Explorations in statistics: regression

Review of guidance papers on regression modeling in statistical series of medical journals

Although regression models play a central role in the analysis of medical research projects, there still exist many misconceptions on various aspects of modeling leading to faulty analyses. Indeed, the rapidly developing statistical methodology and its recent advances in regression modeling do not seem to be adequately reflected in many medical publications. This problem of knowledge transfer from statistical research to application was identified by some medical journals, which have published series of statistical tutorials and (shorter) papers mainly addressing medical researchers. The aim of this review was to assess the current level of knowledge with regard to regression modeling contained in such statistical papers. We searched for target series by a request to international statistical experts. We identified 23 series including 57 topic-relevant articles. Within each article, two independent raters analyzed the content by investigating 44 predefined aspects on regression modeling. We assessed to what extent the aspects were explained and if examples, software advices, and recommendations for or against specific methods were given. Most series (21/23) included at least one article on multivariable regression. Logistic regression was the most frequently described regression type (19/23), followed by linear regression (18/23), Cox regression and survival models (12/23) and Poisson regression (3/23). Most general aspects on regression modeling, e.g. model assumptions, reporting and interpretation of regression results, were covered. We did not find many misconceptions or misleading recommendations, but we identified relevant gaps, in particular with respect to addressing nonlinear effects of continuous predictors, model specification and variable selection. Specific recommendations on software were rarely given. Statistical guidance should be developed for nonlinear effects, model specification and variable selection to better support medical researchers who perform or interpret regression analyses.

Blood oxygenation level dependent magnetic resonance imaging and diffusion weighted MRI imaging for benign and malignant breast cancer discrimination

PURPOSE

The purpose of this study is to assess Blood oxygenation level dependent Magnetic Resonance Imaging (BOLD-MRI) and Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) in the differentiation of benign and malignant breast lesions.

METHODS

Fifty-nine breast lesions (26 benign and 33 malignant lesions) pathologically proven in 59 patients were included in this retrospective study. As BOLD parameters were estimated basal signal S₀ and the relaxation rate R2*, diffusion and perfusion parameters were derived by DWI (pseudo-diffusion coefficient (Dp), perfusion fraction (fp) and tissue diffusivity (Dt)). Wilcoxon-Mann-Whitney U test and Receiver operating characteristic (ROC) analyses were calculated and area under ROC curve (AUC) was obtained. Moreover, pattern recognition approaches (linear discrimination analysis (LDA), support vector machine, k-nearest neighbours, decision tree) with least absolute shrinkage and selection operator (LASSO) method and leave one out cross validation approach were considered.

RESULTS

A significant discrimination was obtained by the standard deviation value of S0, as BOLD parameter, that reached an AUC of 0.76 with a sensitivity of 65%, a specificity of 85% and an accuracy of 76%. No significant discrimination was obtained considering diffusion and perfusion parameters. Considering LASSO results, the features to use as predictors were all extracted parameters except that the mean value of R2* and the best result was obtained by a LDA that obtained an AUC = 0.83, with a sensitivity of 88%, a specificity of 77% and an accuracy of 83%.

CONCLUSIONS

Good performance to discriminate benign and malignant lesions could be obtained using BOLD and DWI derived parameters with a LDA classification approach. However, these findings should be proven on larger and several dataset with different MR scanners.

Statistical considerations in reporting cardiovascular research

The problem of inadequate statistical reporting is long standing and widespread in the biomedical literature, including in cardiovascular physiology. Although guidelines for reporting statistics have been available in clinical medicine for some time, there are currently no guidelines specific to cardiovascular physiology. To assess the need for guidelines, we determined the type and frequency of statistical tests and procedures currently used in the American Journal of Physiology-Heart and Circulatory Physiology. A PubMed search for articles published in the American Journal of Physiology-Heart and Circulatory Physiology between January 1, 2017, and October 6, 2017, provided a final sample of 146 articles evaluated for methods used and 38 articles for indepth analysis. The t-test and ANOVA accounted for 71% (212 of 300 articles) of the statistical tests performed. Of six categories of post hoc tests, Bonferroni and Tukey tests were used in 63% (62 of 98 articles). There was an overall lack in details provided by authors publishing in the American Journal of Physiology-Heart and Circulatory Physiology, and we compiled a list of recommended minimum reporting guidelines to aid authors in preparing manuscripts. Following these guidelines could substantially improve the quality of statistical reports and enhance data rigor and reproducibility.

