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Biological parametric mapping: A statistical toolbox for multimodality brain image analysis.

In recent years, multiple brain MR imaging modalities have emerged; however, analysis methodologies have mainly remained modality-specific. In addition, when comparing across imaging modalities, most researchers have been forced to rely on simple region-of-interest type analyses, which do not allow the voxel-by-voxel comparisons necessary to answer more sophisticated neuroscience questions. To overcome these limitations, we developed a toolbox for multimodal image analysis called biological parametric mapping (BPM), based on a voxel-wise use of the general linear model. The BPM toolbox incorporates information obtained from other modalities as regressors in a voxel-wise analysis, thereby permitting investigation of more sophisticated hypotheses. The BPM toolbox has been developed in Matlab with a user-friendly interface for performing analyses, including voxel-wise multimodal correlation, ANCOVA, and multiple regression. It has a high degree of integration with the SPM (statistical parametric mapping) software relying on it for visualization and statistical inference. Furthermore, statistical inference for a correlation field, rather than a widely used T-field, has been implemented in the correlation analysis for more accurate results. An example with in vivo data is presented, demonstrating the potential of the BPM methodology as a tool for multimodal image analysis.

Brain↗

Wavelet-based multi-resolution statistics for optical imaging signals: Application to automated detection of odour activated glomeruli in the mouse olfactory bulb.

Optical imaging techniques offer powerful solutions to capture brain networks processing in animals, especially when activity is distributed in functionally distinct spatial domains. Despite the progress in imaging techniques, the standard analysis procedures and statistical assessments for this type of data are still limited. In this paper, we perform two in vivo non-invasive optical recording techniques in the mouse olfactory bulb, using a genetically expressed activity reporter fluorescent protein (synaptopHfluorin) and intrinsic signals of the brain. For both imaging techniques, we show that the odour-triggered signals can be accurately parameterized using linear models. Fitting the models allows us to extract odour specific signals with a reduced level of noise compared to standard methods. In addition, the models serve to evaluate statistical significance, using a wavelet-based framework that exploits spatial correlation at different scales. We propose an extension of this framework to extract activation patterns at specific wavelet scales. This method is especially interesting to detect the odour inputs that segregate on the olfactory bulb in small spherical structures called glomeruli. Interestingly, with proper selection of wavelet scales, we can isolate significantly activated glomeruli and thus determine the odour map in an automated manner. Comparison against manual detection of glomeruli shows the high accuracy of the proposed method. Therefore, beyond the advantageous alternative to the existing treatments of optical imaging signals in general, our framework propose an interesting procedure to dissect brain activation patterns on multiple scales with statistical control.

Algorithms↗

Implicit learning and statistical learning: one phenomenon, two approaches.

The domain-general learning mechanisms elicited in incidental learning situations are of potential interest in many research fields, including language acquisition, object knowledge formation and motor learning. They have been the focus of studies on implicit learning for nearly 40 years. Stemming from a different research tradition, studies on statistical learning carried out in the past 10 years after the seminal studies by Saffran and collaborators, appear to be closely related, and the similarity between the two approaches is strengthened further by their recent evolution. However, implicit learning and statistical learning research favor different interpretations, focusing on the formation of chunks and statistical computations, respectively. We examine these differing approaches and suggest that this divergence opens up a major theoretical challenge for future studies.

Attention↗

Encoding and stability of image statistics in working memory.

Visual working memory contains a representation of certain image statistics (Victor & Conte, 2004), in addition to a pixel-by-pixel representation. Here, we show that the representation of statistics is more stable in time (up to 3000 ms) than the pixel-by-pixel representation, especially for changes in luminance and local high-order statistics, and is not affected by visual masking. Bilaterally symmetric arrays and arrays with local correlations are more readily encoded than random ones, but a change in the presence of bilateral symmetry, per se, contributes only modestly to the ability to detect that an array has changed.

