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Evaluating group distributional characteristics: why psychophysiologists should be interested in qualitative departures from the normal distribution.

Real data often do not approximate the normal distribution. Under nonnormal conditions, psycho-physiologists who use parametric statistics may be testing with inadequate power and/or testing a measure of location (i.e., the mean) that does not represent the desired portion of the distribution for statistical comparison. The purpose of this paper is: first, to provide psycho-physiologists with a method to investigate group distributional characteristics; second, to evaluate the distributional characteristics of heart period and respiratory sinus arrhythmia in human adults and newborns; third, to demonstrate the increased statistical power that can accompany the selection of an alternative statistical analysis for nonnormal data. Suggestions are provided on how to analyze nonnormal data.

Adult↗

Comparison of methods for survival analysis of dependent data.

Analysis of dependent survival data by conventional partial likelihood methods produces unbiased estimates of the regression coefficients but incorrectly estimates their variance. Here we compared the conventional partial likelihood methods with two alternative methods for analyzing dependent survival data. The first alternative method estimated the regression coefficient by the partial likelihood approach but adjusted the variance to account for clustering. The second alternative method used marginal likelihoods to estimate both the regression coefficient and its variance. We evaluated the performance of the three methods using simulated and actual data. Simulated data were used to examine bias, efficiency, type I errors, and power. An Old Order Amish genealogy was analyzed under these models to illustrate their performance on real data. The simulation study showed that all three methods provided unbiased estimates of the regression coefficient, but the efficiency of the estimated regression coefficient varied according to the simulation conditions. The standard partial likelihood method showed increasing type I error as the dependence increased within clusters. Both alternative methods had acceptable levels of type I errors at all dependence levels. In the analysis of genealogic data, the regression coefficient was similar in the three methods showing stable estimates of the regression coefficients. The variance estimates from the alternative methods were slightly different from the conventional method, suggesting a flow level of dependence. This study displays the effect of violating the independence assumption and provides guidelines for using alternative statistical methods.

Analysis of Variance↗

Breast Cancer Detection Demonstration Project data can determine whether the prognosis of breast cancer is affected by the time of surgery during the menstrual cycle.

The purpose of this study was to determine the feasibility of using Breast Cancer Detection Demonstration Project (BCDDP) data to ascertain whether the prognosis of breast cancer in premenopausal women is affected when surgery is performed relative to the different phases of the menstrual cycle. In the Louisville BCDDP only 40 cases were available for study, but even with this small number, the data indicate that survivorship was superior when the surgery was performed between days 7-20 of the menstrual cycle (P < 0.06). One thousand eighty-seven premenopausal women underwent surgery for breast cancer during the first 5 years of the national BCDDP, beginning in 1972. This large number of cases, plus the long period of follow-up should provide sufficient statistical power for us to evaluate if there is any relationship between the day of the menstrual cycle, the day surgery was performed, and prognosis. This feasibility study indicates that these women should be followed up and the appropriate statistical studies should be done.

Adult↗

A bibliography and comments on the use of statistical models in epidemiology in the 1980s.

This paper reviews developments in statistical modelling in epidemiology in the 1980's, with emphasis on cohort and case-control studies. The central roles of the logistic and proportional hazard models are highlighted, and it is shown how these models lead to a deeper understanding of classical designs and methods of analysis as well as to efficient new designs and analytical procedures. The important area of model misspecification is discussed, including the problems of omitted latent structure, mis-modelling of available measurements, missing data and errors in measurements. Various designs motivated by the logistic model are illustrated numerically, and designs based on the proportional hazards model are discussed, as are papers on sample size determination. There are brief introductions to the literature on other topics, including attributable risk, disease clustering, family studies and genetics, analysis of disease incidence data, infectious disease, longitudinal data, screening and miscellaneous related topics in statistics. An extensive bibliography is indexed according to the outline of the paper.

Data Interpretation, Statistical↗

Analysis of a clinical trial involving a combined mortality and adherence dependent interval censored endpoint.

Clinical trials often involve a variety of clinical and laboratory measures that are used as endpoints and sometimes two of these measures are combined in one endpoint. When the individual components of such a combined endpoint are 'time to event' measurements, the analysis is straightforward if each of the components is measured frequently and regularly over time. However, the analysis of the combined endpoint is more difficult when one component of the endpoint is right censored and the other is interval censored. This paper describes a statistic, based on a rank ordering of events for such a combined measure. The power of the test statistic is explored.

