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Statistical process control as a tool for monitoring nonoperative time.

BACKGROUND: Administrators need simple tools to quickly identify even small changes in the performance of perioperative systems. This applies both to established systems and to impact assessments of deliberate perioperative system design changes. METHODS: Statistical process control was originally developed to detect nonrandom variation in manufacturing processes by continuous comparison to previous performance. The authors applied the technique to assess the nonoperative time performance between successive cases for same surgeon following themselves in a redesigned operating room. This operating room specifically implemented a new patient care pathway that improves throughput by reducing the nonoperative time. The authors tested how quickly statistical process control detected reductions in nonoperative time. They also tested the ability of statistical process control to detect successively smaller performance changes and investigated its utility for longitudinal process monitoring. RESULTS: Statistical process control detected a clear reduction in nonoperative time after the new operating room had been used for only 2 days. The method could detect nonoperative time changes of between 5 and 10 min per case for a single operating room within one fiscal quarter. Nonoperative time for the new process was globally stable over the 31 months analyzed, but late in the analysis period, the authors detected small performance decrements, mostly attributable to factors external to the new operating room. CONCLUSIONS: Statistical process control is useful for detecting changes in perioperative system performance, represented in this study by nonoperative time. The technique is able to detect changes quickly and to detect small changes over time.

Algorithms↗

Randomization, statistics, and causal inference.

This paper reviews the role of statistics in causal inference. Special attention is given to the need for randomization to justify causal inferences from conventional statistics, and the need for random sampling to justify descriptive inferences. In most epidemiologic studies, randomization and random sampling play little or no role in the assembly of study cohorts. I therefore conclude that probabilistic interpretations of conventional statistics are rarely justified, and that such interpretations may encourage misinterpretation of nonrandomized studies. Possible remedies for this problem include deemphasizing inferential statistics in favor of data descriptors, and adopting statistical techniques based on more realistic probability models than those in common use.

Bayes Theorem↗

Dichotomizing continuous outcome variables: dependence of the magnitude of association and statistical power on the cutpoint.

Dichotomizing a continuous outcome variable casts that variable in traditional epidemiologic terms (that is, disease, no disease). One consequence is overall reduced statistical power. A more fundamental concern is that the magnitude of various measures of association (for example, prevalence ratio, odds ratio) and statistical power depend on the cutpoint used to dichotomize the variable. The phenomenon is illustrated with a hypothetical situation assuming a two-level predictor variable and a normally distributed outcome variable. As the cutpoint is increased from lower to higher values, the prevalence ratio increases steadily, the odds ratio is described by a U-shaped curve, and statistical power is described by an inverted U-shaped curve. Furthermore, the extent of these effects depends on the difference between the means of the continuous outcome variable for the two levels of the predictor variable. An empirical example is given using data on education and blood pressure (dichotomized to create a high blood pressure vs low blood pressure variable). Except at each end of the distribution, the results follow the hypothetical example. The observation has implications for public health and medical treatment; different cutpoints should be examined to determine the optimal cutpoint in terms of policy and/or treatment decisions. The observation described here also has implications for statistical interpretation; statements about the magnitude of association or statistical significance have limited meaning unless both the cutpoint and the distribution of the outcome variable are specified.

Bias↗

Comparison of statistical indicators for the automatic detection of 80 Hz auditory steady state responses.

OBJECTIVE: To evaluate, using receiver operation characteristic (ROC) curves, the performance of several statistical indicators in the objective detection of 80 Hz steady state auditory evoked responses. DESIGN: Steady state auditory evoked responses elicited by amplitude modulated tones of 500 and 1000 Hz, were obtained in 16 normal adults. Recordings were made at intensities ranging from 80 to 30 dB SPL and without stimulation. Four statistics: coherence synchrony measure, circular T2, a new variant of Hotelling T2 (labeled HT2) and a test for hidden periodicity (F test) were calculated. The statistics were compared using ROC curves and bootstrapping techniques. Two outcome measures were considered: behavioral threshold prediction and averaging efficiency. RESULTS: All indicators were highly accurate to detect a response (8 to 9 dB above mean behavioral threshold for the 1000 Hz and 14 to 16 dB for the 500 Hz carrier). Responses could be reliable detected after averaging about five individual epochs of long duration. No statistically significant differences were evidenced though in their capability to predict behavioral threshold or their averaging efficiency. CONCLUSIONS: Despite the more adequate statistical properties of some of these indicators no significant differences were found in their performance. Thus all of these indicators could be recommended for automatic detection of 80 Hz auditory steady state responses.

Adolescent↗

Mastering research critique and statistical interpretation. Guidelines and golden rules.

Mastery of statistical analysis research critique is an important skill for professional nurses. A Guideline for Statistical Analysis and Golden Rules for Statistical Analysis Adequacy are presented and applied to classroom use. Students who learn how to critique research and statistics usage effectively are satisfied consumers and report using knowledge in other clinical courses. Effective strategies to teach statistical analysis critique are discussed.

