Sign-flip Simpson: nurse staffing and mortality

Question

Across many hospitals, plotting nurses-per-patient against patient mortality gives an upward slope: hospitals with more nurses per patient have higher mortality. Yet within each hospital, adding nurses is associated with lower mortality: a downward slope.

Reconcile the positive cross-hospital slope with the negative within-hospital slopes. Which relationship should guide a staffing decision?

Accepted Answer

This is Simpson's paradox in continuous form. The confounder is how sick each hospital's patients are (case severity). What is happening. The sickest patients go to tertiary and ICU-heavy hospitals, which respond by staffing many nurses per patient, and which also have higher mortality because their patients are gravely ill. Across hospitals, then, "more nurses" travels with "sicker patients," and sicker patients die more, so the pooled slope is positive, driven by severity, not by the nurses. Within a single hospital, where the patient mix is roughly fixed, more nursing coverage improves out…

Sign-flip Simpson: nurse staffing and mortality

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