## What should you consider when choosing a regression analysis?

A: Researchers use regression analysis to understand the relationship between dependent and independent variables and to define models for prediction. Prior to choosing a regression analysis, it is important to identify what data types your experiment produced and to define the question you are trying to answer with your data. It is also imperative to understand that regression models have different assumptions and limitations that affect how they’re interpreted, such as assumption of normal distribution of data, required number of data for analysis, and tendency to be affected by outliers. Therefore, checking that the data obtained meet a regression model’s assumptions is vital in choosing the appropriate statistics and arriving at the correct conclusions.

Graphical representations of data such as scatter plots, histograms, and residual plots are exploratory analyses that can help you determine if some of the assumptions are met prior to data analysis. After exploratory analysis, you can then move on to appropriate data manipulation. For example, data transformation could be done to fit the requirement of normality for parametric tests. But if data transformation does not pass the normality test, then nonparametric tests can be pursued.

## What are the different types of data?

Clinical laboratory data can usually be divided into two general categories: quantitative and qualitative results. Quantitative data can be discreet or continuous while qualitative data can be binary, nominal, or ordinal data. Understanding the difference between these types of data is important in choosing a regression analysis and in deciding how to interpret the results.

## What are some practical applications of regression analysis in the clinical laboratory?

In clinical laboratories, two of the most routine uses of regression analysis are for method comparison and assessing the linearity of an analytical measurement range. In these instances, Ordinary Least Squares (OLS) regression, Deming regression, and Passing-Bablok regression are commonly employed. You can use all of these methods to analyze two variables of the quantitative data type, but it’s important to note that they have different assumptions and limitations. OLS assumes that the independent variable has no error, while Deming and Passing-Bablok assume that the error exists in both the dependent and independent variables.

For comparison of qualitative methods, there are different statistical tests you can perform instead of regression analysis. These include the Chi-Squared test, McNemar test, and Wilcoxon signed rank test. Again, each has its own assumptions and limitations.

## How do you interpret statistical data obtained in linear regression analysis?

When used for method comparison, linear regression analysis can determine statistics such as correlation coefficient, slope, intercept, and confidence intervals. The correlation coefficient measures the strength and direction of the relationship of two variables. A Pearson correlation (r) of 1 suggests a perfect positive linear relationship. However, in a method comparison where the goal is to assess equivalent results, an r of 1 does not necessarily mean the results are equal. The slope indicates the proportional relationship of the data, hence a slope of 1 indicates that x=y if the intercept is 0. The intercept, on the other hand, determines the constant bias. In practice, no two instruments provide the exact same values all the time. The confidence interval of the slope and intercept are used to determine whether the slope is statistically different than 1 and whether the intercept is different than 0.

Overall, understanding a test’s clinical utility is just as important as correctly interpreting the statistical data obtained in a regression analysis. For example, analysis may indicate that two methods are not statistically different, but the difference may be clinically significant. The reverse is also possible.

Jayson V. Pagaduan, PhD, DABCC, is the Chemistry Work Group medical director at Intermountain Health and laboratory director for Intermountain Life Flight in Salt Lake City. +Email: [email protected]