Data Interpretation, Statistical↗

Should level of measurement considerations affect the choice of statistic?

The belief that the level of measurement (nominal, ordinal, interval, ratio) achieved in the data constrains the type of statistic that may be used legitimately for analysis is examined in general, and in an optometric-vision science context. Theoretical considerations indicate that statistical statements about the data may be made independently of the level of measurement, and that although researchers must be concerned about the quality of their measurement, the role of measurement theory is in the interpretation of the meaning of the investigation's results as a whole not in the governance of the choice of statistic. Empirical studies indicate that measurement considerations can be ignored for the purposes of testing the null hypothesis with little or no resultant error. Finally, adherence to the belief that level of measurement considerations limits statistical choice would result in the use of generally less powerful statistical tests--an undesirable and, all things considered, an unwarranted consequence.

Optics and Photonics↗

Advances in statistical methodology and their application in critical care.

PURPOSE OF REVIEW: To review some of the major advances in statistical methodology of the past two decades and their application to investigations in critical care. RECENT FINDINGS: The introduction of new technologies and the ready availability of advanced computer resources have led to significant developments in statistical methodology. These include the development of computationally intensive methods, improved methods for modeling correlated outcome data, and new methods for handling missing data. Although many of these tools are available in standard statistical software, they remain underutilized in the medical literature. SUMMARY: By becoming familiar with advances in statistical methodology, researchers and clinicians can enhance collaboration with their statistical colleagues, toward the goal of better study design and analysis.

Critical Care↗

The influence of display and statistical factors on the interpretation of metaanalysis results by physicians.

OBJECTIVE: The objective of this study was to determine the extent to which various factors affect the interpretation of metaanalytic results by physicians. STUDY DESIGN: A sample of 120 physicians, selected from The Royal College of Physicians and Surgeons of Canada (RCPSC), was randomly assigned to 1 of 6 groups (n = 20) created from a combination of 3 summary measures and 2 levels of disease severity. The intervention consisted of a written scenario and 4 individual displays of metaanalyses (M-A), each followed by questions related to the interpretation of results of M-A. Two final questions examined statistical familiarity/proficiency with the summary measures used. DATA ANALYSIS: Analyses of variance examined main effects and interactions among 4 factors: summary measure, disease severity, effect size, and statistical consistency of the studies comprising the metaanalysis. Two outcomes were examined: interpretation of the treatment effect and confidence in the interpretation of the treatment effect. PRINCIPAL FINDINGS: Physicians were more likely to favor treatment when the results of the primary randomized, controlled trials (RCTs) were statistically homogeneous (P = 0.001) and when the overall effect size was large (P = 0.001). Also, physicians were more likely to be confident when the results were homogeneous (P = 0.001) and when effect size was large (P = 0.000). Interactions also revealed that the effect of statistical consistency of contributing to RCTs was greatest when data were presented as risk difference for treatment outcome (P = 0.026) and when effect size was small (P = 0.000). CONCLUSIONS: The interpretation of metaanalytic displays is influenced by the overall effect size of M-A, the statistical consistency of the contributing RCTs, and interactions of these factors with display factors.

Adult↗

Emerging standards in statistical practice: implications for clinical trials in rehabilitation medicine.

This article discusses selected issues in statistical practice that occur during the conduct of clinical trials in medical rehabilitation: (1) supplementing null hypothesis statistical testing and P values, (2) determining sample size and statistical power, (3) handling missing data, and (4) dealing with multiplicity (i.e., multiple endpoints, multiple statistical comparisons, and repeated measurements). Suggested strategies to address these issues are offered in light of the International Conference on Harmonisation guideline "Statistical Principles for Clinical Trials."

Clinical Trials as Topic↗

Replica model for an unusual directed polymer in 1+1 dimensions and prediction of the extremal parameter of gapped sequence alignment statistics.

Sequence alignment is one of the most important bioinformatics tools for modern molecular biology. The statistical characterization of gapped alignment scores has been a long-standing problem in sequence alignment research. In this paper, we provide a self-contained exposition of sequence alignment, a short review about how this problem is related to the directed polymer problem in statistical physics, and some analytical results that can be used for predicting alignment score statistics. Basically, we present two classes of solutions for the gapped alignment statistics by explicitly calculating the evolution of the few-replica partition function in 1+1 dimensions. We have obtained the conditions under which the more important extremal parameter lambda, characterizing the alignment score statistics, becomes predictable.

Algorithms↗

Score statistics of global sequence alignment from the energy distribution of a modified directed polymer and directed percolation problem.

