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PubMed1987

Statistical problems in the reporting of clinical trials. A survey of three medical journals.

Reports of clinical trials often contain a wealth of data comparing treatments. This can lead to problems in interpretation, particularly when significance testing is used extensively. We examined 45 reports of comparative trials published in the British Medical Journal, the Lancet, or the New England Journal of Medicine to illustrate these statistical problems. The issues we considered included the analysis of multiple end points, the analysis of repeated measurements over time, subgroup analyses, trials of multiple treatments, and the overall number of significance tests in a trial report. Interpretation of large amounts of data is complicated by the common failure to specify in advance the intended size of a trial or statistical stopping rules for interim analyses. In addition, summaries or abstracts of trials tend to emphasize the more statistically significant end points. Overall, the reporting of clinical trials appears to be biased toward an exaggeration of treatment differences. Trials should have a clearer predefined policy for data analysis and reporting. In particular, a limited number of primary treatment comparisons should be specified in advance. The overuse of arbitrary significance levels (for example, P less than 0.05) is detrimental to good scientific reporting, and more emphasis should be given to the magnitude of treatment differences and to estimation methods such as confidence intervals.

Clinical Trials as Topic↗
PubMed2004

Dynamical origin of enhanced conformational searches of Tsallis statistics sampling.

The characteristic sampling dynamics of importance samplings driven by the Tsallis weight [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] has been analyzed in terms of recently developed Langevin stochastic model by considering the effects of the density of states and the potential smoothing of the Tsallis transformation. Our study reveals that the fixed points, which are determined by the crossing points of the statistical temperature and the Tsallis effective temperature, play a critical role in overall dynamics of the Tsallis statistics sampling. The dynamical origin of enhanced conformational searches of the Tsallis weight has been investigated by unveiling the intimate relationship between the sampling dynamics and the stability change of corresponding fixed points. Based on this stochastic analysis, we propose one effective method to realize a broad energy distribution in the Tsallis statistics sampling by determining optimal Tsallis parameters systematically based on preliminary canonical samplings. The effectiveness of our method has been validated in the folding simulation of Met-Enkephalin and liquid-solid transition simulation of Lennard-Jones cluster systems.

Algorithms↗
PubMed2002

Significance and statistical errors in the analysis of DNA microarray data.

DNA microarrays are important devices for high throughput measurements of gene expression, but no rational foundation has been established for understanding the sources of within-chip statistical error. We designed a specialized chip and protocol to investigate the distribution and magnitude of within-chip errors and discovered that, as expected from theoretical expectations, measurement errors follow a Lorentzian-like distribution, which explains the widely observed but unexplained ill-reproducibility in microarray data. Using this specially designed chip, we examined a data set of repeated measurements to extract estimates of the distribution and magnitude of statistical errors in DNA microarray measurements. Using the common "ratio of medians" method, we find that the measurements follow a Lorentzian-like distribution, which is problematic for subsequent analysis. We show that a method of analysis dubbed "median of ratios" yields a more Gaussian-like distribution of errors. Finally, we show that the bootstrap algorithm can be used to extract the best estimates of the error in the measurement. Quantifying the statistical error in such measurements has important applications for estimating significance levels, clustering algorithms, and process optimization.

Algorithms↗
PubMed2000

Control error statistics.

Control in general, and manual control in particular, are traditional topics in ergonomics. Numerous studies on these topics have focused on vehicular control or tracking, as experimenters have attempted to describe control performance in terms of control errors, typically using the 'root-mean-square' (RMS) error. The authors of this study believe that this and related statistics are not well understood by the ergonomics community and that additional or alternative performance measurements would be more appropriate as measurements of the particular criteria of concern. Accordingly, this paper shows some background of the RMS and similar statistics of control error, some new statistics, and their interrelationships. This development is intended as a guide to selection of criteria for use in tracking and manual control and their measurement.

Automobile Driving↗
PubMed2001

Applying signal statistical analysis to TEOAE measurements.

Automated detection of TEOAE gains increasing importance in screening applications. Conventional signal statistical analysis methods (buffer correlation and +/- difference) of TEOAE waveforms are compared with one another and with a method based on binomial statistics. It turns out that binomial statistics are more reliable and valid than conventional methods with common criteria. In particular, under narrowband noise conditions they are also faster. A frequency specific evaluation is hardly possible by means of conventional methods because of the high random correlation of narrow band signals.

Data Interpretation, Statistical↗
PubMed2002

Statistical methods for analysing discrete and categorical data recorded in performance analysis.