Clinical Trials as Topic↗

Effect of continuous versus dichotomous outcome variables on study power when sample sizes of orthopaedic randomized trials are small.

It is often not feasible to conduct large trials in orthopaedic surgery. Therefore, surgeons must identify strategies to optimize the statistical power of their smaller studies. The aim of this study was to compare study power in randomized trials with continuous versus dichotomous outcome variables. We performed a systematic review of the literature to identify randomized trials in orthopaedic trauma. Of these, we examined only those trials with small sample sizes (50 patients or less). The outcomes in each eligible study were categorized as continuous or dichotomous. Standard power calculations were performed for each study, and comparisons were made between continuous and dichotomous outcome variables. We identified 196 randomized trials in orthopaedic trauma. Of these, 76 trials had a sample size of 50 patients or fewer (29 trials with continuous outcomes, 47 trials with dichotomous outcomes). Studies that reported continuous outcomes had a significantly higher mean power than those that reported dichotomous variables (power 49% vs 38%, p=0.042). Twice as many trials with continuous outcome variables reached acceptable levels of study power (i.e. >80% power) when compared with trials with dichotomous variables (37% vs 18.6%, p=0.04). When orthopaedic surgeons anticipate small sample sizes for their study, they can optimize their study's statistical power by choosing a continuous outcome variable.

Cluster Analysis↗

Detection of muscle artefact in the normal human awake EEG.

OBJECTIVES: A study was performed to investigate automatic detection of muscle artefact, using time domain and frequency domain methods. The evaluation focussed on epoch length and performance of detection. METHODS: EEG data were recorded in 21 normal adult subjects for 50 min during awake state. Investigated positions included central, temporal and parietal scalp electrodes. Expert annotation of muscle artefact was performed by accurate visual marking in a randomised test-set of the data, which allowed for intra-expert comparison. For time domain detection, the parameter set consisted of slope and maximum/minimum amplitude. Parameters in the frequency domain were absolute and relative 'high beta' power (>25 Hz) and spectral edge frequency. Distributions as calculated from a reference period in each subject were used to investigate the statistics of the parameter ranges. Detection thresholds were calculated from these distributions per subject, and performance was compared to constant (empirical) thresholds for the entire data set. RESULTS: Results indicate a 1 s epoch length as optimal for detection of muscle artefact. The analysis using a slope threshold or absolute 'high beta' power showed the best results in sensitivity (80%) and specificity (90%), matching the expert's performance. CONCLUSIONS: Constant threshold settings performed better than statistical thresholds per subject.

Adult↗

BJ: an S-Plus program to fit linear regression models to censored data using the Buckley-James method.

Most researchers are familiar with ordinary multiple regression models, most commonly fitted using the method of least squares. The method of Buckley and James (J. Buckley, I. James, Linear regression with censored data, Biometrika 66 (1979) 429-436.) is an extension of least squares for fitting multiple regression models when the response variable is right-censored as in the analysis of survival time data. The Buckley-James method has been shown to have good statistical properties under usual regularity conditions (T.L. Lai, Z. Ying, Large sample theory of a modified Buckley-James estimator for regression analysis with censored data, Ann. Stat. 19 (1991) 1370-1402.). Nevertheless, even after 20 years of its existence, it is almost never used in practice. We believe that this is mainly due to lack of software and we describe here an S-Plus program that through its inclusion in a public domain function library fully exploits the power of the S-Plus programming environment. This environment provides multiple facilities for model specification, diagnostics, statistical inference, and graphical depiction of the model fit.

Data Interpretation, Statistical↗

[Cluster sampling: consequences of data analysis on drawing conclusions].

