# Readmission Rate 9 Times As High?

Peer review doesn’t guarantee accuracy, or even plausibility. In their Health Services Research article

“Validation of patient and nurse short forms of the readiness for hospital discharge scale and their relationship to return to the hospital,”

Weiss, Costa, Yakusheva, and Bobay tell us that patients discharged before they are truly ready are as much as nine times as likely to readmit. Hmmm. Suppose the baseline readmission rate were the national average of 18%. Would these patients’ rate be 162%?

Errors like these are extremely common in the health care research literature. The authors have confused two distinct quantities: odds and risk.

You’ll recall that if a hypothetical patient had an 18% risk of readmitting, his/her odds of readmitting would be (.18)/(1-.18). This translates to (.18)/(.82) = .22.

Odds *ratios* are by extension distinct from risk ratios. Suppose patients found to be “not ready for discharge” had readmission odds that were 9 times as great as the baseline. Their odds would then be 9*.22 = 1.98. Or, 1.98/.22 = an odds ratio of 9.0. Now, what would these patients’ risk (their readmission rate) be? To convert, we divide: risk = odds/(odds + 1), and so we obtain 1.98/(1.98 + 1) = 66%.

This is what the authors must have intended. To be sure, 66% is a very high readmission rate, but at least it is mathematically possible.