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PubMed2006

Error in statistical tests of error in statistical tests.

BACKGROUND: A recent paper found that terminal digits of statistical values in Nature deviated significantly from an equiprobable distribution, indicating errors or inconsistencies in rounding. This finding, as well as the discovery that a large percentage of p values were inconsistent with reported test statistics, led to a great deal of concern in the popular press and scientific community. The findings ultimately led to new guidelines for all Nature Research Journals. METHODS: We checked the statistical analysis behind the original paper's tests of equiprobability. RESULTS: The original paper tested equiprobability with the Kolmogorov-Smirnov test outside its regime of validity. Correct tests find no statistically significant deviations from equiprobability for the statistical values in Nature. CONCLUSION: Statistical tests should be used correctly.

Confidence Intervals↗
PubMed2006

Statistics for correlated data: phylogenies, space, and time.

Here we give an introduction to the growing number of statistical techniques for analyzing data that are not independent realizations of the same sampling process--in other words, correlated data. We focus on regression problems, in which the value of a given variable depends linearly on the value of another variable. To illustrate different types of processes leading to correlated data, we analyze four simulated examples representing diverse problems arising in ecological studies. The first example is a comparison among species to determine the relationship between home-range area and body size; because species are phylogenetically related, they do not represent independent samples. The second example addresses spatial variation in net primary production and how this might be affected by soil nitrogen; because nearby locations are likely to have similar net primary productivity for reasons other than soil nitrogen, spatial correlation is likely. In the third example, we consider a time-series model to ask whether the decrease in density of a butterfly species is the result of decreases in its host-plant density; because the population density of a species in one generation is likely to affect the density in the following generation, time-series data are often correlated. The fourth example combines both spatial and temporal correlation in an experiment in which prey densities are manipulated to determine the response of predators to their food supply. For each of these examples, we use a different statistical approach for analyzing models of correlated data. Our goal is to give an overview of conceptual issues surrounding correlated data, rather than a detailed tutorial in how to apply different statistical techniques. By dispelling some of the mystery behind correlated data, we hope to encourage ecologists to learn about statistics that could be useful in their own work. Although at first encounter these techniques might seem complicated, they have the power to simplify ecological research by making more types of data and experimental designs open to statistical evaluation.

Animals↗
PubMed1994

Seven ways to increase power without increasing N.

Many readers of this monograph may wonder why a chapter on statistical power was included. After all, by now the issue of statistical power is in many respects mundane. Everyone knows that statistical power is a central research consideration, and certainly most National Institute on Drug Abuse grantees or prospective grantees understand the importance of including a power analysis in research proposals. However, there is ample evidence that, in practice, prevention researchers are not paying sufficient attention to statistical power. If they were, the findings observed by Hansen (1992) in a recent review of the prevention literature would not have emerged. Hansen (1992) examined statistical power based on 46 cohorts followed longitudinally, using nonparametric assumptions given the subjects' age at posttest and the numbers of subjects. Results of this analysis indicated that, in order for a study to attain 80-percent power for detecting differences between treatment and control groups, the difference between groups at posttest would need to be at least 8 percent (in the best studies) and as much as 16 percent (in the weakest studies). In order for a study to attain 80-percent power for detecting group differences in pre-post change, 22 of the 46 cohorts would have needed relative pre-post reductions of greater than 100 percent. Thirty-three of the 46 cohorts had less than 50-percent power to detect a 50-percent relative reduction in substance use. These results are consistent with other review findings (e.g., Lipsey 1990) that have shown a similar lack of power in a broad range of research topics. Thus, it seems that, although researchers are aware of the importance of statistical power (particularly of the necessity for calculating it when proposing research), they somehow are failing to end up with adequate power in their completed studies. This chapter argues that the failure of many prevention studies to maintain adequate statistical power is due to an overemphasis on sample size (N) as the only, or even the best, way to increase statistical power. It is easy to see how this overemphasis has come about. Sample size is easy to manipulate, has the advantage of being related to power in a straight-forward way, and usually is under the direct control of the researcher, except for limitations imposed by finances or subject availability. Another option for increasing power is to increase the alpha used for hypothesis-testing but, as very few researchers seriously consider significance levels much larger than the traditional .05, this strategy seldom is used. Of course, sample size is important, and the authors of this chapter are not recommending that researchers cease choosing sample sizes carefully. Rather, they argue that researchers should not confine themselves to increasing N to enhance power. It is important to take additional measures to maintain and improve power over and above making sure the initial sample size is sufficient. The authors recommend two general strategies. One strategy involves attempting to maintain the effective initial sample size so that power is not lost needlessly. The other strategy is to take measures to maximize the third factor that determines statistical power: effect size.