BACKGROUND: Cluster sampling is commonly used since it does not require a sampling frame which lists all the individual enumeration units. However, this sampling design is often less precise than simple random sampling due to frequent homogeneity of individuals within clusters. This note illustrates that the precision of parameters such as mean, prevalence and odds ratio can be biased when the data analysis ignores the sampling design, yielding to possibly erroneous conclusions. METHODS: Data from a cluster sampling among clandestine sex workers in Senegal were used. Two analyses were performed and their results were compared. The first analysis took into account the sampling design (design-based analysis) while the second did not (naïve analysis). RESULTS: The range of confidence intervals in design-based analysis differed from -43% to +84% with regard to those of naive analysis, and different conclusions could be drawn. For instance, the human immunodeficiency virus (HIV) infection in clandestine sex workers was associated with condoms use and perceived risk of HIV infection in design-based analysis but not in naive analysis. CONCLUSION: The data analysis must take into account the sampling design, and this is facilitated by the availability of statistical software with survey analysis capabilities.

Adult↗

1996 Remington lecture: modeling multivariate longitudinal data that are incomplete.

PURPOSE: We describe the impact that missing data may have on model selection for longitudinal multivariate data. METHODS: Maximum likelihood was used to fit several models to ultrasonographic measurements from the Asymptomatic Carotid Artery Progression Study (ACAPS). Graphical techniques were used to examine evidence concerning the underlying missing data mechanisms associated with each model. RESULTS: Using statistical methodology that addressed missing data substantially increased the statistical efficiency of our analysis of ultrasonographic data. Only complex models that included segment-specific parameterizations for longitudinal correlations appeared to allow missing data to be assumed to occur at random. CONCLUSION: Ignoring the nature of missing data in conducting statistical analyses can have serious consequences when missingness is not rare. It may be necessary to fit models of high dimension with maximum likelihood techniques to address missing data appropriately, however these approaches may improve statistical efficiency.

Carotid Stenosis↗

Inferences concerning exponential distributions in the presence of randomly right censored data with missing censored values.

Inferences concerning exponential distributions are considered from a sampling theory viewpoint when the data are randomly right censored and the censored values are missing. Both one-sample and m-sample (m > or = 2) problems are considered. Likelihood functions are obtained for situations in which the censoring mechanism is informative which leads to natural and intuitively appealing estimators of the unknown proportions of censored observations. For testing hypotheses about the unknown parameters, three well-known test statistics, namely, likelihood ratio test, score test, and Wald-type test are considered.

Data Interpretation, Statistical↗

How do statistical properties influence findings of tracking (maintenance) in epidemiologic studies? An example of research in tracking of obesity.

There is great interest in studying the tracking (maintenance) of health conditions and risk factors over the life span. Tracking is often defined as the maintenance of a distribution position (e.g., quintile or percentile) in a study population over time. This study investigated how statistical properties might influence research findings of tracking with a special attention on the tracking of extreme ranking. Our results show that when repeated measures over time were positively correlated, the probability of tracking in extreme rankings was greater than other rankings and this was closely influenced by the overall correlation (r) and by the categorization. For example, when r = 0.4, 38% remained in the bottom and upper quintile (Q1, Q5) respectively, while only 22% remained in the middle quintile (Q3); when r = 0.8, the figure became 65% vs. 32%. When r = 0.4 and 0.8, 19 and 50% remained in the upper 95th percentile (or under the 5th percentile), respectively. Our real data show that children in the upper body mass index (= weight(kg)/height(m)(2)) quintile were more likely to maintain their ranking (54%) than others (about 30%), but not significantly higher than the expected (47%, p > 0.05). In conclusion, the overall correlation should be considered when studying tracking. Our proposed methods and predicted probabilities of tracking can help test whether one's observed tracking patterns are different from the statistically predicted ones.

Body Mass Index↗

Finding motifs in promoter regions.

A central issue in molecular biology is understanding the regulatory mechanisms that control gene expression. The availability of whole genome sequences opens the way for computational methods to search for the key elements in transcription regulation. These include methods for discovering the binding sites of DNA-binding proteins, such as transcription factors. A common representation of transcription factor binding sites is a position specific score matrix (PSSM). We developed a probabilistic approach for searching for putative binding sites. Given a promoter sequence and a PSSM, we scan the promoter and find the position with the maximal score. Then we calculate the probability to get such a maximal score or higher on a random promoter. This is the p-value of the putative binding site. In this way, we searched for putative binding sites in the upstream sequences of Saccharomyces cerevisiae, where some binding sites are known (according to the Saccharomyces cerevisiae Promoters Database, SCPD). Our method produces either exact p-values, or a better estimate for them than other methods, and this improves the results of the search. For each gene we found its statistically significant putative binding sites. We measured the rates of true positives, by a comparison to the known binding sites, and also compared our results to these of MatInspector, a commercially available software that looks for putative binding sites in DNA sequences according to PSSMs. Our results were significantly better. In contrast with us, MatInspector doesn't calculate the exact statistical significance of its results.

