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A Gaussian statistical mechanical model for the equilibrium thermodynamics of barnase folding.

Given an all non-hydrogen-atom potential function that implicitly includes solvation effects, it is possible to adjust its parameters to favor the correct native structure for several proteins over decoys produced by ungapped threading. It is also possible to further train it to reproduce the experimental free energy of unfolding in aqueous solution at 298 K for wild-type barnase and 66 mutants. For this, the native state is represented by the crystal structure at a single energy level with a calculated low degeneracy; the denatured state is represented by the extended conformation and a high calculated degeneracy. The same two-state model can be extended to account for the stability of all 67 sequences toward urea denaturation at 298 K by building in a solvation term that depends on urea concentration. With the addition of one more parameter set to give the correct heat capacity of unfolded barnase in solution, it is possible to approximate the experimental thermodynamics of barnase thermal denaturation: melting temperature, width of thermal transition, deltaG, deltaH, deltaS, and deltaCp. This requires a novel sort of statistical mechanical model where the two states each have a Gaussian density of microscopic state distribution as a function of energy.

Bacillus↗

Exact histogram specification.

While in the continuous case, statistical models of histogram equalization/specification would yield exact results, their discrete counterparts fail. This is due to the fact that the cumulative distribution functions one deals with are not exactly invertible. Otherwise stated, exact histogram specification for discrete images is an ill-posed problem. Invertible cumulative distribution functions are obtained by translating the problem in a K-dimensional space and further inducing a strict ordering among image pixels. The proposed ordering refines the natural one. Experimental results and statistical models of the induced ordering are presented and several applications are discussed: image enhancement, normalization, watermarking, etc.

Algorithms↗

Statistical cerebrovascular segmentation in three-dimensional rotational angiography based on maximum intensity projections.

Segmentation of three-dimensional rotational angiography (3D-RA) can provide quantitative 3D morphological information of vasculature. The expectation maximization-(EM-) based segmentation techniques have been widely used in the medical image processing community, because of the implementation simplicity, and computational efficiency of the approach. In a brain 3D-RA, vascular regions usually occupy a very small proportion (around 1%) inside an entire image volume. This severe imbalance between the intensity distributions of vessels and background can lead to inaccurate statistical modeling in the EM-based segmentation methods, and thus adversely affect the segmentation quality for 3D-RA. In this paper we present a new method for the extraction of vasculature in 3D-RA images. The new method is fully automatic and computationally efficient. As compared with the original 3D-RA volume, there is a larger proportion (around 20%) of vessels in its corresponding maximum intensity projection (MIP) image. The proposed method exploits this property to increase the accuracy of statistical modeling with the EM algorithm. The algorithm takes an iterative approach to compiling the 3D vascular segmentation progressively with the segmentation of MIP images along the three principal axes, and use a winner-takes-all strategy to combine the results obtained along individual axes. Experimental results on 12 3D-RA clinical datasets indicate that the segmentations obtained by the new method exhibit a high degree of agreement to the ground truth segmentations and are comparable to those produced by the manual optimal global thresholding method.

Algorithms↗

Subject-domain approach to the study of air pollution effects on schoolchildren's illness absence.

In this paper, the authors propose a new statistical modeling technique, the subject-domain approach, which is theoretically proven to be equivalent to the time-domain approach in detecting an association between exposure and response with time trends. The authors use an empirical data set from a school absence monitoring study conducted during the 1994-1995 school year in Taiwan to demonstrate this subject-domain approach's application to environmental epidemiologic studies. Because the subject-domain models can control the influential personal confounding factors in the models, they show greater statistical power than the traditional time-domain approaches in determining the relation between air pollution and illness absences. The authors' models found that the schoolchildren's risks of illness absence were significantly related to acute exposures to nitrogen dioxide and nitrogen oxides with a 1-day lag (p < 0.01) at levels below the World Health Organization's guidelines. By contrast, the authors could not detect significant associations between air pollution and schoolchildren's absenteeism using time-domain approaches. Such findings imply that the models built on subject domain may be a general solution to the problem of the ecologic fallacy, which is commonly encountered in environmental and social epidemiologic studies.

Absenteeism↗

Enoxaparin in unstable angina/non-ST-segment elevation myocardial infarction: treatment benefits in prespecified subgroups.

