Explaining Variations in Hospital Death Rates

To the Editor. — Park et al¹present a sophisticated analysis describing factors that influence hospital death rate. Such research helps place current assessments of hospital performance in proper perspective. However, their simulation model of randomness may be misleading. By invoking crude age-sex-race estimates of death rate, the article may have exaggerated the element of chance and thereby underestimated the importance of quality of care. Consider a hypothetical cohort of 100 patients with congestive heart failure (Table). The age-sex-race probability ofdeath for each patient is 5%. However, the cohort actually contains 95 patients with an excellent prognosis (probability of death, 1%) and five patients with a dismal prognosis (probability of death, 80%). Calculation using the refined probability estimates yields an expected death rate of five patients. Calculation using the crude age-sex-race probability yields a similar number of deaths. However, the variance of the first estimate would be much