6 Best practices in regression analysis that biomedical researchers need to know
As biomedical researchers, we frequently are interested in specific directions between variables: do higher levels of X biomarker indicate greater severity of Y disease? Does a decrease in J affect K health outcome? Regression analysis is a valuable statistical tool for assessing these relationships. We previously looked at the different types of regression analyses and what each could be used for, as well as the differences between correlation and regression analyses. In this blogpost, we’ll look at certain best practices to strengthen your regression analyses and make sure you’re generating high-quality, robust evidence.
1. Always Report the Regression Equation
Think of the regression equation as the sauce for a pizza: the base (research question) and toppings (your results) just don’t go together without it. The regression equation basically shows how the independent variables (predictors) relate to the dependent variable (outcome) in your study. When you report the equation, it helps others understand the nature and strength of the relationships you've found. For example, if we're examining the relationship between blood pressure (dependent variable) and age (independent variable), a simple linear regression equation might look like this: "Blood Pressure = 120 + 0.5 * Age."
2. Report the Model's Goodness of Fit
Alright, let's see how well our regression model fits the data. We need a measure for that, for example, r-squared for simple regression and R-squared for multiple regression. This little gem ranges from 0 to 1, with higher values indicating a better fit. It tells us the proportion of the variability in the dependent variable that's explained by the independent variables. So, if your R² is 0.80, it means a whopping 80% of the variation in the outcome can be attributed to the predictors!
3. Present the Results Graphically Where Possible
A picture is worth a thousand words, right? So, when dealing with simple linear regression, plot those data points on a scatter plot! It helps you visualize the relationship between the variables and gives readers a better understanding of what you’ve found out. Remember to label your axes and title your plot to keep it nice and clear.
4. Don't Extend the Regression Line Beyond Data Range
Whoops, our excitement can sometimes lead us astray. When plotting your regression line on the scatter plot, resist the urge to extend it beyond the minimum and maximum values of your data. Doing so might lead to unrealistic predictions, like negative blood pressure (!). Let's stick to what we know and keep things grounded in reality.
5. Address Collinearity and Interaction Between Multiple Predictors
Multiple regression can be powerful but tricky. Before you dive in, it's crucial to check for collinearity, which occurs when your independent variables are strongly correlated. If this happens, it becomes challenging to disentangle their individual effects on the dependent variable. One way to spot collinearity is by examining the correlation matrix. Also, keep an eye out for interaction effects, where the relationship between one predictor and the outcome depends on the value of another predictor.
6. Specify How the Final Model Was Developed
When you've finished tinkering with your multiple regression model, be transparent about how you arrived at the final version. Two common approaches are "stepwise" and "forward" model building. Stepwise involves gradually adding or removing predictors based on statistical criteria, while forward involves adding predictors one by one based on theoretical reasoning. Make it clear which method you used to develop your model.
Our expert biostatisticians can guide you through every step of conducting and reporting a regression analysis. Check out Editage’s Statistical Analysis & Review Services.
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