In this paper, we identify appropriate statistical methods for analysing categorical differences in discrete variables or 'performance indicators' resulting from performance analysis. The random mechanisms associated with discrete events do not follow a normal distribution; that is, the normal distribution is a continuous not a discrete probability distribution. We propose appropriate statistical methods based on two key discrete probability distributions, the Poisson and binomial distributions. Two approaches are proposed and compared using examples from notational analysis. The first approach is based on the classic chi-square test of significance (both the goodness-of-fit test and the test of independence). The second approach adopts a more contemporary method based on log-linear and logit models fitted using the statistical software GLIM. Provided relatively simple one-way and two-way comparisons in categorical data are required, both of these approaches result in very similar conclusions. However, as soon as more complex models or higher-order comparisons are required, the approach based on log-linear and logit models is shown to be more effective. Indeed, when investigating those factors and categorical differences associated with binomial or binary response variables, such as the proportion of winners when attempting decisive shots in squash or the proportion of goals scored from all shots in association football, logit models become the only realistic method available. By applying log-linear and logit models to discrete events resulting from notational analysis, greater insight into the underlying mechanisms associated with sport performance can be achieved.

Humans↗
PubMed1997

A statistical model for ultrasound diagnosis of soft-tissue tumours in the hand and forearm.

PURPOSE: The ultrasound characteristics of 5 common tumours of the hand and forearm were used to build a statistical model that could assess the weight of each trait or combination of traits in the correct diagnosing of the tumours. The model was used for calculating the first and second diagnostic alternatives. MATERIAL AND METHODS: The basic data of the model were the ultrasound findings in previously presented material on the 5 common benign soft-tissue tumours. The material consisted of 96 tumours: 18 villonodular synovites, 26 haemangiomas, 14 lipomas, 27 nerve tumours, and 11 glomus tumours. To build the statistical model, the ultrasound characteristics that were significant at 5% level were calculated. With stepwise logistic regression, 3 of these were selected as explaining variables. The degree of influence of the explaining variable on the response variable was calculated by way of odds quotients. The material was then analysed by means of the statistical model. The correct diagnosis was calculated as first and second alternatives for each tumour and for the whole material. RESULTS: The diagnostic accuracy for the whole material was 51% in the first choice and 77% in first plus second choices. CONCLUSION: Ultrasound should be the first imaging modality for soft-tissue tumours of the hand. However, MR should also be performed when diagnosis continues to be obscure and when malignancy is suspected.

Diagnosis, Differential↗
PubMed1995

A statistical analytical approach to decipher information from biological sequences: application to murine splice-site analysis and prediction.

A simple statistical approach for the analysis of biological sequences, such as splice-sites, promoter regions, helices and extended structure forming regions or any other sequence dependent functional entities in proteins, is presented. The approach has been proved useful to develop a method for prediction of such entities in newly available sequences. We first search for invariant sequence features of each functional entity from the experimentally available sequences and identify a set of 'like' sequences with similar sequence features. In the next step, concrete features of sequence entities in terms of occurrences of smaller subsequences are identified at various positions which are used as a knowledge base to select potential functional entities from the identified 'like' sequences. The third step consists of refinement of this pattern learning, statistical improvements of the knowledge base weight matrices, and finally its application to predict functional entities in newly available sequences. Such an analysis is operationally described for murine splice-site predictions. Regions comprising -30 to +30 nucleotides from the splice-junction at the murine splice-sites (donors and acceptors), reported earlier, were analyzed. Invariant sequence-specific features in terms of monomer frequency average were used to identify splice-site-like sequences in the EMBL murine DNA sequence data base. The frequencies of occurrence of mono-, di-, tri- and tetranucleotides in the known splice-sites were studied in comparison with the splice-site-like sequences; the significant differences in their occurrences were extracted as statistical knowledge coded in weight matrices for computer to identify potential splice-sites. The algorithm was refined and a method was developed to predict potential splice-sites in a given murine DNA; the analysis was also extended to human DNA. The success rate of the method to predict correct splice-sites in these species is found to be 80% and 85%, respectively. The major strength of this method lies in reducing significantly the number of false positives which are normally picked up in such analysis.

Algorithms↗
PubMed2004

Quantifying uncertainties in the assessment of sediment quality: statistical criteria and guidelines for sediment quality assessments.

