Understanding data in clinical research: a simple graphical display for plotting data (up to four independent variables) after binary logistic regression analysis

Abstract

In clinical research, suitable visualization techniques of data after statistical analysis are crucial for the researches' and physicians' understanding. Common statistical techniques to analyze data in clinical research are logistic regression models. Among these, the application of binary logistic regression analysis (LRA) has greatly increased during past years, due to its diagnostic accuracy and because scientists often want to analyze in a dichotomous way whether some event will occur or not. Such an analysis lacks a suitable, understandable, and widely used graphical display, instead providing an understandable logit function based on a linear model for the natural logarithm of the odds in favor of the occurrence of the dependent variable, Y. By simple exponential transformation, such a logit equation can be transformed into a logistic function, resulting in predicted probabilities for the presence of the dependent variable, P(Y-1/X). This model can be used to generate a simple graphical display for binary LRA. For the case of a single predictor or explanatory (independent) variable, X, a plot can be generated with X represented by the abscissa (i.e., horizontal axis) and P(Y-1/X) represented by the ordinate (i.e., vertical axis). For the case of multiple predictor models, I propose here a relief 3D surface graphic in order to plot up to four independent variables (two continuous and two discrete). By using this technique, any researcher or physician would be able to transform a lesser understandable logit function into a figure easier to grasp, thus leading to a better knowledge and interpretation of data in clinical research. For this, a sophisticated statistical package is not necessary, because the graphical display may be generated by using any 2D or 3D surface plotter.