Data Interpretation, Statistical↗
PubMed2007

Data exploration in meta-analysis with smooth latent distributions.

Meta-analysis with discrete outcomes is interpreted as the estimation (in one or two dimensions) of a non-parametric smooth latent distribution of event probabilities (or rates). A simple but efficient EM algorithm is presented. A fine grid is used and fast smoothing is done by penalized least squares. Data exploration is the primary goal, but the estimated distribution can also be used to compute useful statistics of treatment effects.

Algorithms↗
PubMed1996

Interlaboratory variability in fluorescence in situ hybridization analysis. The NCI Bladder Tumor Marker Network.

Reliable interpretation of fluorescence in situ hybridization (FISH) data, especially data that have been generated in more than one laboratory, requires knowledge of the sources of variability inherent in FISH analysis. Possible sources of variation may derive from differences in sample preparation, probes used, intrasample heterogeneity, hybridization protocols, counting criteria within and between scorers, fluorescence microscopes, and filters. This study characterized the relative weight of some of these factors in order to determine the degree to which FISH results are comparable between laboratories. We used a hierarchical partitioned chi 2 analysis to measure sources of variation. We found that replicate counts varied no more than expected based on counting statistics (i.e., multinomial variation). However, with replicate hybridizations done in two separate laboratories, the variability increased significantly. Thus, care must be taken when interpreting FISH data that are derived from more than one institution. Previously agreed upon counting criteria as well as standardized FISH hybridization protocols may decrease this variability.

Chi-Square Distribution↗
PubMed2005

Evolutionary clues to eukaryotic DNA clamp-loading mechanisms: analysis of the functional constraints imposed on replication factor C AAA+ ATPases.

Ring-shaped sliding clamps encircle DNA and bind to DNA polymerase, thereby preventing it from falling off during DNA replication. In eukaryotes, sliding clamps are loaded onto DNA by the replication factor C (RFC) complex, which consists of five distinct subunits (A-E), each of which contains an AAA+ module composed of a RecA-like alpha/beta ATPase domain followed by a helical domain. AAA+ ATPases mediate chaperone-like protein remodeling. Despite remarkable progress in our understanding of clamp loaders, it is still unclear how recognition of primed DNA by RFC triggers ATP hydrolysis and how hydrolysis leads to conformational changes that can load the clamp onto DNA. While these questions can, of course, only be resolved experimentally, the design of such experiments is itself non-trivial and requires that one first formulate the right hypotheses based on preliminary observations. The functional constraints imposed on protein sequences during evolution are potential sources of information in this regard, inasmuch as these presumably are due to and thus reflect underlying mechanisms. Here, rigorous statistical procedures are used to measure and compare the constraints imposed on various RFC clamp-loader subunits, each of which performs a related but somewhat different, specialized function. Visualization of these constraints, within the context of the RFC structure, provides clues regarding clamp-loader mechanisms--suggesting, for example, that RFC-A possesses a triggering component for DNA-dependent ATP hydrolysis. It also suggests that, starting with RFC-A, four RFC subunits (A-D) are sequentially activated through a propagated switching mechanism in which a conserved arginine swings away from a position that disrupts the catalytic Walker B region and into contact with DNA thread through the center of the RFC/clamp complex. Strong constraints near regions of interaction between subunits and with the clamp likewise provide clues regarding possible coupling of hydrolysis-driven conformational changes to the clamp's release and loading onto DNA.

