Most likely you have seen a TV commercial for one of the “statin” drugs, say Lipitor or Crestor, which are used to reduce “bad cholesterol” (LDL) and raise “good cholesterol” (HDL). Presumably these do, in fact, cause these level changes for some high fraction of patients ( … who do not have liver disease, who are not nursing, who are not pregnant nor might become pregnant!).
Also, presumably the medical studies that show a link between above median levels of LDL and heart disease are valid.
Why is it then that the drug description sheet (for Crestor, from the manufacturer: http://multivu.prnewswire.com/mnr/astrazeneca/41126/docs/41126-crestor_differentiators_fact_sheet.pdf) states that: “CRESTOR has not been determined to prevent heart disease, heart attacks or strokes.”? Surely the company has tried to show this!
Unfortunately, I don’t know this answer and won’t try to provide some wild speculation (in this particular case at least). But, I will point out that a possible approach is a well thought out engineering model analysis, hopefully supported by some detailed experiments. Ok, I have to speculate at least to the point of giving an example. Suppose that the morphology of the “plaque” buildup or the plaque “deposition” process is altered by the statin. Then even if the blood level is lower (for LDL), then complications from the disease, say a stroke, is not altered.
One type of analysis that could be done is to model the deposition process. You would have to use a PDE and account for the transport of the plaque precursors across the blood flow in arteries, mass transfer to the surface of the blood vessel, an effective reaction rate that causes deposition, perhaps some break off and changes in these caused by alterations in the elasticity of the blood vessel. Some key “numbers” and even qualitative behavior is probably not known. So you would want to proceed with caution.
I can cite a very interesting example of this approach, which while it does not appear to have changed the world of cancer therapy, was nonetheless an important paper and perhaps fundamental concept. Suppose that you develop an anticancer drug treatment that uses a compound that is a strong cancer cell killer with a binding agent that will preferentially bind the cancer killing compound to cancer cells. Thus you expect that concentrations of your treatment will be much higher in a tumor than in other tissue. The idea would be that you could increase the effectiveness of a finite amount of the (toxic) compound that is active against cancer cells and reduce the overall patient side-effects. Now you test an anticancer drug on “tumor prone” rats and find that for low binding there is an average tumor shrinkage of 30%, for medium binding strength the tumor shrinkage is 60% and for strong binding the shrinkage is…. unfortunately only about 15%. How could this be explained? In the publication: C. Graff, K.D. Wittrup, Theoretical analysis of antibody targeting of tumor spheroids: importance of dosage for penetration, and afinity for retention, Cancer Res. 63 (2003) 1288–1296., the authors provide a mechanistically based explanation. They solved the reaction - diffusion equation for a spherical tumor. This equation has been used by chemical engineers for decade to analyze catalyst particles. You can get a Mathematica note book that I developed to try some calculations yourself at ( http://www.nd.edu/~mjm/tumor_calcs_1.nb) . What you would find as you increase the binding strength, is that the “front” of the diffusion of the drug into the tumor gets sharper. The sharp front is between the outer tissue of the tumor, which would receive the effect of the drug, and the inner tissue of the tumor, which would be treated. The result of the analysis is that while there is an advantage to some specific binding, if it is too strong, the active drug will not get to the middle of the tumor.
So what is the take home message? Statistical analysis is essential to determine if apparent correlations are valid or due to mere random chance. However, even when correlations are valid, if the mechanism that determines the correlation is not known, then the result either may be useless or at least further generalizations cannot be made. The tools of engineering analysis can provide a way to investigate possible mechanisms of action. Just be careful to verify these models at every length and time scale. Humans and even cells are very complex and hence it is easy to develop a completely meaningless model.
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