Correlation in the broadest sense is a measure of an association between variables. In correlated data, the change in the magnitude of 1 variable is associated with a change in the magnitude of another variable, either in the same (positive correlation) or in the opposite (negative correlation) direction. Most often, the term correlation is used in the context of a linear relationship between 2 continuous variables and expressed as Pearson product-moment correlation. The Pearson correlation coefficient is typically used for jointly normally distributed data (data that follow a bivariate normal distribution). For nonnormally distributed continuous data, for ordinal data, or for data with relevant outliers, a Spearman rank correlation can be used as a measure of a monotonic association. Both correlation coefficients are scaled such that they range from –1 to +1, where 0 indicates that there is no linear or monotonic association, and the relationship gets stronger and ultimately approaches a straight line (Pearson correlation) or a constantly increasing or decreasing curve (Spearman correlation) as the coefficient approaches an absolute value of 1. Hypothesis tests and confidence intervals can be used to address the statistical significance of the results and to estimate the strength of the relationship in the population from which the data were sampled. The aim of this tutorial is to guide researchers and clinicians in the appropriate use and interpretation of correlation coefficients.

Conventional cardiovascular monitoring may not detect tissue hypoxia, and conventional cardiovascular support aiming at global hemodynamics may not restore tissue oxygenation. NIRS offers non-invasive online monitoring of tissue oxygenation in a wide range of clinical scenarios. NIRS monitoring is commonly used to measure cerebral oxygenation (rSO₂), e.g. during cardiac surgery. In this review, we will show that tissue hypoxia occurs frequently in the perioperative setting, particularly in cardiac surgery. Therefore, measuring and obtaining adequate tissue oxygenation may prevent (postoperative) complications and may thus be cost-effective. NIRS monitoring may also be used to detect tissue hypoxia in (prehospital) emergency settings, where it has prognostic significance and enables monitoring of therapeutic interventions, particularly in patients with trauma. However, optimal therapeutic agents and strategies for augmenting tissue oxygenation have yet to be determined.

Survival analysis, or more generally, time-to-event analysis, refers to a set of methods for analyzing the length of time until the occurrence of a well-defined end point of interest. A unique feature of survival data is that typically not all patients experience the event (eg, death) by the end of the observation period, so the actual survival times for some patients are unknown. This phenomenon, referred to as censoring, must be accounted for in the analysis to allow for valid inferences. Moreover, survival times are usually skewed, limiting the usefulness of analysis methods that assume a normal data distribution. As part of the ongoing series inAnesthesia & Analgesia, this tutorial reviews statistical methods for the appropriate analysis of time-to-event data, including nonparametric and semiparametric methods—specifically the Kaplan-Meier estimator, log-rank test, and Cox proportional hazards model. These methods are by far the most commonly used techniques for such data in medical literature. Illustrative examples from studies published inAnesthesia & Analgesiademonstrate how these techniques are used in practice. Full parametric models and models to deal with special circumstances, such as recurrent events models, competing risks models, and frailty models, are briefly discussed.

Researchers reporting results of statistical analyses, as well as readers of manuscripts reporting original research, often seek guidance on how numeric results can be practically and meaningfully interpreted. With this article, we aim to provide benchmarks for cutoff or cut-point values and to suggest plain-language interpretations for a number of commonly used statistical measures of association, agreement, diagnostic accuracy, effect size, heterogeneity, and reliability in medical research. Specifically, we discuss correlation coefficients, Cronbach’s alpha, I ², intraclass correlation (ICC), Cohen’s and Fleiss’ kappa statistics, the area under the receiver operating characteristic curve (AUROC, concordance statistic), standardized mean differences (Cohen’s d, Hedge’s g, Glass’ delta), and z scores. We base these cutoff values on what has been previously proposed by experts in the field in peer-reviewed literature and textbooks, as well as online statistical resources. We integrate, adapt, and/or expand previous suggestions in attempts to (a) achieve a compromise between divergent recommendations, and (b) propose cutoffs that we perceive sensible for the field of anesthesia and related specialties. While our suggestions provide guidance on how the results of statistical tests are typically interpreted, this does not mean that the results can universally be interpreted as suggested here. We discuss the well-known inherent limitations of using cutoff values to categorize continuous measures. We further emphasize that cutoff values may depend on the specific clinical or scientific context. Rule-of-the thumb approaches to the interpretation of statistical measures should therefore be used judiciously.

Anesthesia, critical care, perioperative, and pain research often involves study designs in which the same outcome variable is repeatedly measured or observed over time on the same patients. Such repeatedly measured data are referred to as longitudinal data, and longitudinal study designs are commonly used to investigate changes in an outcome over time and to compare these changes among treatment groups. From a statistical perspective, longitudinal studies usually increase the precision of estimated treatment effects, thus increasing the power to detect such effects. Commonly used statistical techniques mostly assume independence of the observations or measurements. However, values repeatedly measured in the same individual will usually be more similar to each other than values of different individuals and ignoring the correlation between repeated measurements may lead to biased estimates as well as invalid P values and confidence intervals. Therefore, appropriate analysis of repeated-measures data requires specific statistical techniques. This tutorial reviews 3 classes of commonly used approaches for the analysis of longitudinal data. The first class uses summary statistics to condense the repeatedly measured information to a single number per subject, thus basically eliminating within-subject repeated measurements and allowing for a straightforward comparison of groups using standard statistical hypothesis tests. The second class is historically popular and comprises the repeated-measures analysis of variance type of analyses. However, strong assumptions that are seldom met in practice and low flexibility limit the usefulness of this approach. The third class comprises modern and flexible regression-based techniques that can be generalized to accommodate a wide range of outcome data including continuous, categorical, and count data. Such methods can be further divided into so-called “population-average statistical models” that focus on the specification of the mean response of the outcome estimated by generalized estimating equations, and “subject-specific models” that allow a full specification of the distribution of the outcome by using random effects to capture within-subject correlations. The choice as to which approach to choose partly depends on the aim of the research and the desired interpretation of the estimated effects (population-average versus subject-specific interpretation). This tutorial discusses aspects of the theoretical background for each technique, and with specific examples of studies published in Anesthesia & Analgesia, demonstrates how these techniques are used in practice.