BACKGROUND: Two large-scale phase III clinical trials, the Efficacy and Safety of Subcutaneous Enoxaparin in Non-Q-wave Coronary Events (ESSENCE) trial and the Thrombolysis in Myocardial Infarction (TIMI) 11B study, have shown the low-molecular-weight heparin, enoxaparin, to be more effective than unfractionated heparin (UFH) in reducing the risk of death and severe cardiac events in patients with rest unstable angina and/or non-ST-segment elevation myocardial infarction (NSTEMI). However, patients with NSTEMI acute coronary syndromes are a heterogeneous group. METHODS: A meta-analysis using pooled data from ESSENCE and TIMI 11B was performed to examine the efficacy of enoxaparin in different patient subgroups. In addition, a statistical model was developed to test which factors best predicted an enhanced treatment effect. RESULTS: Enoxaparin was more effective than intravenous dose-adjusted UFH in reducing the incidence of the composite endpoint (including death, myocardial infarction or recurrent angina prompting urgent revascularization) in the majority of subgroups at 43 days after randomization. Univariate analyses revealed that there was a greater benefit with enoxaparin in patients with ST-segment deviation or elevated cardiac enzyme markers on admission, women, nonsmokers and patients with characteristics indicative of higher cardiac risk, including prior percutaneous coronary interventions, being at least 65 years old, prior angina and prior aspirin use. Multivariate statistical modelling of treatment effect revealed that ST-segment depression and electrocardiographic changes were the best predictors of an enhanced treatment effect. CONCLUSIONS: These data reinforce previous evidence suggesting that enoxaparin administered subcutaneously twice daily may be considered as an alternative to intravenous UFH in the acute treatment of a broad range of patients with unstable coronary artery disease.

Adult↗

Improving macromolecular atomic models at moderate resolution by automated iterative model building, statistical density modification and refinement.

An iterative process for improving the completeness and quality of atomic models automatically built at moderate resolution (up to about 2.8 A) is described. The process consists of cycles of model building interspersed with cycles of refinement and combining phase information from the model with experimental phase information (if any) using statistical density modification. The process can lead to substantial improvements in both the accuracy and completeness of the model compared with a single cycle of model building. For eight test cases solved by MAD or SAD at resolutions ranging from 2.0 to 2.8 A, the fraction of models built and assigned to sequence was 46-91% (mean of 65%) after the first cycle of building and refinement, and 78-95% (mean of 87%) after 20 cycles. In an additional test case, an incorrect model of gene 5 protein (PDB code 2gn5; r.m.s.d. of main-chain atoms from the more recent refined structure 1vqb at 1.56 A) was rebuilt using only structure-factor amplitude information at varying resolutions from 2.0 to 3.0 A. Rebuilding was effective at resolutions up to about 2.5 A. The resulting models had 60-80% of the residues built and an r.m.s.d. of main-chain atoms from the refined structure of 0.20 to 0.62 A. The algorithm is useful for building preliminary models of macromolecules suitable for an experienced crystallographer to extend, correct and fully refine.

Algorithms↗

Generation and statistical mechanical modeling of Z-DNA in the mouse metallothionein I promoter.

The mouse metallothionein I promoter has a potential Z-DNA sequence 86-102 bases upstream from the transcription start. The alternating purine/pyrimidine nature of this sequence, d-(GCGCGTGACTATGCGTG), is interrupted by a central d(AC) dinucleotide. We reversed the d(AC) to d(CA) by site-directed mutagenesis and subcloned the wild-type and mutated 218 base pair (bp) SstI-BglII fragment containing this region into pUC12. By two-dimensional chloroquine gel analysis, the mutant promoter clearly underwent a B-Z transition with a resulting loss of at least five twists. Purines within this sequence exhibited diethyl pyrocarbonate (DEP) sensitivity, which extended in both the 5' and 3' direction encompassing a region of approximately 32 base pairs. When subjected to sufficient torsional stress, the wild-type sequence showed weak evidence of a transition on chloroquine gels and clear DEP sensitivity with a similar, yet distinct pattern. Statistical mechanical modeling of the chloroquine gel analysis demonstrated that the average free energy of propagation for the mutant sequence (0.7-0.9 kcal mol-1 bp-1) was approximately twice that for d(CG)n sequences and that the sequence d(GACGCGGGGCGCGTGCATATGCGTGG) forms the core Z-DNA region.

Animals↗

Can we determine a threshold level for allergenic foods by statistical analysis of published data in the literature?