Adult↗

A statistical model to compare road mortality in OECD countries.

The objective of this paper is to compare safety levels and trends in OECD countries from 1980 to 1994 with the help of a statistical model and to launch international discussion and further research about international comparisons. Between 1980 and 1994, the annual number of fatalities decreased drastically in all the selected countries except Japan (+ 12%), Greece (+ 56%) and ex-East Germany (+ 50%). The highest decreases were observed in ex-West Germany (- 48%), Switzerland (- 44%), Australia (- 40%), and UK (- 39%). In France, the decrease in fatalities over the same period reached 34%. The fatality rate, an indicator of risk, decreased in the selected countries from 1980 to 1994 except in the east-European countries during the motorization boom in the late 1980s. As fatality rates are not sufficient for international comparisons, a statistical multiple regression model is set up to compare road safety levels in 21 OECD countries over 15 years. Data were collected from IRTAD (International Road Traffic and Accident Database) and other OECD statistical sources. The number of fatalities is explained by seven exogenous (to road safety) variables. The model, pooling cross-sectional and time series data, supplies estimates of elasticity to the fatalities for each variable: 0.96 for the population; 0.28 for the vehicle fleet per capita; -0.16 for the percentage of buses and coaches in the motorised vehicle fleet; 0.83 for the percentage of youngsters in the population; - 0.41 for the percentage of urban population; 0.39 for alcohol consumption per capita; and 0.39 for the percentage of employed people. The model also supplies a rough estimate of the safety performance of a country: the regression residuals are supposed to contain the effects of essentially endogenous and unobserved variables, independent to the exogenous variables. These endogenous variables are safety performance variables (safety actions, traffic safety policy, network improvements and social acceptance). A new indicator, better than the mortality rate, is then set upon the residuals. Mean estimates of this indicator for the years 1980-1982 and the years 1992-1994 rank the countries in the beginning and at the end of the study period. Countries showing the best ranks (and thus the best performance) in 1980 and 1994 are Sweden, the Netherlands and Norway. The UK and Switzerland reach the top 5 in 1994. Greece, Belgium, Portugal and Spain are the last countries in the classification along with, surprisingly, the USA. France was ranked 18th in 1980 and 15th in 1994 but is ranked amongst the five countries that most improved from 1980 to 1994. This model remains non definitive because it is not able to distinguish between safety performance and unobserved exogenous variables although these exogenous variables could explain more about the differences in levels and trends between the countries. More complex models, particularly highly sophisticated models regarding the number of fatalities with breakdowns by road users or road classes would be needed to give a precise and profound ranking of safety levels and safety improvements between countries.

Accidents, Traffic↗

Statistical analysis of wound-healing rates for pressure ulcers.

To establish a functional model for determining wound-healing rates to use in the evaluation of efficacy of wound therapies, a review was conducted of statistical analysis methods from past wound-healing studies. Because most wounds do not usually close within the period of observation, that is, 12 weeks, evaluating time to 100% closure is not practical. Thus, a new, practical model for statistical analysis was formulated. A Gompertz-like function was applied to wound-healing rates of pressure ulcers, in the context of repeated measures for a nonlinear model. Photographing the wounds weekly, tracing their area with planimetry, and applying this new statistical model allows for the calculation of the expected rate of healing as a function of time. This approach yields a model useful for identifying prognostic factors, evaluating treatments, and improving our understanding of the variables that affect the wound-healing process.

Body Weights and Measures↗

Direct superoxide anion scavenging by a disodium disuccinate astaxanthin derivative: Relative efficacy of individual stereoisomers versus the statistical mixture of stereoisomers by electron paramagnetic resonance imaging.

