How *Not* to Attribute Causality from Statistical Results

[From a major outlet for health care research findings, Fierce Health Care. I've reproduced key passages in blue-black and commented inline in orange.]

Employment status is the top socioeconomic factor affecting 30-day [US hospital] readmissions for heart failure, heart attacks or pneumonia, according to a new study from Truven Health Analytics.

[Such a conclusion is on very shaky ground, as you'll see.]

As readmission penalties reach record highs, analyzing causes is more important than ever.

[Granted!]

Researchers, led by David Foster, Ph.D., collected 2011 and 2012 data from the Centers for Medicare & Medicaid Services and used a statistical test called the Variance Inflation Factor (VIF) for correlations among the nine factors in the Community Need Index (CNI): elderly poverty, single parent poverty, child poverty, uninsurance, minority, no high school, renting, unemployment and limited English.

[In truth, the VIF tells not what is the most important factor, but only to what extent the different factors, or independent variables, overlap with one another, potentially confounding the results. In this case, trying to isolate one indicator of socioeconomic status (SES) while controlling for eight others will surely distort any connections found. These SES indicators are too much "part and parcel of" one another, too inseparable, to allow for valid use of control in this way.

To explain further:  it's a mistake to ask "How much does SES (indicator 1) relate to readmission if we statistically remove SES (indicators 2-9) from the relationship?" That'd be much like saying, "How addicted am I to desserts if you discount my intake of cookies, pie, and ice cream?" Or there's Monty Python's question, "Apart from the sanitation, the medicine, education, wine, public order, irrigation, roads, the fresh-water system, and public health, what have the Romans ever done for us?"]

Their analysis found unemployment and lack of high school education were the only statistically significant factors in connection with readmissions, carrying a risk of 18.1 percent and 5.3 percent, respectively, according to the study.

[As explained above, these are not valid conclusions to be drawn. But even if the numbers were somehow accurate, what could such statements mean? That readmission risk becomes on average 5.3% for non-high-school graduates? It can't be -- that'd be far too low. That it's 5.3 points higher than it would be otherwise? It can't be that either -- too high. How about 5.3% higher in relative terms? Maybe, but that's about 1 point, which would hardly merit calling high school education an important factor. So what's left?]