Statistical significance of quantitative PCR.

BACKGROUND: PCR has the potential to detect and precisely quantify specific DNA sequences, but it is not yet often used as a fully quantitative method. A number of data collection and processing strategies have been described for the implementation of quantitative PCR. However, they can be experimentally cumbersome, their relative performances have not been evaluated systematically, and they often remain poorly validated statistically and/or experimentally. In this study, we evaluated the performance of known methods, and compared them with newly developed data processing strategies in terms of resolution, precision and robustness. RESULTS: Our results indicate that simple methods that do not rely on the estimation of the efficiency of the PCR amplification may provide reproducible and sensitive data, but that they do not quantify DNA with precision. Other evaluated methods based on sigmoidal or exponential curve fitting were generally of both poor resolution and precision. A statistical analysis of the parameters that influence efficiency indicated that it depends mostly on the selected amplicon and to a lesser extent on the particular biological sample analyzed. Thus, we devised various strategies based on individual or averaged efficiency values, which were used to assess the regulated expression of several genes in response to a growth factor. CONCLUSION: Overall, qPCR data analysis methods differ significantly in their performance, and this analysis identifies methods that provide DNA quantification estimates of high precision, robustness and reliability. These methods allow reliable estimations of relative expression ratio of two-fold or higher, and our analysis provides an estimation of the number of biological samples that have to be analyzed to achieve a given precision.

Self-play: statistical significance

Heinz recently completed a comprehensive experiment in self-play using the FRITZ chess engine to establish the ‘decreasing returns’ hypothesis with specific levels of statistical confidence. This note revisits the results and recalculates the confidence levels of this and other hypotheses. These appear to be better than Heinz’ initial analysis suggests.

Self-play: statistical significance

Heinz recently completed a comprehensive experiment in self-play using the FRITZ chess engine to establish the ‘decreasing returns’ hypothesis with specific levels of statistical confidence. This note revisits the results and recalculates the confidence levels of this and other hypotheses. These appear to be better than Heinz’ initial analysis suggests.

Testing the statistical significance of sector & regional diversification

The question as to whether it is better to diversify a real estate portfolio within a property type across the regions or within a region across the property types is one of continuing interest for academics and practitioners alike. The current study, however, is somewhat different from the usual sector/regional analysis taking account of the fact that holdings in the UK real estate market are heavily concentrated in a single region, London. As a result this study is designed to investigate whether a real estate fund manager can obtain a statistically significant improvement in risk/return performance from extending out of a London based portfolio into firstly the rest of the South East of England and then into the remainder of the UK, or whether the manger would be better off staying within London and diversifying across the various property types. The results indicating that staying within London and diversifying across the various property types may offer performance comparable with regional diversification, although this conclusion largely depends on the time period and the fund manager’s ability to diversify efficiently.

Statistical significance of protein structure prediction by threading

In this study, we estimate the statistical significance of structure prediction by threading. We introduce a single parameter ɛ that serves as a universal measure determining the probability that the best alignment is indeed a native-like analog. Parameter ɛ takes into account both length and composition of the query sequence and the number of decoys in threading simulation. It can be computed directly from the query sequence and potential of interactions, eliminating the need for sequence reshuffling and realignment. Although our theoretical analysis is general, here we compare its predictions with the results of gapless threading. Finally we estimate the number of decoys from which the native structure can be found by existing potentials of interactions. We discuss how this analysis can be extended to determine the optimal gap penalties for any sequence-structure alignment (threading) method, thus optimizing it to maximum possible performance.

Indexes and boundaries for "quantitative significance" in statistical decisions.

Boundaries for delta, representing a "quantitatively significant" or "substantively impressive" distinction, have not been established, analogous to the boundary of alpha, usually set at 0.05, for the stochastic or probabilistic component of "statistical significance". To determine what boundaries are being used for the "quantitative" decisions, we reviewed pertinent articles in three general medical journals. For each contrast of two means, contrast of two rates, or correlation coefficient, we noted the investigators' decisions about stochastic significance, stated in P values or confidence intervals, and about quantitative significance, indicated by interpretive comments. The boundaries between impressive and unimpressive distinctions were best formed by a ratio of greater than or equal to 1.2 for the smaller to the larger mean in 546 comparisons, by a standardized increment of greater than or equal to 0.28 and odds ratio of greater than or equal to 2.2 in 392 comparisons of two rates; and by an r value of greater than or equal to 0.32 in 154 correlation coefficients. Additional boundaries were also identified for "substantially" and "highly" significant quantitative distinctions. Although the proposed boundaries should be kept flexible, indexes and boundaries for decisions about "quantitative significance" are particularly useful when a value of delta must be chosen for calculating sample size before the research is done, and when the "statistical significance" of completed research is appraised for its quantitative as well as stochastic components.

Regression-based techniques for statistical decision making in single-case designs

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions regarding intervention effectiveness in single-case designs. Ordinary least squares estimation is compared to two correction techniques dealing with general trend and one eliminating autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approximate the nominal ones in presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.

