1-ETO fusions in childhood leukemia.

T(8;21) AML1(CBFA2)-ETO(MTG8) is the most common chromosomal translocation in acute myeloid leukemia (AML) in both children and adults. We sought to understand the structure and gain insight into the fusion process between AML1 and ETO by sequencing genomic fusions in 17 primary childhood AMLs and two cell lines with t(8;21). Reciprocal translocations were sequenced for seven of the 19 samples. We assumed a null hypothesis that the translocation breakpoints would be evenly distributed along the intronic breakpoint cluster regions. Testing for multimodality via smoothed bootstrap statistical methods suggested, however, the presence of two separate cluster regions within both the AML1 and ETO breakpoint cluster regions. ETObreakpoints were predominantly located in intron 1B in a defined cluster 5' of exon 1A (scan statistic P value = 0.00001). All patients with available RNA expressed an AML1-ETO mRNA fusion between exon 5 of AML1 and exon 2 of ETO. Since the structural restraints for the fusion protein of AML1-ETO exclude exon 1A, we reason that ETO intron 1B harbors a structural feature with propensity for breakage and/or recombination. Chromosomal breakpoints displayed evidence of fusion by a non-homologous end joining process, with microhomologies and nontemplate nucleotides at some fusion junctions. Breakpoints in general displayed similar complexity of duplications, deletions, and insertions to other common pediatric leukemia translocations (TEL-AML1, MLL-AF4, PML-RARA, CBFB-MYH11) that we and others have analyzed.

Direct solid sample analysis of geological samples with SS-GF-AAS and use of 3D calibration.

These results from direct solid-sample trace-element analysis, with 3D calibration, follow those of earlier publications. Cd, Cr, Cu, Ni, Pb, and Zn have been determined in complex inorganic powder samples, e.g. sediments, soils, rocks, and minerals. The measurements were performed with two SS-GF-AAS spectrometers which differ in the type of graphite furnace (transverse and longitudinal tube) and the background-correction technique (with and without the Zeeman system). The performance of the 3D calibration method was optimized by systematic investigation and the 2D- and 3D calibration techniques were compared. Another feature is the determination of confidence limits of the 3D calibration. This calibration error was calculated by the statistical bootstrap method. The results of calibration experiments and the precision and accuracy of the determination of trace elements in CRMs show that 3D calibration becomes increasingly essential as the refractory character of the analyte increases. Although there are large differences between the state of development and technical performance of the instruments used, 3D-calibration works with both SS-GF-AAS spectrometers.

Response of gray whales to low-frequency sounds

One transducer from the U.S. Navy SURTASS-LFA source was used during January 1998 to expose migrating gray whales off the California coast to low-frequency sound. These transmissions were 42 s in duration, repeating every 6 min, and 160–330 Hz. The whales were observed from shore stations north and south of the source location. Each pod of whales’ closest point of approach (CPA) to the sound source was estimated from the shore observations. The received level (RL) at the CPA was estimated using measured transmission loss curves and the known source level. The probability of observing whale pods at each RL is computed under both playback and control conditions. The difference between these probabilities as a function of RL provides a measure of avoidance for the animals. Previous work [Malme et al. (1984)] found a 50% change in these probabilities at a RL of 120 dB re:1μPa. For an inshore source location, the current work found 50% avoidance occurred at a RL of 141 dB, with 95% confidence bounds of ±3 dB derived by bootstrap statistical methods. For the offshore source location, 50% avoidance was not achieved for any observed RL. [Work supported by ONR.]

Spatial Pattern Analysis and Sequential Sampling for the Incidence of Leaf Spot on Strawberry in Ohio.

Spatial pattern of the incidence of strawberry leaf spot, caused by Mycosphaerella fragariae (Ramularia brunnea), was quantified on commercial strawberry farms in Ohio. For each planting of strawberry, one or two transects were randomly chosen, and the proportion of leaflets (out of 15) with leaf spot was determined from N = 29 to 87 evenly spaced sampling units. Based on a likelihood ratio test, the beta-binomial distribution described the frequency of diseased leaflets better than the binomial in 93% of the 59 data sets over 3 years. Estimates of mean incidence ranged from 0.0009 to 0.82, with a median of 0.05. Estimates of the beta-binomial aggregation parameter, θ, ranged from 0 to 1.06, with a median of 0.20. Moreover, the estimate of the slope of the binary power law, fitted to the variance data for the 59 data sets, was significantly (P < 0.01) greater than one, indicating that heterogeneity, and hence the pattern of disease incidence at the spatial scale of the sampling units or smaller, was dependent on mean incidence. Spatial autocorrelation and Spatial Analysis by Distance IndicEs (SADIE) analyses detected significant positive association of disease incidence among sampling units in approximately 40% of the data sets, indicating that disease clusters extended beyond the borders of the sampling units in these fields. Collectively, the results show that strawberry leaf spot was characterized by relatively tight clusters of disease (based on θ) that extended beyond the borders of the sampling units in a little under half of the data sets (based on correlations). The information on heterogeneity was used to develop fixed and sequential sampling curves to precisely estimate disease incidence. The sequential-estimation procedure was evaluated using statistical bootstrap methods and performed well over the range of disease incidences encountered.

The bootstrap method as a test for non-centrosymmetricity – Application to tazheranite (Zr,Ca,Ti)O2

Abstract The bootstrap statistical method is applied to the analysis of single-crystal X-ray diffraction data of tazheranite [(Zr,Ca,Ti)O2; cubic, a = 5.117 Å], in order to establish the significance of statistical estimators of noncentrosymmetricity. The lack of the inversion centre is successfully proved showing that the average structure of tazheranite has space group F[unk]3m, due to a different repartition of oxygen vacancies between two sites of the fluorite-type structure. Instead, classical estimators of the intensity distribution and of the refinements were not able to discriminate between Fm[unk]m and F[unk]3m space groups.

The use of the bootstrap statistical method for the pharmacoeconomic cost analysis of skewed data.

In pharmacoeconomics, the comparison of the costs of 2 different drugs used for the same treatment is of great interest. The problem is especially challenging when the drugs are likely to produce costly adverse effects in a small number of patients, which is often the case. The data are then skewed and traditional statistical methods to analyse the difference in the mean costs produced by 2 treatments may be inappropriate. The bootstrap method is presented as an alternative approach. A pharmacoeconomic cost-analysis example is presented and used throughout this article.