Current sediment quality guidelines generally adopt a tiered approach in order to assess sediment quality more cost-effectively. The uncertainties involved in the tiered approach of an integrative assessment, however have not been quantified resulting in a risk of committing type I error or type II error at the final confirmatory stage. This study develops statistical criteria and guidelines for the sediment chemistry component of an integrative assessment of sediment quality. At the tier 1 screening stage, historical data or an initial survey is required to determine the minimum sample numbers that will be required to be representative of the study site. Understanding the guiding principles which have underpinned the setting of sediment quality criteria for contaminant is an important factor in tier 1 evaluations. To reduce cost and uncertainty in data, sampling should include the least number of samples necessary to minimise uncertainties by estimating the probability distribution function (which represents the variability of the natural environment at the location of concern), with subsequent application of kriging and sequential simulation methods on data obtained. Implementation of statistical criteria and guidelines in sediment quality assessments can provide a foundation for a further quantitative cost/benefit analysis and decrease the risk of committing type I and type II statistical errors at later classification stages.

Environmental Monitoring↗
PubMed2005

Sensitivity of the estimated air pollution-respiratory admissions relationship to statistical model choice.

The objective of this study was to demonstrate the methodological shortcomings of currently available analytical methods for single-city time series data. We analyzed daily Chronic Obstructive Pulmonary Disease (COPD) and daily asthma hospital admissions in Melbourne, Australia from July 1989 to December 1992. Air pollution data comprised nitrogen dioxide, ozone and sulphur dioxide and air particles index consistent with particulates between 0.1 and 1 microm in aerodynamic diameter. Statistical analyses were performed using generalized linear models, generalized additive models, Poisson autoregressive models and transitional regression models. The estimated effect of nitrogen dioxide on COPD hospital admissions was similar across the different statistical models, RR = 1.06 (95% CI 1.01-1.11). Similarly the estimated effect of nitrogen dioxide on asthma hospital admissions was also consistent, RR = 1.05 (95% CI 1.01-1.09). However, the effects of ozone, air particles index and sulphur dioxide were highly sensitive to model specification for both COPD and asthma hospital admissions. In single-city studies of air pollution and respiratory disease, very different conclusions can be drawn from competing models. Furthermore, real time series data have greater complexity than any of the commonly-used existing models allow. Consequently, single-city studies should use several statistical models to demonstrate the stability of estimated effects.

Air Pollution↗
PubMed2001

Statistical methods in epidemiology. VII. An overview of the chi2 test for 2 x 2 contingency table analysis.

PURPOSE: The odds ratio is an appropriate method of analysis for data in 2 x 2 contingency tables. However, other methods of analysis exist. One such method is based on the chi2 test of goodness-of-fit. Key players in the development of statistical theory include Pearson, Fisher and Yates. METHOD: Data are presented in the form of 2 x 2 contingency tables and a method of analysis based on the chi2 test is introduced. There are many variations of the basic test statistic, one of which is the chi2 test with Yates' continuity correction. The usefulness (or not) of Yates' continuity correction is discussed. Problems of interpretation when the method is applied to k x m tables are highlighted. RESULTS: Some properties of the chi2 the test are illustrated by taking examples from the author's teaching experiences. CONCLUSION: Journal editors should be encouraged to give both observed and expected cell frequencies so that better information comes out of the chi2 test statistic.

Breast Neoplasms↗
PubMed2000

Predicting particulate (PM10) personal exposure distributions using a random component superposition statistical model.