Carotenoids are a related group of greater than 600 natural compounds, irrespective of geometric- and stereoisomers, with demonstrated antioxidant efficacy. The carotenoids are broadly divided into "carotenes," or non-oxygen substituted hydrocarbon carotenoids, and "xanthophylls," oxygen-substituted carotenoids. The natural compounds are excellent singlet oxygen quenchers as well as lipid peroxidation chain-breakers; this dual antioxidant capacity is generally attributed to the activity of the polyene chain, and increases with the number of conjugated double bonds along the polyene chain length. However, the poor aqueous solubility of most carotenes and the vast majority of xanthophylls limits their use as aqueous-phase singlet oxygen quenchers and direct radical scavengers. A variety of introduction vehicles (e.g., organic solvents, cyclodextrins) have been used to introduce the insoluble carotenoids into aqueous test systems. Hawaii Biotech, Inc. (HBI) successfully synthesized a novel carotenoid derivative, the disodium disuccinate derivative of astaxanthin (3,3(')-dihydroxy-beta,beta-carotene-4,4(')-dione) in all-trans (all-E) form. The novel derivative is a water-dispersible symmetric chiral molecule with two chiral centers, yielding four stereoisomeric forms: 3R,3(')R and 3S,3(')S (enantiomers), and the diastereomeric meso forms (3R,3(')S and 3(')R,3S). The individual stereoisomers were synthesized at high purity (>90% by HPLC) and compared directly for efficacy with the statistical mixture of stereoisomers obtained from the synthesis from the commercial source of astaxanthin (1:2:1 ratio of 3S,3(')S, meso, and 3R,3(')R, respectively). Direct scavenging of superoxide anion was evaluated in a standard in vitro isolated human neutrophil assay by electron paramagnetic resonance (EPR) imaging, employing the spin-trap DEPMPO. Each novel derivative was tested in pure aqueous formulation and in ethanolic formulation shown to completely disaggregate the compounds in solution. In each case, the ethanolic formulation was a more potent scavenging vehicle. No significant differences in scavenging efficiency were noted among the individual stereoisomers and the statistical mixture of stereoisomers, suggesting that the polyene chain alone was responsible for superoxide scavenging. Dose-ranging revealed that the statistical mixture of stereoisomers of the novel derivative, at millimolar (mM) concentrations, could nearly completely eliminate the superoxide anion signal generated in the activated human neutrophil assay. All ethanolic formulations of the novel derivatives exhibited increased scavenging efficiency over equimolar concentrations of non-esterified astaxanthin delivered in a dimethyl sulfoxide (DMSO) vehicle. These novel compounds will likely find utility in applications requiring aqueous delivery of a highly potent direct radical scavenger.

Cyclic N-Oxides↗

Statistical analysis of motor unit firing patterns in a human skeletal muscle.

A statistical analysis of the firing pattern of single motor units in the human brachial biceps muscle is presented. Single motor unit spike trains are recorded and analyzed. The statistical treatment of these spike trains is as stochastic point processes, the theory of which is briefly discussed. Evidence is presented that motor unit spike trains may be modelled by a renewal process with an underlying gaussian probability density. Statistical independence of successive interspike intervals is shown using scatter diagrams; the hypothesis of a gaussian distribution is accepted at the 99th percentile confidence limit, chi-square test, in 90% of the units tested. A functional relationship between the mean and standard deviation is shown and discussed; its implications in obtaining sample size are presented in an appendix.The results of higher order analysis in the form of autocorrelograms and grouped interval histograms are presented. Grouped interval histograms are discussed in the context of motor unit data, and used to confirm the hypothesis that a stable probability density function does not represent a good model of the data at this level of analysis.

Action Potentials↗

An intelligent system for multivariate statistical process monitoring and diagnosis.