Adenosine Triphosphatases↗
PubMed2006

The race model inequality: interpreting a geometric measure of the amount of violation.

An inequality by J. O. Miller (1982) has become the standard tool to test the race model for redundant signals reaction times (RTs), as an alternative to a neural summation mechanism. It stipulates that the RT distribution function to redundant stimuli is never larger than the sum of the distribution functions for 2 single stimuli. When many different experimental conditions are to be compared, a numerical index of violation is very desirable. Widespread practice is to take a certain area with contours defined by the distribution functions for single and redundant stimuli. Here this area is shown to equal the difference between 2 mean RT values. This result provides an intuitive interpretation of the index and makes it amenable to simple statistical testing. An extension of this approach to 3 redundant signals is presented.

Auditory Perception↗
PubMed1997

Feature extraction and modeling of the variability of performance in terms of biomechanical motion patterns during MMH tasks.

In investigating manual material handling (MMH) jobs, such as lifting, the quantification of the various kinematic and kinetic parameters of the lift is an important step towards functional assessment and evaluation. Experimental data collection generates a large quantity of data for the different kinetic, kinematic, and electromyographic parameters over the various lifting cycles. In order to efficiently manage and interpret the data, it is important to use appropriate tools which would reduce the dimension of the original data set without sacrificing any important features. Furthermore, the generated parameters are often expressed as a function of the lifting cycle resulting in complex waveforms as the unit of analysis. Appropriate statistical analysis of these waveforms or motion profiles should reflect their vectorial constitution as a function of the lifting cycle rather than the usual method of using traditional descriptive statistics based on collapsing the data over the cycle.

Adult↗
PubMed2005

On analyzing circadian rhythms data using nonlinear mixed models with harmonic terms.

Wang, Ke, and Brown (2003, Biometrics59, 804-812) developed a smoothing-based approach for modeling circadian rhythms with random effects. Their approach is flexible in that fixed and random covariates can affect both the amplitude and phase shift of a nonparametrically smoothed periodic function. In motivating their approach, Wang et al. stated that a simple sinusoidal function is too restrictive. In addition, they stated that "although adding harmonics can improve the fit, it is difficult to decide how many harmonics to include in the model, and the results are difficult to interpret." We disagree with the notion that harmonic models cannot be a useful tool in modeling longitudinal circadian rhythm data. In this note, we show how nonlinear mixed models with harmonic terms allow for a simple and flexible alternative to Wang et al.'s approach. We show how to choose the number of harmonics using penalized likelihood to flexibly model circadian rhythms and to estimate the effect of covariates on the rhythms. We fit harmonic models to the cortisol circadian rhythm data presented by Wang et al. to illustrate our approach. Furthermore, we evaluate the properties of our procedure with a small simulation study. The proposed parametric approach provides an alternative to Wang et al.'s semiparametric approach and has the added advantage of being easy to implement in most statistical software packages.

Circadian Rhythm↗
PubMed2001

[Roaming through methodology. XXXVI. Likelihood ratios and Bayes' rule].

In practice, the terms 'sensitivity' and 'specificity' are often used in a different sense to that found in textbooks. Their value depends on the composition of the groups in which the test was applied. It is rarely recognised that sensitivity and specificity change during the course of a disease. The interpretation of their value appears to be difficult. The likelihood ratio combines sensitivity and specificity, and is therefore associated with the same problems. The likelihood ratio is Bayes' rule in its simplest form: how does a given probability (in this case that of a particular disease being present) change with the addition of a single new fact (i.e., the result of a diagnostic test)? The Bayesian approach is applied in various fields but rarely in clinical practice, because the prior probability of a diagnosis is difficult to quantify. Likelihood ratios are useful when studying the diagnostic process and when teaching the diagnostic thought process. They can also be applied in the statistical interpretation of clinical trial results.

Bayes Theorem↗
PubMed1997

Interpreting health outcomes.

