[Regression I - How to describe the linear dependence of a medical parameter from an explanatory variable]

Regression models describe the dependence of a response variable from one or several explanatory variables. Typical indications are prognosis, diagnosis and the description of cause-effect relationships. The basic model is a simple linear regression that relates a continuous response variable (dependent variable) to one independent variable. Situations with an error-free independent variable without biological variation (standard regression models) have to be distinguished from others (errors-in-variables models). In the latter case the standard regression line will describe the regression-to-the-mean phenomenon and should not be interpreted as a treatment effect.Misinterpretations result mainly from ignored deviations from the model assumptions, such as the leverages of outliers, inhomogeneities/overlooked further explanatory variables, and from extrapolations beyond the range of measurements that cannot be justified by substantial knowledge.Grafical representations can demonstrate the good fit/lack of fit of a model and should be used more extensively. If the assumption of independent, identically distributed normal errors is justified, then tests, confidence limits, and prediction limits are extremely useful.