Explorations in statistics: the log transformation

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This thirteenth installment of Explorations in Statistics explores the log transformation, an established technique that rescales the actual observations from an experiment so that the assumptions of some statistical analysis are better met. A general assumption in statistics is that the variability of some response Y is homogeneous across groups or across some predictor variable X. If the variability-the standard deviation-varies in rough proportion to the mean value of Y, a log transformation can equalize the standard deviations. Moreover, if the actual observations from an experiment conform to a skewed distribution, then a log transformation can make the theoretical distribution of the sample mean more consistent with a normal distribution. This is important: the results of a one-sample t test are meaningful only if the theoretical distribution of the sample mean is roughly normal. If we log-transform our observations, then we want to confirm the transformation was useful. We can do this if we use the Box-Cox method, if we bootstrap the sample mean and the statistic t itself, and if we assess the residual plots from the statistical model of the actual and transformed sample observations.

Explorations in statistics: the assumption of normality

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This twelfth installment of Explorations in Statistics explores the assumption of normality, an assumption essential to the meaningful interpretation of a t test. Although the data themselves can be consistent with a normal distribution, they need not be. Instead, it is the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means that must be roughly normal. The most versatile approach to assess normality is to bootstrap the sample mean, the difference between sample means, or t itself. We can then assess whether the distributions of these bootstrap statistics are consistent with a normal distribution by studying their normal quantile plots. If we suspect that an inference we make from a t test may not be justified-if we suspect that the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means is not normal-then we can use a permutation method to analyze our data.

An Index to Objectively Score Supraglottic Abnormalities in Refractory Asthma

BACKGROUND

Patients with refractory asthma frequently have elements of laryngopharyngeal reflux (LPR) with potential aspiration contributing to their poor control. We previously reported on a supraglottic index (SGI) scoring system that helps in the evaluation of LPR with potential aspiration. However, to further the usefulness of this SGI scoring system for bronchoscopists, a teaching system was developed that included both interobserver and intraobserver reproducibility.

METHODS

Five pulmonologists with expertise in fiber-optic bronchoscopy but novice to the SGI participated. A training system was developed that could be used via Internet interaction to make this learning technique widely available.

RESULTS

By the final testing, there was excellent interreader agreement (κ of at least 0.81), thus documenting reproducibility in scoring the SGI. For the measure of intrareader consistency, one reader was arbitrarily selected to rescore the final test 4 weeks later and had a κ value of 0.93, with a 95% CI of 0.79 to 1.00.

CONCLUSIONS

In this study, we demonstrate that with an organized educational approach, bronchoscopists can develop skills to have highly reproducible assessment and scoring of supraglottic abnormalities. The SGI can be used to determine which patients need additional intervention to determine causes of LPR and gastroesophageal reflux. Identification of this problem in patients with refractory asthma allows for personal, individual directed therapy to improve asthma control.

Explorations in statistics: statistical facets of reproducibility

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This eleventh installment of Explorations in Statistics explores statistical facets of reproducibility. If we obtain an experimental result that is scientifically meaningful and statistically unusual, we would like to know that our result reflects a general biological phenomenon that another researcher could reproduce if (s)he repeated our experiment. But more often than not, we may learn this researcher cannot replicate our result. The National Institutes of Health and the Federation of American Societies for Experimental Biology have created training modules and outlined strategies to help improve the reproducibility of research. These particular approaches are necessary, but they are not sufficient. The principles of hypothesis testing and estimation are inherent to the notion of reproducibility in science. If we want to improve the reproducibility of our research, then we need to rethink how we apply fundamental concepts of statistics to our science.