This paper presents a new statistical model designed to extend our understanding from prior personal exposure field measurements of urban populations to other cities where ambient monitoring data, but no personal exposure measurements, exist. The model partitions personal exposure into two distinct components: ambient concentration and nonambient concentration. It is assumed the ambient and nonambient concentration components are uncorrelated and add together; therefore, the model is called a random component superposition (RCS) model. The 24-hr ambient outdoor concentration is multiplied by a dimensionless "attenuation factor" between 0 and 1 to account for deposition of particles as the ambient air infiltrates indoors. The RCS model is applied to field PM10 measurement data from three large-scale personal exposure field studies: THEES (Total Human Environmental Exposure Study) in Phillipsburg, NJ; PTEAM (Particle Total Exposure Assessment Methodology) in Riverside, CA; and the Ethyl Corporation study in Toronto, Canada. Because indoor sources and activities (smoking, cooking, cleaning, the personal cloud, etc.) may be similar in similar populations, it was hypothesized that the statistical distribution of nonambient personal exposure is invariant across cities. Using a fixed 24-hr attenuation factor as a first approximation derived from regression analysis for the respondents, the distributions of nonambient PM10 personal exposures were obtained for each city. Although the mean ambient PM10 concentrations in the three cities varied from 27.9 micrograms/m3 in Toronto to 60.9 micrograms/m3 in Phillipsburg to 94.1 micrograms/m3 in Riverside, the mean nonambient components of personal exposures were found to be closer: 52.6 micrograms/m3 in Toronto; 52.4 micrograms/m3 in Phillipsburg; and 59.2 micrograms/m3 in Riverside. The three frequency distributions of the nonambient components of exposure also were similar in shape, giving support to the hypothesis that nonambient concentrations are similar across different cities and populations. These results indicate that, if the ambient concentrations were completely controlled and set to zero in all three cities, the median of the remaining personal exposures to PM10 would range from 32.0 micrograms/m3 (Toronto) to 34.4 micrograms/m3 (Phillipsburg) to 48.8 micrograms/m3 (Riverside). The highest-exposed 30% of the population in the three cities would still be exposed to 24-hr average PM10 concentrations of 47-74 micrograms/m3; the highest 20% would be exposed to concentrations of 56-92 micrograms/m3; the highest 10% to concentrations of 88-131 micrograms/m3; and the highest 5% to 133-175 micrograms/m3, due only to indoor sources and activities. The distribution for the difference between personal exposures and indoor concentrations, or the "personal cloud," also was similar in the three cities, with a mean of 30-35 micrograms/m3, suggesting that the personal cloud accounts for more than half of the nonambient component of PM10 personal exposure in the three cities. Using only the ambient measurements in Toronto, the nonambient data from THEES in Phillipsburg was used to predict the entire personal exposure distribution in Toronto. The PM10 exposure distribution predicted by the model showed reasonable agreement with the PM10 personal exposure distribution measured in Toronto. These initial results suggest that the RCS model may be a powerful tool for predicting personal exposure distributions and statistics in other cities where only ambient particle data are available.

Air Pollution↗
PubMed2005

The Steubenville comprehensive air monitoring program (SCAMP): overview and statistical considerations.

Average concentrations of particulate matter with an aerodynamic diameter less than or equal to 2.5 microm (PM2.5) in Steubenville, OH, have decreased by more than 10 microg/m3 since the landmark Harvard Six Cities Study associated the city's elevated PM2.5 concentrations with adverse health effects in the 1980s. Given the promulgation of a new National Ambient Air Quality Standard (NAAQS) for PM2.5 in 1997, a current assessment of PM2.5 in the Steubenville region is warranted. The Steubenville Comprehensive Air Monitoring Program (SCAMP) was conducted from 2000 through 2002 to provide such an assessment. The program included both an outdoor ambient air monitoring component and an indoor and personal air sampling component. This paper, which is the first in a series of four that will present results from the outdoor portion of SCAMP, provides an overview of the outdoor ambient air monitoring program and addresses statistical issues, most notably autocorrelation, that have been overlooked by many PM2.5 data analyses. The average PM2.5 concentration measured in Steubenville during SCAMP (18.4 microg/m3) was 3.4 microg/m3 above the annual PM2.5 NAAQS. On average, sulfate and organic material accounted for approximately 31% and 25%, respectively, of the total PM2.5 mass. Local sources contributed an estimated 4.6 microg/m3 to Steubenville's mean PM2.5 concentration. PM2.5 and each of its major ionic components were significantly correlated in space across all pairs of monitoring sites in the region, suggesting the influence of meteorology and long-range transport on regional PM2.5 concentrations. Statistically significant autocorrelation was observed among time series of PM2.5 and component data collected at daily and 1-in-4-day frequencies during SCAMP. Results of spatial analyses that accounted for autocorrelation were generally consistent with findings from previous studies that did not consider autocorrelation; however, these analyses also indicated that failure to account for autocorrelation can lead to incorrect conclusions about statistical significance.

Air Pollutants↗
PubMed2006

Statistical considerations for noninferiority/equivalence trials in vaccine development.

Noninferioritylequivalence designs are often used in vaccine clinical trials. The goal of these designs is to demonstrate that a new vaccine, or new formulation or regimen of an existing vaccine, is similar in terms of effectiveness to the existing vaccine, while offering such advantages as easier manufacturing, easier administration, lower cost, or improved safety profile. These noninferioritylequivalence designs are particularly useful in four common types of immunogenicity trials: vaccine bridging trials, combination vaccine trials, vaccine concomitant use trials, and vaccine consistency lot trials. In this paper, we give an overview of the key statistical issues and recent developments for noninferioritylequivalence vaccine trials. Specifically, we cover the following topics: (i) selection of study endpoints; (ii) formulation of the null and alternative hypotheses; (iii) determination of the noninferioritylequivalence margin; (iv) selection of efficient statistical methods for the statistical analysis of noninferioritylequivalence vaccine trials, with particular emphasis on adjustment for stratification factors and missing pre-or post-vaccination data; and (v) the calculation of sample size and power.

