Consider this scenario: scientists hypothesize that a particular disease occurs when levels of a particular hormone are high. They gather data: 1000 people with the disease, 1000 without, and measure their hormone levels.
Assuming the data has normal distribution, the scientists can do a t-test or one-way anova to test if the difference in hormone levels between the disease and non-disease group is significantly different from zero. (I guess this would be a one-sided t-test). In R, the Anova would be expressed like
model <- lm( HormoneLevel ~ Disease, ...)
where Disease is 0/1 according to disease|non-disease, and HormoneLevel is a continuous value (amount per litre or something).
HOWEVER, can the test also be done in the other direction, with HormoneLevel as the independent variable?
model <- lm( Disease ~ HormoneLevel, ...)
Perhaps this makes more sense conceptually as a regression, since the scientists believe that the hormone level may be a cause of the disease.
So the question: is it valid and desirable to switch the dependent and independent variables in this way? If so, are there restrictions on when it can be done?