Relationship between right atrial pressure and the Model For End-Stage Liver Disease (MELD) score in patients with advanced heart failure: Correlation analysis and ROC curve method

Abstract

Researchers may examine the variables related to the events one by one, or they may have a desire to explain and understand the relationship between the variables. Correlation analysis is a statistical method that reveals the direction, degree, and importance of the relationship between variables. The coefficient indicating the direction and degree of the relationship is called the correlation coefficient and is denoted by “r”. The correlation coefficient takes values between “-1” and “+1”. If the r value is close to -1, it indicates a negative relationship between the variables, and if it takes values close to +1, there is a positive relationship. As the correlation coefficient value goes toward “0”, the relationship between the two variables would be weaker. If the value is near ± 1, then there is a perfect correlation: as one variable increases, the other variable tends to also increase (if positive) or decrease (if negative). If the coefficient value lies between ± 0.50 and ± 1, there is a strong correlation. If the value lies between ± 0.30 and ± 0.49, it refers to a medium correlation. When the value lies below 0.29, there is a small correlation. When the value is zero, there is no correlation. Four types of correlations are used in statistical analysis: Pearson correlation, Kendall Rank correlation (Kendall’s tau), Spearman Rank correlation (Spearman’s rho) and the Point-Biserial correlation. In particular, studies using the Pearson and Spearman correlation coefficients are frequently encountered. Pearson’s correlation coefficient is the test statistics that measures the statistical relationship between two continuous variables. Pearson “r” correlation is the most widely used correlation statistic to measure the degree of the relationship between linearly related variables. For the Pearson “r” correlation, both variables should be normally distributed (normally distributed variables have a bell-shaped curve). Other assumptions include linearity and homoscedasticity. Linearity assumes a straight-line relationship between each of the two variables and homoscedasticity assumes that data is equally distributed about the regression line. Spearman rank correlation is a non-parametric test that is used to measure the degree of association between two variables and it is the non-parametric version of the Pearson correlation coefficient. The Spearman rank correlation test does not carry any assumptions about the distribution of the data and is the appropriate correlation analysis, when the variables are measured on a scale that is at least ordinal. If one or both of the variables do not fit the normal distribution, Spearman's rank correlation is used to determine the direction and degree of the relationship between the variables. It is not correct to comment on the cause-effect relationship while interpreting the correlation coefficient. As the correlation shows the direction and degree of the relationship between two variables, while it does not give information about the cause-effect relationship. It is also desired to include explanations that are thought to be guiding for studies in which Kendal's rank correlation and point biserial correlation analyzes are planned to be used. The Kendal's tau coefficient, which is usually smaller than Spearman's rank correlation, is insensitive to errors in the data. However, “p” values are more accurate with smaller sample sizes. In most cases, the interpretations of Kendall’s tau and Spearman’s rank correlation coefficient are very similar and, thus, invariably lead to the same inferences. The point biserial correlation coefficient is a special form of the Pearson correlation coefficient and it is used to measure the strength and direction of the association that exists between one continuous variable and one dichotomous variable. There should be no outliers for the continuous variable for each category of the dichotomous variable and continuous variable should be approximately normally distributed for each category of the dichotomous variable. In this study, the Pearson correlation coefficient between the right atrial pressure (RAP) and Model for End-Stage Liver Disease (MELD) scores of the patients was obtained as r=0.510 and a strong correlation was detected between the variables. By using the correlation coefficient, it is possible to test the null hypothesis stating that there is no relationship between the two variables (r=0). If the obtained “p” value is less than the alpha significance level, the null hypothesis is rejected and the existence of a relationship between the variables is mentioned. In this study, the p value for the correlation coefficient between RAP and MELD score was obtained as “0.001” and considering that the study was conducted at the 0.05 significance level, the null hypothesis of “no relationship” was rejected. In other words, there is a relationship between RAP and MELD variables.