A knowledge-based system (KBS) was designed for automated system identification, process monitoring, and diagnosis of sensor faults. The real-time KBS consists of a supervisory system using G2 KBS development software linked with external statistical modules for system identification and sensor fault diagnosis. The various statistical techniques were prototyped in MATLAB, converted to ANSI C code, and linked with the G2 Standard Interface. The KBS automatically performs all operations of data collection, identification, monitoring, and sensor fault diagnosis with little or no input from the user. Navigation throughout the KBS is via menu buttons on each user-accessible screen. Selected process variables are displayed on charts showing the history of the variables over a period of time. Multivariate statistical tests and contribution plots are also shown graphically. The KBS was evaluated using simulation studies with a polymerization reactor through a nonlinear dynamic model. Both normal operation conditions as well as conditions of process disturbances were observed to evaluate the KBS performance. Specific user-defined disturbances were added to the simulation, and the KBS correctly diagnosed both process and sensor faults when present.

Algorithms↗

Clinical importance of directional statistics for electrocardiographic differentiation of smoking habits.

Statistical methods for the analysis of directional data are of relatively recent origin and have not been generally applied in clinical investigations where they are appropriate. This study compares spherical means and standard deviations for directional polarcardiographic variables with the linear means and standard deviations of the same variables for a typical industrial cohort of male white collar workers. Normal subjects were classified by smoking status and by independent clinical evidence of the presence of CHD, and both directional and linear statistics are applied to compare the PCG variables in these groups. Directional statistics more accurately define the spherical means and variances of heart vectors and thereby permit more reliable differentiation of directions, or angles to aid diagnosis.

Adult↗

The statistical merits of various methods of calculating transfer coefficients between environmental media--development of the ideal formula for data-sets with a log-normal distribution.

The statistical treatment of data-sets from environmental pollutant studies in which different measurements are combined to produce averages or comparative factors (e.g., transfer coefficients (TCs), input-output balance values) are considered here, with particular reference to the analysis of data from input-output balance studies of pollutants such as PCBs in animals and humans. Many methods of statistical analysis ignore the fact that all measurements are subject to error, and generally assume that the normal distribution applies to all data-sets, which is commonly inappropriate for environmental (and particularly biological system) data. Considerably different estimations can be obtained by applying different, commonly used, statistical methods, as shown in a simulation study presented here and when applied to data from an input-output balance study of PCBs in humans. Alternative average and combined factor estimators for the treatment of data from these types of studies that give considerable advantages in terms of bias and the ease of assessment of accuracy are proposed.

Animals↗

Evaluating the evidence about therapies. What the clinician needs to know about statistics.

Study design is the most important determinant of whether the study conclusions are likely to be biased or misleading. Clinical practice should be based on the most rigorously designed studies to address a particular question. If a study is well designed and sufficiently powered to give an unbiased and precise estimate of treatment effect, the statistical analyses are usually straightforward and evaluating the statistical methods is not difficult. The statistical methods used in observational studies are more complex and much more difficult to evaluate, but study design (selection of subjects and controls, selection and measurement of confounders) is still a critical determinant of bias in the study results. When clinical practice is based on observational studies, extreme caution must be exercised in concluding that associations imply a causal relationship between the treatment or exposure and the outcome.

Biomedical Research↗

Histopathologic study of human lacrimal gland. Statistical analysis with special reference to aging.