Automatic Detection and Classification of Glioma Tumors using Statistical Features

The characterization and grading of glioma tumors, via image derived features, for diagnosis, prognosis, and treatment response has been an active research area in medical image computing. This paper presents a novel method for automatic detection and classification of glioma from conventional T2 weighted MR images. Automatic detection of the tumor was established using newly developed method called Adaptive Gray level Algebraic set Segmentation Algorithm (AGASA).Statistical Features were extracted from the detected tumor texture using first order statistics and gray level co-occurrence matrix (GLCM) based second order statistical methods. Statistical significance of the features was determined by t-test and its corresponding p-value. A decision system was developed for the grade detection of glioma using these selected features and its p-value. The detection performance of the decision system was validated using the receiver operating characteristic (ROC) curve. The diagnosis and grading of glioma using this non-invasive method can contribute promising results in medical image computing

Testing for significance of phase synchronisation dynamics in the EEG

A number of tests exist to check for statistical significance of phase synchronisation within the Electroencephalogram (EEG); however, the majority suffer from a lack of generality and applicability. They may also fail to account for temporal dynamics in the phase synchronisation, regarding synchronisation as a constant state instead of a dynamical process. Therefore, a novel test is developed for identifying the statistical significance of phase synchronisation based upon a combination of work characterising temporal dynamics of multivariate time-series and Markov modelling. We show how this method is better able to assess the significance of phase synchronisation than a range of commonly used significance tests. We also show how the method may be applied to identify and classify significantly different phase synchronisation dynamics in both univariate and multivariate datasets.

Statistical assessment of annual patterns in coastal extreme wave conditions

[EN]The annual cycle in extreme values of significant wave height is examined by transforming the timing ofthe storm peaks in a circular variable, with the aim of taking advantage of the many tests devised to explore uniformity on the circle. The use of four different but complementary uniformity tests makes possible a robust assessment of the annual cycle statistical significance. Seasonality of storms in a long time series of significant wave heights, measured in a coastal zone, is examined. The presence of a seasonal pattem is statistically beyond doubt.

Does published orthodontic research account for clustering effects during statistical data analysis?

In orthodontics, multiple site observations within patients or multiple observations collected at consecutive time points are often encountered. Clustered designs require larger sample sizes compared to individual randomized trials and special statistical analyses that account for the fact that observations within clusters are correlated. It is the purpose of this study to assess to what degree clustering effects are considered during design and data analysis in the three major orthodontic journals. The contents of the most recent 24 issues of the American Journal of Orthodontics and Dentofacial Orthopedics (AJODO), Angle Orthodontist (AO), and European Journal of Orthodontics (EJO) from December 2010 backwards were hand searched. Articles with clustering effects and whether the authors accounted for clustering effects were identified. Additionally, information was collected on: involvement of a statistician, single or multicenter study, number of authors in the publication, geographical area, and statistical significance. From the 1584 articles, after exclusions, 1062 were assessed for clustering effects from which 250 (23.5 per cent) were considered to have clustering effects in the design (kappa = 0.92, 95 per cent CI: 0.67-0.99 for inter rater agreement). From the studies with clustering effects only, 63 (25.20 per cent) had indicated accounting for clustering effects. There was evidence that the studies published in the AO have higher odds of accounting for clustering effects [AO versus AJODO: odds ratio (OR) = 2.17, 95 per cent confidence interval (CI): 1.06-4.43, P = 0.03; EJO versus AJODO: OR = 1.90, 95 per cent CI: 0.84-4.24, non-significant; and EJO versus AO: OR = 1.15, 95 per cent CI: 0.57-2.33, non-significant). The results of this study indicate that only about a quarter of the studies with clustering effects account for this in statistical data analysis.

The estimation of statistical parameters for local alignment score distributions

The distribution of optimal local alignment scores of random sequences plays a vital role in evaluating the statistical significance of sequence alignments. These scores can be well described by an extreme-value distribution. The distribution’s parameters depend upon the scoring system employed and the random letter frequencies; in general they cannot be derived analytically, but must be estimated by curve fitting. For obtaining accurate parameter estimates, a form of the recently described ‘island’ method has several advantages. We describe this method in detail, and use it to investigate the functional dependence of these parameters on finite-length edge effects.

Statistical modeling of large microarray data sets to identify stimulus-response profiles

A statistical modeling approach is proposed for use in searching large microarray data sets for genes that have a transcriptional response to a stimulus. The approach is unrestricted with respect to the timing, magnitude or duration of the response, or the overall abundance of the transcript. The statistical model makes an accommodation for systematic heterogeneity in expression levels. Corresponding data analyses provide gene-specific information, and the approach provides a means for evaluating the statistical significance of such information. To illustrate this strategy we have derived a model to depict the profile expected for a periodically transcribed gene and used it to look for budding yeast transcripts that adhere to this profile. Using objective criteria, this method identifies 81% of the known periodic transcripts and 1,088 genes, which show significant periodicity in at least one of the three data sets analyzed. However, only one-quarter of these genes show significant oscillations in at least two data sets and can be classified as periodic with high confidence. The method provides estimates of the mean activation and deactivation times, induced and basal expression levels, and statistical measures of the precision of these estimates for each periodic transcript.

A unified statistical framework for sequence comparison and structure comparison

We present an approach for assessing the significance of sequence and structure comparisons by using nearly identical statistical formalisms for both sequence and structure. Doing so involves an all-vs.-all comparison of protein domains [taken here from the Structural Classification of Proteins (scop) database] and then fitting a simple distribution function to the observed scores. By using this distribution, we can attach a statistical significance to each comparison score in the form of a P value, the probability that a better score would occur by chance. As expected, we find that the scores for sequence matching follow an extreme-value distribution. The agreement, moreover, between the P values that we derive from this distribution and those reported by standard programs (e.g., blast and fasta validates our approach. Structure comparison scores also follow an extreme-value distribution when the statistics are expressed in terms of a structural alignment score (essentially the sum of reciprocated distances between aligned atoms minus gap penalties). We find that the traditional metric of structural similarity, the rms deviation in atom positions after fitting aligned atoms, follows a different distribution of scores and does not perform as well as the structural alignment score. Comparison of the sequence and structure statistics for pairs of proteins known to be related distantly shows that structural comparison is able to detect approximately twice as many distant relationships as sequence comparison at the same error rate. The comparison also indicates that there are very few pairs with significant similarity in terms of sequence but not structure whereas many pairs have significant similarity in terms of structure but not sequence.