Correlation Analysis in Medical Research

See Article, p 333KEY POINT: Correlation coefficients quantify the strength of a linear (Pearson correlation) or monotonic (Spearman correlation) relationship between 2 continuous variables.In this issue of Anesthesia & Analgesia, Schwenk et al1 report results of a study on the relationship between the number of attendees at anesthesiology conferences and several Twitter metrics. The authors used Spearman rank correlation to analyze the data (Figure).Figure.: Excerpt from Schwenk et al1 (Table 2). The relationship between attendees/registrants of anesthesiology conferences and Twitter metrics is appropriately analyzed with Spearman correlation. The estimates of Spearman ρ (here referred to as “r s”) are appropriately accompanied by 95% CIs. CI indicates confidence interval.Correlation is a measure of the strength of the relationship between 2 variables.2 Of the several available correlation statistics, Pearson correlation (abbreviated as “r”) and Spearman rank correlation (abbreviated as “ρ” or rho) are probably most widely used. Their coefficients quantify the strength of a linear (Pearson) or monotonic (Spearman) relationship. A relationship is monotonic when the value of one variable consistently increases (positive correlation) or decreases (negative correlation) as the value of the other variable increases. A linear relationship is a special case of a monotonic relationship, in which the rate of change is constant. Pearson and Spearman correlation coefficients range from –1 to +1, with absolute values increasingly closer to 1 indicating an increasingly stronger relationship. Various somewhat arbitrary cut-points have been proposed to categorize the strength of the relationship using descriptors like “weak” (eg, r < 0.40), “moderate” (eg, r = 0.40 to 0.69), or “strong” (eg, r ≥ 0.70).2 The interpretation should also take into account the confidence interval of the observed coefficient as an estimate of what the correlation could plausibly be in the population from which the data were sampled. Valid inference relies on several assumptions being met2: 1. The sample is representative of the population of interest. 2. Each pair of values is measured independently (ie, there are no multiple observations from the same subject or patient). Additional assumptions apply to Pearson correlation: 3. Both variables are continuous and approximately normally distributed random variables. 4. The relationship between the variables is linear. 5. There are no extreme outliers. Alternatives are available when assumptions 2 through 5 are violated. When data pairs are not independent, analysis techniques such as linear mixed-effects models may be applied.3 When one variable is not an observed random variable, but is rather manipulated by the researchers, linear regression can be appropriate.4 When at least one variable is not normally distributed, when the relationship between the variables is not linear, or when there are relevant outliers, Spearman correlation is recommended. Spearman correlation is based on the ranks of the values of each variable instead of their actual values, and it can basically be used for all data that can be ranked, including ordinal and nonnormally distributed continuous data. In contrast to the appropriate use of correlation coefficients by Schwenk et al,1 correlation is often misused in the medical literature. In particular, correlation coefficients do not allow conclusions on whether the change in one variable is causally related to the change in the other variable. Also, correlation coefficients do not describe the agreement between 2 variables (eg, between values measured by 2 devices).5 Variables can have a high correlation, but at the same time, low agreement (eg, when one measurement technique consistently underestimates or overestimates the other).