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 in Anesthesia & 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 in Anesthesia & Analgesia demonstrate 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.
Designing, conducting, analyzing, reporting, and interpreting the findings of a research study require an understanding of the types and characteristics of data and variables. Descriptive statistics ...are typically used simply to calculate, describe, and summarize the collected research data in a logical, meaningful, and efficient way. Inferential statistics allow researchers to make a valid estimate of the association between an intervention and the treatment effect in a specific population, based upon their randomly collected, representative sample data. Categorical data can be either dichotomous or polytomous. Dichotomous data have only 2 categories, and thus are considered binary. Polytomous data have more than 2 categories. Unlike dichotomous and polytomous data, ordinal data are rank ordered, typically based on a numerical scale that is comprised of a small set of discrete classes or integers. Continuous data are measured on a continuum and can have any numeric value over this continuous range. Continuous data can be meaningfully divided into smaller and smaller or finer and finer increments, depending upon the precision of the measurement instrument. Interval data are a form of continuous data in which equal intervals represent equal differences in the property being measured. Ratio data are another form of continuous data, which have the same properties as interval data, plus a true definition of an absolute zero point, and the ratios of the values on the measurement scale make sense. The normal (Gaussian) distribution (“bell-shaped curve”) is of the most common statistical distributions. Many applied inferential statistical tests are predicated on the assumption that the analyzed data follow a normal distribution. The histogram and the Q–Q plot are 2 graphical methods to assess if a set of data have a normal distribution (display “normality”). The Shapiro-Wilk test and the Kolmogorov-Smirnov test are 2 well-known and historically widely applied quantitative methods to assess for data normality. Parametric statistical tests make certain assumptions about the characteristics and/or parameters of the underlying population distribution upon which the test is based, whereas nonparametric tests make fewer or less rigorous assumptions. If the normality test concludes that the study data deviate significantly from a Gaussian distribution, rather than applying a less robust nonparametric test, the problem can potentially be remedied by judiciously and openly(1) performing a data transformation of all the data values; or (2) eliminating any obvious data outlier(s).
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.This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal.
Descriptive statistics are specific methods basically used to calculate, describe, and summarize collected research data in a logical, meaningful, and efficient way. Descriptive statistics are ...reported numerically in the manuscript text and/or in its tables, or graphically in its figures. This basic statistical tutorial discusses a series of fundamental concepts about descriptive statistics and their reporting. The mean, median, and mode are 3 measures of the center or central tendency of a set of data. In addition to a measure of its central tendency (mean, median, or mode), another important characteristic of a research data set is its variability or dispersion (ie, spread). In simplest terms, variability is how much the individual recorded scores or observed values differ from one another. The range, standard deviation, and interquartile range are 3 measures of variability or dispersion. The standard deviation is typically reported for a mean, and the interquartile range for a median. Testing for statistical significance, along with calculating the observed treatment effect (or the strength of the association between an exposure and an outcome), and generating a corresponding confidence interval are 3 tools commonly used by researchers (and their collaborating biostatistician or epidemiologist) to validly make inferences and more generalized conclusions from their collected data and descriptive statistics. A number of journals, including Anesthesia & Analgesia, strongly encourage or require the reporting of pertinent confidence intervals. A confidence interval can be calculated for virtually any variable or outcome measure in an experimental, quasi-experimental, or observational research study design. Generally speaking, in a clinical trial, the confidence interval is the range of values within which the true treatment effect in the population likely resides. In an observational study, the confidence interval is the range of values within which the true strength of the association between the exposure and the outcome (eg, the risk ratio or odds ratio) in the population likely resides. There are many possible ways to graphically display or illustrate different types of data. While there is often latitude as to the choice of format, ultimately, the simplest and most comprehensible format is preferred. Common examples include a histogram, bar chart, line chart or line graph, pie chart, scatterplot, and box-and-whisker plot. Valid and reliable descriptive statistics can answer basic yet important questions about a research data set, namely“Who, What, Why, When, Where, How, How Much?”
Inferential statistics relies heavily on the central limit theorem and the related law of large numbers. According to the central limit theorem, regardless of the distribution of the source ...population, a sample estimate of that population will have a normal distribution, but only if the sample is large enough. The related law of large numbers holds that the central limit theorem is valid as random samples become large enough, usually defined as an n ≥ 30. In research-related hypothesis testing, the term “statistically significant” is used to describe when an observed difference or association has met a certain threshold. This significance threshold or cut-point is denoted as alpha (α) and is typically set at .05. When the observed P value is less than α, one rejects the null hypothesis (Ho) and accepts the alternative. Clinical significance is even more important than statistical significance, so treatment effect estimates and confidence intervals should be regularly reported. A type I error occurs when the Ho of no difference or no association is rejected, when in fact the Ho is true. A type II error occurs when the Ho is not rejected, when in fact there is a true population effect. Power is the probability of detecting a true difference, effect, or association if it truly exists. Sample size justification and power analysis are key elements of a study design. Ethical concerns arise when studies are poorly planned or underpowered. When calculating sample size for comparing groups, 4 quantities are neededα, type II error, the difference or effect of interest, and the estimated variability of the outcome variable. Sample size increases for increasing variability and power, and for decreasing α and decreasing difference to detect. Sample size for a given relative reduction in proportions depends heavily on the proportion in the control group itself, and increases as the proportion decreases. Sample size for single-group studies estimating an unknown parameter is based on the desired precision of the estimate. Interim analyses assessing for efficacy and/or futility are great tools to save time and money, as well as allow science to progress faster, but are only 1 component considered when a decision to stop or continue a trial is made.
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, I2, 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.
Perioperative medicine remains an evolving, interdisciplinary subspecialty, which encompasses the unique perspectives and incorporates the respective vital expertise of numerous stakeholders. This ...integrated model of perioperative medicine and care has a wide-ranging set of clinical, strategic, and operational goals. Among these various programmatic goals, a subset of 4, specific, interdependent goals include (1) enhancing patient-centered care, (2) embracing shared decision-making, (3) optimizing health literacy, and (4) avoiding futile surgery. Achieving and sustaining this subset of 4 goals requires continued innovative approaches to perioperative care. The burgeoning field of narrative medicine represents 1 such innovative approach to perioperative care. Narrative medicine is considered the most prominent recent development in the medical humanities. Its central tenet is that attention to narrative-in the form of the patient's story, the clinician's story, or a story constructed together by the patient and clinician-is essential for optimal patient care. If we can view the health care experience through the patient's eyes, we will become more responsive to patients' needs and, thereby, better clinicians. There is a potential clinical nexus between the perioperative medicine practice and narrative medicine skills, which, if capitalized, can maximize perioperative patient care. There are a number of untapped educational and research opportunities in this fruitful nexus between perioperative medicine and narrative medicine.
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