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In page Correlation does not imply causation:

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Causality is actually the other way around, since some diseases, such as cancer, cause low cholesterol due to a myriad of factors, such as weight loss, and they also cause an increase in mortality.[1] This can also be seen in alcoholics.[citation needed] As alcoholics become diagnosed with cirrhosis of the liver, many quit drinking. However, they also experience an increased risk of mortality. In these instances, it is the diseases that cause an increased risk of mortality, but the increased mortality is attributed to the beneficial effects that follow the diagnosis, making healthy changes look unhealthy.