Sequence alignment is one of the most important bioinformatics tools for modern molecular biology. The statistical characterization of gapped alignment scores has been a long-standing problem in sequence alignment research. Using a variant of the directed path in random media model, we investigate the score statistics of global sequence alignment taking into account, in particular, the compositional bias of the sequences compared. Such statistics are used to distinguish accidental similarity due to compositional similarity from biologically significant similarity. To accommodate the compositional bias, we introduce an extra parameter p indicating the probability for positive matching scores to occur. When p is small, a high scoring alignment obviously cannot come from compositional similarity. When p is large, the highest scoring point within a global alignment tends to be close to the end of both sequences, in which case we say the system percolates. By applying finite-size scaling theory on percolating probability functions of various sizes (sequence lengths), the critical p at infinite size is obtained. For alignment of length t, the fact that the score fluctuation grows as chi(t)1/3 is confirmed upon investigating the scaling form of the alignment score. Using the Kolmogorov-Smirnov statistics test, we show that the random variable , if properly scaled, follows the Tracy-Widom distributions: Gaussian orthogonal ensemble for p slightly larger than pc and Gaussian unitary ensemble for larger p. Although these results deepen our understanding of the distribution of alignment scores, the use of these results in practical applications remains somewhat heuristic and needs to be further developed. Nevertheless, the possibility of characterizing score statistics for modest system size (sequence lengths), via proper reparametrization of alignment scores, is illustrated.

Algorithms↗

Optimizing statistical Shake-and-Bake for Se-atom substructure determination.

A novel statistical approach to the phase problem in X-ray crystallography was introduced in a recent paper [Xu & Hauptman (2004), Acta Cryst. A60, 153-157]. In this approach, a new minimal function based on the statistical distribution of structure-invariant values serves as the foundation of an optimization procedure called statistical Shake-and-Bake. Favorable application of this procedure to Se-atom substructure determination depends on the choice of the statistical interval over which the function is defined. The effects of interval variation have been studied for 19 Se-atom substructures ranging in size from five to 70 Se atoms in the asymmetric unit and the results have shown an overall improvement in success rate relative to traditional Shake-and-Bake. Statistical Shake-and-Bake is being incorporated as the default optimization procedure in newly distributed versions of the SnB and BnP computer programs.

Crystallography, X-Ray↗

A mean blood velocity statistic for the Doppler signal from a narrow ultrasound beam.

An easily calculable statistic proportional to the instantaneous spatial mean blood velocity through a vessel cross section is derived from Doppler power spectral estimates for the case where the Doppler beam is assumed to be of negligible thickness compared to the vessel diameter. This is an alternative statistic to that derived where uniform insonation is assumed, an assumption thought to be poorer in many real cases. The main requirement is that the velocity profile is monotonic increasing from the vessel wall to the vessel center. Errors in each statistic are compared for a variety of true beam dimensions, using a variety of velocity profiles, and the new statistic is shown to incur less error for Gaussian beam response profiles with a standard deviation less than 0.4 of the vessel radius, or for rectangular response profiles with a width less than 0.65 of the vessel diameter. If an estimate can be made of the true beam dimensions and vessel diameter, a weighted sum of the two statistics can give a more accurate estimate of mean velocity. The case of a beam displaced from the center of the vessel is also considered, and errors are found to be less than 4% for a displacement of 20% of the vessel radius.

Bias↗

Statistical analysis of topographic maps of short-latency somatosensory evoked potentials in normal and parkinsonian subjects.

This work had the following objectives: i) to integrate temporal analysis (N30 peak) with power-spectrum topographic mapping of short-latency somatosensory evoked potentials (SEP's) recorded in parkinsonian and normal control subjects; and ii) to analyze with a new statistical approach the between-group topographical differences in both the time and frequency domains. The principal aim was to better determine the topography of the scalp frontal areas where the amplitude of the N30 wave was previously found to be significantly reduced in parkinsonians. The statistical procedure was based on the combined use of descriptive data analysis (DDA) and multivariate analysis. In the context of DDA, an improved version of significance probability mapping (SPM) was used by which it is possible to evaluate homo- and nonhomoscedastic data with parametric tests. The statistical evaluation of between-group differences was performed with the multivariate Hotelling's T2 test and the associated post hoc test. With this statistical procedure, it was possible to determine that the between-group statistical differences in both the temporal and power spectrum distributions were localized only in midline and contiguous contralateral frontal areas of the scalp.

Brain Mapping↗

Activation detection in fMRI using a maximum energy ratio statistic obtained by adaptive spatial filtering.

