Howlers caused by using stepwise regression I am well aware of the problems of stepwise/forward/backward selection in regression models.  There are numerous cases of researchers denouncing the methods and pointing to better alternatives.  I was  curious if there are any stories that exist where a statistical analysis:


*

*has used stepwise regression;

*made some important conclusions based on the final model

*the conclusion was wrong, resulting in negative consequences for the individual, their research, or their organisation


My thought on this if stepwise methods are bad, then there should be consequences in the "real world" for using them.
 A: There is more than one question being asked. The most narrow one is asking for an example of when stepwise regression has caused harm because it was perfomed stepwise. This is of course true, but can only be established unequivocally when the data used for stepwise regression is also published, and someone reanalyses it and publishes a peer reviewed correction with a published primary authors' retraction. To make accusations in any other context risks legal action, and, if we use a different data set, we could suspect that a mistake was made, but "statistics is never proving anything" and we would not be able to establish that a mistake was made; "beyond a reasonable doubt". 
As a point of fact, one frequently gets different results depending on whether one does stepwise elimination or stepwise buildup of a regression equation, which suggest to us that neither approach is sufficiently correct to recommend its usage. Clearly, something else is going on, and that brings us to a broader question, also asked above, but in bullet form, amounting to "What are the problems with stepwise regression, anyhow? That is the more useful question to answer and has the added benefit that I will not have a law suit filed against me for answering it. 
Doing it right for stepwise MLR, means using 1) physically correct units (see below), and 2) appropriate variable transformation for best correlations and error distribution type (for homoscedasticity and physicality), and 3) using all permutations of variable combinations, not step-wise, all of them, and 4) if one performs exhaustive regression diagnostics then one avoids missing high VIF (collinearity) variable combinations that would otherwise be misleading, then the reward is better regression. 
As promised for #1 above, we next explore the correct units for a physical system. Since good results from regression are contingent upon the correct treatment of variables, we need to be mindful of the usual dimensions of physical units and balance our equations appropriately. Also, for biological applications, an awareness and accounting for the dimensionality of allometric scaling is needed.  
Please read
this example of physical investigation of a biologic system for how to extend the balancing of units to biology.
In that paper, steps 1) through 4) above were followed and a best formula was found using extensive regression analysis namely, $GFR=k∗W^{1/4}V^{2/3}$, where $GFR$ is glomerular filtration rate, a marker of catabolism, where the units are understood using fractal geometry such that $W$, weight was a four dimensional fractal geometric construct, and V, volume, was called a Euclidean, or three dimensional variable. Then $1=\frac{1}{4} \frac{4}{3}+\frac{2}{3}$. So that the formula is dimensionally consistent with metabolism. That is not an easy statement to grasp. Consider that 1) It is generally unappreciated (unknown) that $GFR$ is a marker of metabolism. 2) Fractal geometry is only infrequently taught and the physical interpretation of the formula presented is difficult to grasp even for someone who has mathematical training.