Algorithms↗

Practical FDR-based sample size calculations in microarray experiments.

MOTIVATION: Owing to the experimental cost and difficulty in obtaining biological materials, it is essential to consider appropriate sample sizes in microarray studies. With the growing use of the False Discovery Rate (FDR) in microarray analysis, an FDR-based sample size calculation is essential. METHOD: We describe an approach to explicitly connect the sample size to the FDR and the number of differentially expressed genes to be detected. The method fits parametric models for degree of differential expression using the Expectation-Maximization algorithm. RESULTS: The applicability of the method is illustrated with simulations and studies of a lung microarray dataset. We propose to use a small training set or published data from relevant biological settings to calculate the sample size of an experiment. AVAILABILITY: Code to implement the method in the statistical package R is available from the authors.

Algorithms↗

A Bayesian change-point analysis of electromyographic data: detecting muscle activation patterns and associated applications.

Many facets of neuromuscular activation patterns and control can be assessed via electromyography and are important for understanding the control of locomotion. After spinal cord injury, muscle activation patterns can affect locomotor recovery. We present a novel application of reversible jump Markov chain Monte Carlo simulation to estimate activation patterns from electromyographic data. We assume the data to be a zero-mean, heteroscedastic process. The variance is explicitly modeled using a step function. The number and location of points of discontinuity, or change-points, in the step function, the inter-change-point variances, and the overall mean are jointly modeled along with the mean and variance from baseline data. The number of change-points is considered a nuisance parameter and is integrated out of the posterior distribution. Whereas current methods of detecting activation patterns are deterministic or provide only point estimates, ours provides distributional estimates of muscle activation. These estimates, in turn, are used to estimate physiologically relevant quantities such as muscle coactivity, total integrated energy, and average burst duration and to draw valid statistical inferences about these quantities.

Bayes Theorem↗

Tutorials in clinical research, part VI: descriptive statistics.

OBJECTIVES: This is the sixth in a series of Tutorials in Clinical Research. The objectives of this tutorial are to produce a brief, step-by-step, user-friendly atlas with clinical scenarios and illustrative examples to serve as ready references and, it is hoped, to open an inviting door to understanding statistics. STUDY DESIGN: Tutorial. METHODS: The authors met weekly for 6 months discussing clinical research articles and the applied statistics. Liberal use of reference texts and discussion focused on constructing a tutorial that is factual as well as easy to read and understand. RESULTS: The tutorial is organized into five sections: Overview, Key to Descriptive Summaries, Steps in Summarizing Descriptive Data, Understanding the Summaries of Specific Data Types, and Understanding Scope or Dispersion of Data. CONCLUSIONS: Assessing the validity of medical studies requires a working knowledge of statistics; however, obtaining this knowledge need not be beyond the ability of the busy surgeon. Desire is the only limiting factor. We have tried to construct an accurate, basic, easy-to-read-and-apply introduction to the task of summarizing the characteristics of a single variable. This is known as descriptive statistics.

Data Interpretation, Statistical↗

A research primer.

Research is critical for the continued development of ET nursing knowledge. Although ET nurses have an interest in research, some may lack understanding of basic terms used in quantitative research. This article is a research primer that focuses on basic information about the research process. Information is presented about a study's purpose, literature review, conceptual framework, questions or hypotheses, instruments, design, sample, and statistics. The reader participates in the process by answering questions placed throughout the article.

Data Interpretation, Statistical↗

HLA typing and retinitis pigmentosa.

Retinitis pigmentosa is a disease whose pathogenesis remains largely obscure. A lot of evidences support the hypothesis that auto-immunity is involved, but no HLA antigen has ever been associated with retinitis pigmentosa. Ten patients with autosomal recessive retinitis pigmentosa were tissue typed for class I and II HLA antigens. The results of the study show a significant increase in the frequency of the antigens Cw4, Cw6 and DR11. High values of relative risk were found also for some class I antigens, but the size of the group of patients with these loci precluded a meaningful statistical analysis.

Adolescent↗