Improving Prognostic Web Calculators: Violation of Preferential Risk Independence Academic Article uri icon

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  • BACKGROUND: Web-based applications are available for prognostication of individual patients. These prognostic models were developed for groups of patients. No one is the average patient, and using these calculators to inform individual patients could provide misleading results. OBJECTIVE: This article gives an example of paradoxical results that may emerge when indices used for prognosis of the average person are used for care of an individual patient. METHODS: We calculated the expected mortality risks of stomach cancer and its associated comorbidities. Mortality risks were calculated using data from 140,699 Veterans Administration nursing home residents. RESULTS: On average, a patient with hypertension has a higher risk of mortality than one without hypertension. Surprisingly, among patients with lung cancer, hypertension is protective and reduces risk of mortality. This paradoxical result is explained by how group-level, average prognosis could mislead individual patients. In particular, average prognosis of lung cancer patients reflects the impact of various comorbidities that co-occur in lung cancer patients. The presence of hypertension, a relatively mild comorbidity of lung cancer, indicates that more serious comorbidities have not occurred. It is not that hypertension is protective; it is the absence of more serious comorbidities that is protective. The article shows how the presence of these anomalies can be checked through the mathematical concept of preferential risk independence. CONCLUSION: Instead of reporting average risk scores, web-based calculators may improve accuracy of predictions by reporting the unconfounded risks.


  • Alemi, Farrokh
  • Levy, Cari
  • Citron, Bruce A
  • Williams, Arthur R
  • Pracht, Etienne
  • Williams, Allison

publication date

  • December 2016