BACKGROUND: The aim of this paper was to investigate whether a statistical model could be developed to estimate a "threshold" dose for foods eliciting allergic reactions in susceptible patients. The threshold dose is defined to be one that elicits allergic reactions in a given (small) proportion of susceptible patients, using data from published studies. METHODS: Based on data available from the literature, we developed a statistical model using the actual allergen content in the four foods, where data for allergen content are available (peanut, soy, egg, milk). RESULTS: The model demonstrated that the threshold doses giving a reaction of one in a million in susceptible patients were within the same order of magnitude for egg, milk and soy, but were an order of magnitude lower for peanut flour: 0.005 mg of cow's milk, 0.002 mg of fresh hen's egg, 0.0007 mg of peanut, or 0.0013 mg of soy flour. CONCLUSIONS: Although several assumptions were made in creating this statistical model, we demonstrated that the previously published differences in threshold doses for various foods can be largely eliminated by comparing actual allergen content; this may therefore serve as a model for further studies.

Allergens↗

An experimental design approach to retrospective exposure assessment.

There are several methods currently in use for retrospective estimation of quantitative exposure levels in occupational and environmental epidemiologic studies. The most popular is a job-exposure matrix approach using a combination of existing data and professional judgment. Another method is the use of statistical models based on available exposure data. The authors present an alternative approach using an experimental design in which several factors thought to affect exposure levels are identified and set at specific levels in a cross-classified design. This approach was used to estimate historical exposures to formaldehyde in a mortality study of embalmers. Exposures were estimated as a function of solution concentration, air exchange rate, and autopsied versus intact body. There were 12 combinations involving these 3 factors and a total of 25 embalming procedures (approximately 2 replicates of each combination) performed at a college of mortuary science. In addition to these design factors several covariates such as temperature, humidity, and the occurrence of spills were considered in an analysis of covariance statistical model. The results of the model prediction were validated against published measurements, and field samples were taken in several funeral homes. The overall accuracy of the model predictions was comparable to the variation found in replicate measurements of identical embalming procedures.

Embalming↗

Forecasting peak daily ozone levels--I. A regression with time series errors model having a principal component trigger to fit 1991 ozone levels.

This research was motivated by the need to warn the population of Milwaukee, WI, on high-ozone days. A statistical model for the peak daily 1-hr ozone level is proposed. A Regression with Time Series Errors (RTSE) model, which includes a principal component (PC) trigger, is the basis for forecasting the peak daily 1-hr ozone level. The RTSE model, with a PC trigger, is first employed to estimate daily peak ozone measured at the University of Wisconsin, Milwaukee-North (UWM-N), during the 1991 ozone season. The RTSE model uses peak daily temperature, morning vector average wind direction, and the PC trigger as predictor variables. The PC trigger was designed to summarize atmospheric circumstances when peak ozone was greater than 100 parts per billion (ppb). It is verified that the RTSE model, with a PC trigger, significantly improves the prediction of peak daily ozone, particularly peak ozone greater than 100 ppb. In comparison with the RTSE model without the PC trigger, the RTSE model with a PC trigger raised the R2 from 0.680 to 0.809. It is suggested that the RTSE model, with the PC trigger, is an adequate statistical model that has the potential for real-time ozone forecasting.

Air Pollutants↗

The spatial association between community air pollution and mortality: a new method of analyzing correlated geographic cohort data.

We present a new statistical model for linking spatial variation in ambient air pollution to mortality. The model incorporates risk factors measured at the individual level, such as smoking, and at the spatial level, such as air pollution. We demonstrate that the spatial autocorrelation in community mortality rates, an indication of not fully characterizing potentially confounding risk factors to the air pollution-mortality association, can be accounted for through the inclusion of location in the model assessing the effects of air pollution on mortality. Our methods are illustrated with an analysis of the American Cancer Society cohort to determine whether all cause mortality is associated with concentrations of sulfate particles. The relative risk associated with a 4.2 microg/m(3) interquartile range of sulfate distribution for all causes of death was 1.051 (95% confidence interval 1.036-1.066) based on the Cox proportional hazards survival model, assuming subjects were statistically independent. Inclusion of community-based random effects yielded a relative risk of 1.055 (1.033, 1.077), which represented a doubling in the residual variance compared to that estimated by the Cox model. Residuals from the random-effects model displayed strong evidence of spatial autocorrelation (p = 0.0052). Further inclusion of a location surface reduced the sulfate relative risk and the evidence for autocorrelation as the complexity of the location surface increased, with a range in relative risks of 1.055-1.035. We conclude that these data display both extravariation and spatial autocorrelation, characteristics not captured by the Cox survival model. Failure to account for extravariation and spatial autocorrelation can lead to an understatement of the uncertainty of the air pollution association with mortality.