Interest in outcomes is universal. To patients, good outcomes represent their highest hopes for therapy; to health care professionals, good outcomes are the desired end-point of a complex web of care. More recently, politicians and health care managers too have shifted their emphasis away from health service activity and towards what is termed 'health gain'. The rise of the outcomes movement appears irresistible. However, the difficulties in interpreting outcomes data will not go away. Outcomes measured using routine data are subject to numerous biases and many practical difficulties. Despite recent statistical, methodological and technological advances, comparisons of outcomes at best provide us with weak evidence of either the effectiveness or the quality of health care. And sometimes they may frankly mislead. The apparent intuitiveness of outcomes monitoring has broad public appeal. But enthusiasm for outcomes needs to be tempered with a clear understanding of their limitations.

Data Interpretation, Statistical↗
PubMed1997

Interpreting profiling data in behavioral health care for a continuous quality improvement cycle.

OUTCOME MEASUREMENT SYSTEM: PsychSentinel, a symptom reduction measure, uses 20 diagnostically defined symptom checklists derived from the Diagnostic and Statistical Manual of Mental Disorders, 4th edition (DSM-IV). Symptoms are enumerated and are assigned weights on the basis of clinical significance, providing an overall assessment of symptom intensity. The availability of multisite benchmark norms makes possible the computation of observed-to-expected ratios. EXAMPLES OF THE CONTINUOUS QUALITY IMPROVEMENT CYCLE: Six examples, drawn from the experience of a number of behavioral health care programs since 1994, illustrate how outcome data can be used to guide and test changes that will effect improvements over current practices. Example 1: Problem identification is one of the most obvious and immediate applications of outcome data relative to a quality improvement process. Data were presented at a meeting of the hospital medical staff; the data showed that one clinician had significantly poorer outcomes in treating bipolar patients. A review of the medical records for bipolar patients treated by this clinician indicated that this clinician was changing medications too rapidly, a problem that was quickly and easily corrected-with improved outcomes. Example 6: Data revealed that patients who were treated in accordance with the critical pathway showed a greater degree of improvement, even though these patients entered treatment with a 10% greater level of symptom intensity. SUMMARY AND CONCLUSIONS: Each example provides a sample of variability in outcomes and therefore an opportunity to study the reasons for the variability and institute changes.

Bipolar Disorder↗
PubMed2004

Data on the migration of health-care workers: sources, uses, and challenges.

The migration of health workers within and between countries is a growing concern worldwide because of its impact on health systems in developing and developed countries alike. Policy decisions need to be made at the national, regional and international levels to manage more effectively this phenomenon, but those decisions will be effective and correctly implemented and evaluated only if they are based on adequate statistical data. Most statistics on the migration of health-care workers are neither complete nor fully comparable, and they are often underused, limited (because they often give only a broad description of the phenomena) and not as timely as required. There is also a conflict between the wide range of potential sources of data and the poor statistical evidence on the migration of health personnel. There are two major problems facing researchers who wish to provide evidence on this migration: the problems commonly faced when studying migration in general, such as definitional and comparability problems of "worker migrations" and those related to the specific movements of the health workforce. This paper presents information on the uses of statistics and those who use them, the strengths and limitations of the main data sources, and other challenges that need to be met to obtain good evidence on the migration of health workers. This paper also proposes methods to improve the collection, analysis, sharing, and use of statistics on the migration of health workers.

Data Collection↗
PubMed2000

Do you see what I mean? Indices of central tendency.

There are many indices of the middle, or central tendency, of a set of numbers, including the mode, median, and mean. Indeed, there are, several "means," of which the arithmetic mean is only one. When data are skewed, or when there are outliers at one or both ends of the distribution that may distort the results, "robust" estimators of the mean, such as the trimmed mean or the bisquare weight mean, give better results than does the arithmetic mean. If the data reflect growth over time, the geometric mean is a more accurate reflection of the middle point than are other indices, and in determining sample size when the sample size varies among groups, the harmonic mean is the one of choice. Finally, this paper discusses the difference between the lay and statistical use of the term "average" and how this difference can lead to problems in interpretation.

Data Interpretation, Statistical↗