Endpoint Determination↗
PubMed2006

Statistical quality control process for traditional Chinese medicine.

The statistical quality control process on raw materials and/or the final product of traditional Chinese medicine (TCM) is examined. We develop a statistical quality control (QC) method to assess a proposed consistency index of raw materials from different sources and/or final products manufactured at different sites. The idea is to construct a 95% confidence interval for a proposed consistency index under a sampling plan. If the constructed 95% confidence lower limit is greater than a prespecified QC lower limit, then we claim that the raw material or final products have passed the QC and hence can be released for further processing or use; otherwise, the raw materials and/or final product should be rejected. For a given component (the most active component if possible), a sampling plan is derived to ensure that there is a desired probability for establishing consistency between sites when there is truly no difference in raw materials or final products between sites. An example concerning the development of a TCM is presented to illustrate the proposed statistical QC method for assessing consistency in raw materials from two sites.

Algorithms↗
PubMed2007

Statistical and regulatory issues with the application of propensity score analysis to nonrandomized medical device clinical studies.

Propensity score analysis is a versatile statistical method used mainly in observational studies for improving treatment comparison by adjusting for up to a relatively large number of potentially confounding covariates. Recently, there has been an increased interest in applying this method to nonrandomized medical device clinical studies. In the application of the methodology, some statistical and regulatory issues arise in both study design and analysis of study results, such as the need for pre-specifying clinically relevant covariates to be measured, appropriate patient populations, and the essential elements of statistical analysis, planning sample size in the context of propensity score methodology, handling missing covariates in generating propensity scores, and assessing the success of the propensity score method by evaluating treatment group overlap in terms of the distributions of propensity scores. In this paper, the advantages and limitations of this methodology will be revisited, and the above issues will be discussed and illustrated with examples from a regulatory perspective.

Algorithms↗
PubMed1993

Statistical estimates and clinical trials.

Statistical estimates and significance tests address distinct (but related) questions using the same data. Point estimates and confidence intervals of differences are statistical estimates that address: "How LARGE is the difference in the population of interest?" A significance test addresses the question: "How LIKELY was the difference to have occurred by chance?" Because p-values deal with the existence of a real nonzero difference between treatments but not the size of that treatment difference, they cannot be used to assess clinical (practical) significance. A confidence interval is a range of values used to infer both the size of a difference and the uncertainty of the estimate. Examples illustrate how confidence intervals help us assess both the clinical significance and the statistical significance of an observed difference. The point estimate is the outcome difference actually observed in the study sample; it is also the best single-number estimate of the unknown difference in the sampled population. Point estimates, confidence intervals, and p-values extract complementary information from study data and should all be reported for major results.

Clinical Trials as Topic↗
PubMed1999

Type I error and the power of the s-test: old lessons from a new, analytically justified statistical test for phylogenies.

We present a new procedure for assessing the statistical significance of the most likely unrooted dichotomous topology inferrable from four DNA sequences. The procedure calculates directly a P-value for the support given to this topology by the informative sites congruent with it, assuming the most likely star topology as the null hypothesis. Informative sites are crucial in the determination of the maximum likelihood dichotomous topology and are therefore an obvious target for a statistical test of phylogenies. Our P-value is the probability of producing through parallel substitutions on the branches of the star topology at least as much support as that given to the maximum likelihood dichotomous topology by the aforementioned informative sites, for any of the three possible dichotomous topologies. The degree of statistical significance is simply the complement of this P-value. Ours is therefore an a posteriori testing approach, in which no dichotomous topology is specified in advance. We implement the test for the case in which all sites behave identically and the substitution model has a single parameter. Under these conditions, the P-value can be easily calculated on the basis of the probabilities of change on the branches of the most likely star topology, because under these assumptions, each site can become informative independently from every other site; accordingly, the total number of informative sites of each kind is binomially distributed. We explore the test's type I error by applying it to data produced in star topologies having all branches equally long, or having two short and two long branches, and various degrees of homoplasy. The test is conservative but we demonstrate, by means of a discreteness correction and progressively assumption-free calculations of the P-values, that (1) the conservativeness is mostly due to the discrete nature of informative sites and (2) the P-values calculated empirically are moreover mostly quite accurate in absolute terms. Applying the test to data produced in dichotomous topologies with increasing internal branch length shows that, despite the test's "conservativeness," its power is much higher than that of the bootstrap, especially when the relevant informative sites are few.

Likelihood Functions↗