Adolescent↗

Can early closure and restenosis after endoluminal stenting be predicted from clinical, procedural, and angiographic variables at the time of intervention?

OBJECTIVES: To develop a statistical model to assess the risk of early closure and restenosis on the basis of the information available at the time of stent implantation. DESIGN: An exploratory forward, stepwise multivariate logistic regression for each adverse event and multivariate polychotomous analysis for both events. SETTING: Tertiary referral centre for interventional treatment of coronary artery disease. PATIENTS: 243 consecutive, successful stenting procedures between 1986 and 1993 with the Wallstent, the Palmaz-Schatz and Wiktor stents with analysis of clinical, procedural, and angiographic variables. MEAN OUTCOME MEASURES: Early closure was defined as angiographically documented stent thrombosis within the first 3 weeks after implantation and restenosis according to the 50% reference diameter reduction criterion. RESULTS: Overall early closure and restenosis rates were 14.4% (35/243) and 19.2% (40/208, for a 97% repeat angiography rate). The statistical model predicted a worse outcome for male patients, with less restenosis in female patients. The only risk factor in female patients was the presence of collaterals to the target lesion. For male patients the following risk factors for closure and restenosis were retained: multiple stent implantation during the same session, the presence of collaterals to the target lesion, stenting of the left anterior descending artery or of the left circumflex artery, and bailout stenting. Only bailout stenting implied a decreased restenosis risk. CONCLUSIONS: Clinical, procedural and angiographic variables increase the risk for early closure and restenosis after endoluminal stenting. The prediction models described above need to be validated prospectively.

Angina Pectoris↗

The third molar controversy: framing the controversy as a public health policy issue.

PURPOSE: This article summarizes the current research available concerning the removal of impacted third molars, and provides a background from which practitioners, public health policy advocates, and third-party payers can more objectively assess the the issues of appropriateness of care and overutilization of third molar surgery. MATERIALS AND METHODS: A literature review was undertaken, with emphasis on noninterventional outcome studies and studies using statistical modeling techniques. RESULTS: The health care resources being devoted to the removal of third molars are in the billions of dollars. There is an attempt at limiting these expenditures by third-party payers. These attempts have focused on the prophylactic removal of asymptomatic third molars. Some sources label the procedure as unnecessary surgery. Analysis of the literature does not answer this question with any degree of confidence. CONCLUSION: There appears to be a need for large population-based studies to provide practitioners with data to help them decide when intervention is indicated and when it is not. There is little agreement on how many third molars are being removed for so-called prophylactic reasons. The studies that are available on the nonintervention course are few and have significant flaws. The studies that argue against prophylactic removal are largely based on statistical models. The application of these models as a basis for clinical decision making is questionable. The effects of provider supply and reimbursement must be considered as an integral part of the controversy.

Consensus Statements as Topic↗

Effects of hemoglobin symmetry in a statistical equilibrium model for oxygen binding.

The effect of hemoglobin symmetry on the statistical mechanics of its motions is considered. Hemoglobin binding equilibrium constants are presented in which symmetry factors appear that differ from one binding step to another. Inclusion of the symmetry factors improves the fit of a symmetry-modified Koshland, Némethy, Filmer expression (1966, Biochemistry, 5:365-385) with tetrahedral oxy-oxyhemoglobin subunit interactions to the high-ionic-strength binding curve of Rossi-Fanelli, Antonini and Caputo (1961, J. Biol. Chem., 236:397-400).

Hemoglobins↗

Multivariate voxel-based morphometry successfully differentiates schizophrenia patients from healthy controls.

Currently available laboratory procedures might provide additional information to psychiatric diagnostic systems for more valid classifications of mental disorders. To identify the correlative pattern of gray matter distribution that best discriminates schizophrenia patients from healthy subjects, we applied discriminant function analysis techniques using the multivariate linear model and the voxel-based morphometry. The first analysis was conducted to obtain a statistical model that classified 30 male healthy subjects and 30 male schizophrenia patients diagnosed according to current operational criteria. The second analysis was performed to prospectively validate the statistical model by successfully classifying a new cohort that consisted of 16 male healthy subjects and 16 male schizophrenia patients. Inferences about the structural relevance of the gray matter distribution could be made if the individual profile of pattern expression could be linked to the specific diagnosis of each subject. The result was that 90% of the subjects were correctly classified by the eigenimage, and the Jackknife approach revealed well above chance accuracy. The pattern of the eigenimage was characterized by positive loadings indicating gray matter decline in the patients in the lateral and medial prefrontal regions, insula, lateral temporal regions, medial temporal structures, and thalamus as well as the negative loadings reflecting gray matter increase in the patients in the putamen and cerebellum. When the eigenimage derived from the original cohort was applied to classify data from the second cohort, it correctly assigned more than 80% of the healthy subjects and schizophrenia patients. These findings suggest that the characteristic distribution of gray matter changes may be of diagnostic value for schizophrenia.