PURPOSE: Histopathologic changes in human lacrimal gland were investigated, and the relation between histopathologic parameters and patient age and sex, as well as the histopathologic differences between palpebral and orbital lobes of the lacrimal gland were analyzed. METHODS: Samples of the main human lacrimal gland that included the palpebral lobes and orbital lobes were taken in 80 autopsies. A statistical analysis was made based on light microscope observations with the following histopathologic changes as parameters: (1) fibrosis (focal, lobular, and diffuse); (2) acinar atrophy (focal, lobular, and diffuse); (3) periductal fibrosis; (4) interlobular ductal dilatation; (5) interlobular ductal proliferation; (6) lymphocytic foci; (7) periductal lymphocytic infiltration; and (8) fatty infiltration. RESULTS: The incidences of these parameters in the palpebral and orbital lobes ranged from 3.8% to 35.0%. Lobular fibrosis, lobular atrophy, diffuse fibrosis, diffuse atrophy, periductal fibrosis, lymphocytic infiltration, and fatty infiltration were more frequent in the orbital lobes with statistical significance, whereas interlobular ductal dilatation was more frequent in the palpebral lobes. There were statistically significant correlations between age and diffuse fibrosis, diffuse atrophy, and periductal fibrosis in the orbital lobes of women, and periductal fibrosis in the palpebral lobes of men. Diffuse fibrosis and diffuse atrophy in the orbital lobes were observed more frequently in elderly women than in elderly men. CONCLUSIONS: Various histopathologic changes were observed in the human lacrimal gland. Diffuse fibrosis, diffuse atrophy, and periductal fibrosis predominantly found in elderly women suggested a relation with keratoconjunctivitis sicca in postmenopausal women. The authors speculate the periductal fibrosis is related to the decrease in tear fluid outflow with age and that interlobular ductal dilatation in the palpebral lobes may be caused by stenosis of the excretory duct in the fornix of conjunctiva. Ductal pathologic changes may be important in lacrimal gland dysfunction.

Adolescent↗

Use of spatial statistics and monitoring data to identify clustering of bovine tuberculosis in Argentina.

The spatial distribution of endemic bovine tuberculosis (TB) in Argentine cattle herds was described using recorded information on the detection of TB-like lesions in cattle slaughtered between March 1995 and 1997 at 126 slaughterhouses with federal inspection. Approximately, 47% (9472396 cattle) of the estimated total number of cattle slaughtered in Argentina during this period was included in the study. Information on the number of cattle per source herd consigned to slaughter, number of cattle with TB-like lesions per herd and the geographical location of counties from which cattle originated was used to investigate spatial clustering of TB. Overall, no evidence of clustering of TB prevalence by county was detected (Moran's autocorrelation statistic I=0.009, P=0.089). However, first- (Cuzick and Edwards' test statistic, T(k)=87, P=0.036) and second-order (T(k)=170, P=0.038) nearest-neighbor case-counties (TB prevalence>median prevalence of all counties, 6.7%) were clustered. Using the spatial scan test based on a Bernoulli model, the most-likely cluster (P=0.001) identified during the study period included 5793 cases of TB (5.2 per 1000 km(2)) in five counties. This cluster coincided with Santa Fe Province, which contains 21% of all dairy cows in Argentina and accounts for 34% of the country's milk production. Several secondary clusters of TB-also located in dairy districts-were identified. Study results demonstrate that bovine TB is clustered in Argentina, and these clusters coincide with dairy cattle production. Identification of clustering can assist efforts to eradicate bovine TB from Argentina. Further spatial investigations need to focus on the reasons why TB is clustered in Argentina. In particular, the relationship between TB clustering and management practices-such as grazing density and production systems-need to be described to assist in the development of disease-control programs. The use of spatial statistics and geographical information systems could meet these needs.

Abattoirs↗

Non-linear effects in dose-time analyses: application of modern statistical techniques.