Central respiratory chemosensitivity and cerebrovascular CO2 reactivity: a rebreathing demonstration illustrating integrative human physiology

One of the most effective ways of engaging students of physiology and medicine is through laboratory demonstrations and case studies that combine 1) the use of equipment, 2) problem solving, 3) visual representations, and 4) manipulation and interpretation of data. Depending on the measurements made and the type of test, laboratory demonstrations have the added benefit of being able to show multiple organ system integration. Many research techniques can also serve as effective demonstrations of integrative human physiology. The "Duffin" hyperoxic rebreathing test is often used in research settings as a test of central respiratory chemosensitivity and cerebrovascular reactivity to CO2. We aimed to demonstrate the utility of the hyperoxic rebreathing test for both respiratory and cerebrovascular responses to increases in CO2 and illustrate the integration of the respiratory and cerebrovascular systems. In the present article, methods such as spirometry, respiratory gas analysis, and transcranial Doppler ultrasound are described, and raw data traces can be adopted for discussion in a tutorial setting. If educators have these instruments available, instructions on how to carry out the test are provided so students can collect their own data. In either case, data analysis and quantification are discussed, including principles of linear regression, calculation of slope, the coefficient of determination (R(2)), and differences between plotting absolute versus normalized data. Using the hyperoxic rebreathing test as a demonstration of the complex interaction and integration between the respiratory and cerebrovascular systems provides senior undergraduate, graduate, and medical students with an advanced understanding of the integrative nature of human physiology.

Explorations in statistics: the analysis of change

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This tenth installment of Explorations in Statistics explores the analysis of a potential change in some physiological response. As researchers, we often express absolute change as percent change so we can account for different initial values of the response. But this creates a problem: percent change is really just a ratio, and a ratio is infamous for its ability to mislead. This means we may fail to find a group difference that does exist, or we may find a group difference that does not exist. What kind of an approach to science is that? In contrast, analysis of covariance is versatile: it can accommodate an analysis of the relationship between absolute change and initial value when percent change is useless.

Statistics in clinical research: Important considerations

Statistical analysis is one of the foundations of evidence-based clinical practice, a key in conducting new clinical research and in evaluating and applying prior research. In this paper, we review the choice of statistical procedures, analyses of the associations among variables and techniques used when the clinical processes being examined are still in process. We discuss methods for building predictive models in clinical situations, and ways to assess the stability of these models and other quantitative conclusions. Techniques for comparing independent events are distinguished from those used with events in a causal chain or otherwise linked. Attention then turns to study design, to the determination of the sample size needed to make a given comparison, and to statistically negative studies.

Explorations in statistics: the analysis of ratios and normalized data

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This ninth installment of Explorations in Statistics explores the analysis of ratios and normalized-or standardized-data. As researchers, we compute a ratio-a numerator divided by a denominator-to compute a proportion for some biological response or to derive some standardized variable. In each situation, we want to control for differences in the denominator when the thing we really care about is the numerator. But there is peril lurking in a ratio: only if the relationship between numerator and denominator is a straight line through the origin will the ratio be meaningful. If not, the ratio will misrepresent the true relationship between numerator and denominator. In contrast, regression techniques-these include analysis of covariance-are versatile: they can accommodate an analysis of the relationship between numerator and denominator when a ratio is useless.

Explorations in statistics: permutation methods

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This eighth installment of Explorations in Statistics explores permutation methods, empiric procedures we can use to assess an experimental result-to test a null hypothesis-when we are reluctant to trust statistical theory alone. Permutation methods operate on the observations-the data-we get from an experiment. A permutation procedure answers this question: out of all the possible ways we can rearrange the observations we got, in what proportion of those arrangements is the sample statistic we care about at least as extreme as the one we got? The answer to that question is the P value.