Principles of Linear Regression

Abstract

In the past chapters we discussed different statistical methods to test statistically experimental data from clinical trials. We did not emphasize correlation and regression analysis. The point is that correlation and regression analysis test correlations, rather than causal relationships. Two samples may be strongly correlated e.g., two different diagnostic tests for assessment of the same phenomenon. This does, however, not mean that one diagnostic test causes the other. In testing the data from clinical trials we are mainly interested in causal relationships. When such assessments were statistically analyzed through correlation analyses mainly, we would probably be less convinced of a causal relationship than we are while using prospective hypothesis testing. So, this is the main reason we so far did not address correlation testing extensively. With epidemiological observational research things are essentially different: data are obtained from the observation of populations or the retrospective observation of patients selected because of a particular condition or illness. Conclusions are limited to the establishment of relationships, causal or not. We currently believe that relationships in medical research between a factor and an outcome can only be proven to be causal when the factor is introduced and subsequently gives rise to the outcome. We are more convinced when such is tested in the form of a controlled clinical trial. A problem with multiple regression and logistic regression analysis as method for analyzing of multiple samples in clinical trials is closely related to this point.