BACKGROUND AND PURPOSE: The non-linear effect of overall treatment time and total dose on the outcome of fractionated head and neck radiotherapy is of interest. This and other non-linear effects can be investigated using recently developed statistical techniques. This article provides an illustration of the ability of these statistical methods. MATERIALS AND METHODS: Recently developed statistical methods (Hastie, T.J. and Tibshirani, R.J. Generalised Additive Models. Chapman-Hall, London, 1990), called generalized additive models, are applied to data from the patterns of fractionation study (Withers, H.R., Peters, L.J., Taylor, J.M.G., Owen, J.B., Morrison, W.H., Schultheiss, T.E., Keane, T., O'Sullivan, B., van Dyk, J., Gupta, N., Wang, C.C., Jones, C.U., Doppke, K.P., Myint, S., Thompson, M., Parsons, J.T., Mendenhall, W.M., Dische, S., Aird, E.G.A., Henk, J.M., Bidmead, M.A.M., Svoboda, V., Chon, Y., Hanlon, A.L., Peters, T.L. and Hanks, G.E. Local control of carcinoma of the tonsil by radiation therapy: an analysis of patterns of fractionation in nine institutions. Int. J. Radiat. Oncol. Biol. Phys. 33: 549-562, 1995) of tonsil cancer. These techniques enable one to develop models which more accurately represent the relationship between multivariate predictor variables and the outcome variable in a regression analysis. These data driven methods allow the effect of each predictor variable on the outcome to be non-linear and estimated from the data. This is achieved by replacing the standard linear model combination of predictor variables, such as 'alpha0 + alpha1dose + alpha2time' by 'S1(dose) + S2(time)', where S1 and S2 are smooth non-linear functions of dose and time, respectively, which are estimated from the data. RESULTS: In the pattern of fractionation study these methods indicate that the effect of total dose on the probability of local recurrence is linear, but there is a suggestion that the effect of overall treatment time is non-linear. There is no effect of dose and time on the latency time to recurrence of those who do recur, but there is a weak suggestion of a non-linear effect of patients age, with younger patients recurring earlier. CONCLUSIONS: Generalized additive models provide a flexible and powerful means of exploring non-linear effects in experimental data.

Adult↗

Simple bootstrap statistical inference using the SAS system.

Nonparametric bootstrap statistical inference is a robust computer intensive method for generating estimates of statistical variability for which formulae are not known or asymptotic assumptions are not met. A SAS macro that implements simple nonparametric bootstrap statistical inference is presented with an example. The program code is easily generalized to any SAS procedure which includes a BY statement, and to cases of clustered data.

Data Interpretation, Statistical↗

Utility and pitfalls of some statistical methods in active controlled clinical trials.

Increasingly often, the study objective in an active controlled clinical trial without a placebo arm is to show that a new treatment is no less effective than the active control treatment within some noninferiority range. Two issues behind this objective are that of whether the new treatment is efficacious relative to a putative placebo and that of whether the new treatment preserves a certain fraction of effect of the active control. To address these issues, two types of statistical analysis methods are employed in recent pharmaceutical applications. In one type of method, a noninferiority margin is determined, and then the relative effect of the new treatment versus the control is compared against the margin to test noninferiority and the efficacy of the new treatment. In the other type of method, a synthetic statistic is constructed to directly estimate or test the effect of the new treatment relative to the putative placebo without resorting to noninferiority argument. Preservation of control effect can also be estimated and tested. These methods carry some crucial assumptions. The effect of active control is often estimated from a collection of historical placebo controlled trials using the random effects modeling of DerSimonian and Laird. In this work we find that statistical validity of the latter method rests highly on the assumptions that control effect is not reduced in the current active controlled trial population compared to the historical trials and that a normal approximation is appropriate in the random effects modeling. This type of method is very sensitive to departure from these assumptions. In contrast, the former method is ultraconservative in terms of type I error when the assumptions are met and can be anticonservative when control effect is substantially less in the active controlled trial than estimated from the historical placebo controlled trials.

Controlled Clinical Trials as Topic↗

An application of the Zucker-Wittes modified ratio estimate statistic in the Post Coronary Artery Bypass Graft (CABG) clinical trial.

In the Post Coronary Artery Bypass Graft (POST CABG) clinical trial, the primary outcome is substantial worsening (i.e., narrowing of the lumen diameter) of the vein grafts upon comparison of the baseline and follow-up angiograms. The patients had one to five non-occluded vein grafts at entry, so there may be from one to five primary outcome responses per patient. A modified ratio estimate (MRE) statistic, as described previously by Zucker and Wittes, may be used to analyze data of this kind. In the present paper we propose a more powerful MRE statistic when the event rates and/ or intraclass correlations vary according to number of grafts per patient. We also adapt this statistic to the factorial treatment design of the POST CABG clinical trial.

Anticholesteremic Agents↗