Genesis and interpretation of differences in distribution of baseline characteristics between cases and non-cases in cohort studies

In cohort studies the transition of an individual from a non-case to a case (or event) can be viewed as a random selection process which is dependent on the values of some baseline risk variables. When true risk factors are studied the cases will be found to have different mean baseline values than the non-cases. The difference at baseline can also extend to other features of the statistical distributions for cases and non-cases. An illustration is given based on data from the Framingham Heart Study with systolic blood pressure and cigarette smoking as baseline risk variables and death due to all causes as an outcome. A mathematical model describing baseline distribution and selection to be a case is developed and discussed. This model is consistent, for example, with the observed differences between cases and non-cases in the regression of baseline systolic blood pressure upon number of cigarettes smoked, as well as other parameters. It is argued that these results should serve as a caution against making inferences concerning biological mechanisms based on differences in statistics for cases and non-cases. The risk function assumed in the mathematical model is shown, by examples, to give results similar to those obtained using the well-known logistic risk function.