Adult↗

Segregation analysis of NIDDM in Caucasian families.

Non-insulin-dependent diabetes mellitus (NIDDM) has a substantial genetic component, but the mode of inheritance and the molecular basis are unknown. We have undertaken segregation analysis of NIDDM after studying 247 subjects in 59 Caucasian nuclear pedigrees ascertained without regard to family history of the disorder. The analyses were performed using POINTER and COMDS, which are computer programs which apply statistical models to the data. POINTER analysis was performed defining the phenotype as a presence or absence of hyperglycaemia. Among single locus hypothesis, the analyses rejected a recessive model and favoured a dominant model, but could not statistically show that this fitted better than a mixed model (a single locus against a polygenic background) or a polygenic model. COMDS analysis assumed a continuum of hyperglycaemia from normality to NIDDM, classified family members into a series of diathesis classes with increasing plasma glucose levels and compared the distribution with that found by screening the normal population. This analysis improved the likelihood of a dominant single locus model and suggested a gene frequency of 7.4%. It raised the possibility of a second locus, but cannot identify or exclude a polygenic model. In conclusion, two types of segregation analyses rejected a recessive model and favoured a dominant model of inheritance, although they could not statistically show that this fitted better than the polygenic model. The results raised the possibility of a common dominant gene with incomplete penetrance, but genetic analysis of NIDDM needs to take into account the likelihood of polygenic inheritance with genetic heterogeneity.

Adult↗

Impact of nonmeasurable borders and variation in cross-section counts on intravascular ultrasound measurement of atherosclerotic plaque volume.

The inability to measure borders and variation in the number of 1-mm cross sections acquired from an identical length of vessel in serial intravascular ultrasound (IVUS) pullbacks represents potential errors in calculating volumes by IVUS. In a clinical IVUS trial, the percentage of nonmeasurable lumen and external elastic membrane borders, and the percent variation in the number of 1-mm cross sections acquired from an identical vessel length at 2 separate time points, were determined. A statistical model that simulated the effect of varying the percentage of the total number of cross sections in a pullback (i.e., sample fraction) was developed using SAS software. Mean and maximum errors for calculation of atheroma volume for each sample fraction were determined. The mean percentage of nonmeasurable lumen and external elastic membrane borders in an individual patient was 8.4 +/- 8.4% and 17.4 +/- 18.4%, respectively. Mean variation in the number of 1-mm cross sections acquired in serial studies was 5.6 +/- 6.2%. A decrease in sample fraction from 95% to 50% was associated with a linear increase in the mean and maximum errors in atheroma volume, from 2.0 +/- 0.9% and 5.9 +/- 3.0%, to 7.1 +/- 2.8% and 23.4 +/- 10.3%, respectively. Thus, nonmeasurable borders and variation in the number of 1-mm cross sections acquired from an identical length of vessel in serial studies are real considerations in clinical IVUS trials. However, given the reported incidence of these considerations in this clinical trial, our statistical model suggests that the impact of each of these considerations on atheroma volume calculation is small.

Coronary Artery Disease↗

Comparison of compact bone failure under two different loading rates: experimental and modelling approaches.

Understanding the mechanical behaviour of bones up to failure is necessary for diagnosis and prevention of accident and trauma. As far as we know, no authors have yet studied the tensile behaviour of compact bone including failure under dynamic loadings (1 m/s). The originality of this study comes from not only the analysis of compact bone failure under dynamic loadings, the results of which are compared to those obtained under quasi-static loadings, but also the development of a statistical model. We developed a protocol using three different devices. Firstly, an X-ray scanner to analyse bone density, secondly, a common tensile device to perform quasi-static experiments, and thirdly, a special device based upon a hydraulic cylinder to perform dynamic tests. For all the tests, we used the same sample shape which took into account the brittleness of the compact bone. We first performed relaxation and hysteresis tests followed by tensile tests up to failure. Viscous and plastic effects were not relevant to the compact bone behaviour so its behaviour was considered elastic and brittle. The bovine compact bone was three to four times more brittle under a dynamic load than under a quasi-static one. Numerically, a statistical model, based upon the Weibull theory, is used to predict the failure stress in compact bone.

Animals↗