An adaptive spatial filtering method is proposed that takes into account contextual information in fMRI activation detection. This filter replaces the time series of each voxel with a weighted average of time series of a small neighborhood around it. The filter coefficients at each voxel are derived so as to maximize a test statistic designed to indicate the presence of activation. This statistic is the ratio of the energy of the filtered time series in a signal subspace to the energy of the residuals. It is shown that the filter coefficients and the maximum energy ratio can be found through a generalized eigenproblem. This approach equates the filter coefficients to the elements of an eigenvector corresponding to the largest eigenvalue of a specific matrix, while the largest eigenvalue itself becomes the maximum energy ratio that can be used as a statistic for detecting activation. The distribution of this statistic under the null hypothesis is derived by a nonparametric permutation technique in the wavelet domain. Also, in this paper we introduce a new set of basis vectors that define the signal subspace. The space spanned by these basis vectors covers a wide range of possible hemodynamic response functions (HRF) and is applicable to both event related and block design fMRI signal analysis. This approach circumvents the need for a priori assumptions about the exact shape of the HRF. Resting-state experimental fMRI data were used to assess the specificity of the method, showing that the actual false-alarm rate of the proposed method is equal or less than its expected value. Analysis of simulated data and motor task fMRI datasets from six volunteers using the method proposed here showed an improved sensitivity as compared to a conventional test with a similar statistic applied to spatially smoothed data.

Algorithms↗

Visually distinct patterns with matching subband statistics.

A commonly used representation of a visual pattern is a statistical distribution measured from the output of a bank of filters (Gaussian, Laplacian, Gabor, etc.). Both marginal and joint distributions of filter responses have been advocated and effectively used for a variety of vision tasks, including texture classification, texture synthesis, object detection, and image retrieval. This paper examines the ability of these representations to discriminate between an arbitrary pair of visual stimuli. Examples of patterns are derived that provably possess the same marginal and joint statistical properties, yet are "visually distinct." This is accomplished by showing sufficient conditions for matching the first k moments of the marginal distributions of a pair of images. Then, given a set of filters, we show how to match the marginal statistics of the subband images formed through convolution with the filter set. Next, joint statistics are examined and images with similar joint distributions of subband responses are shown. Finally, distinct periodic patterns are derived that possess approximately the same subband statistics for any arbitrary filter set.

Algorithms↗

Homogeneity score test for the intraclass version of the kappa statistics and sample-size determination in multiple or stratified studies.

When the intraclass correlation coefficient or the equivalent version of the kappa agreement coefficient have been estimated from several independent studies or from a stratified study, we have the problem of comparing the kappa statistics and combining the information regarding the kappa statistics in a common kappa when the assumption of homogeneity of kappa coefficients holds. In this article, using the likelihood score theory extended to nuisance parameters (Tarone, 1988, Communications in Statistics-Theory and Methods 17(5), 1549-1556) we present an efficient homogeneity test for comparing several independent kappa statistics and, also, give a modified homogeneity score method using a noniterative and consistent estimator as an alternative. We provide the sample size using the modified homogeneity score method and compare it with that using the goodness-of-fit method (GOF) (Donner, Eliasziw, and Klar, 1996, Biometrics 52, 176-183). A simulation study for small and moderate sample sizes showed that the actual level of the homogeneity score test using the maximum likelihood estimators (MLEs) of parameters is satisfactorily close to the nominal and it is smaller than those of the modified homogeneity score and the goodness-of-fit tests. We investigated statistical properties of several noniterative estimators of a common kappa. The estimator (Donner et al., 1996) is essentially efficient and can be used as an alternative to the iterative MLE. An efficient interval estimation of a common kappa using the likelihood score method is presented.

Alcohol Drinking↗

Explorative statistical analysis of planar point processes in microscopy.

Basic methods of explorative statistical analysis for stationary and isotropic planar point processes are briefly and informally reviewed. At the explorative level, planar point patterns may be characterized in terms of the intensity, the K-function and the pair correlation function. These second-order functions enable one to classify a given point process as completely random, clustering or repulsive. The repulsive behaviour may be quantified by an estimate of the hard-core distance. In the exploratory approach, the statistics are essentially free from model assumptions. Second-order spatial functions have been estimated to characterize genuine planar point processes in the macroscopic domain, for example in forestry, geography and epidemiology. For light microscopy and transmission electron microscopy, two situations are distinguished, which may be summarized as the genuine planar case and the stereological case. In the genuine planar case, a direct interpretation of the results of spatial statistics is feasible. Here, monolayers in cell culture, intramembranous particles on freeze fracture specimens and amacrine cells of the retina are mentioned as examples. In the stereological case, point patterns are generated by sections through 3D structures. Here the observed point patterns may arise as the centres of sectional profiles of particles, or as centres of sectional profiles of spatial fibre processes. In both situations, exploratory spatial point process statistics allow a quantitative characterization of sectional images for the purposes of group comparisons and classification. Moreover, for spatial fibre processes it has recently been shown that the observed pair correlation function of the centres of the fibre profiles is an estimate of the reduced pair correlation function of the fibre process in 3D. Hence for fibre processes a stereological interpretation of point process statistics obtained from sections is an additional option.

Data Interpretation, Statistical↗