A COMPARISON OF THE UNCERTAINTY IN MEAN AND INDIVIDUAL RISK REDUCTIONS

   Purpose.  Guidelines recommend risk factor changes to reduce patients' risk of disease and death, while risk equations estimate the associated risk reductions, but published information on the uncertainty of these estimates applies to groups with the same characteristics (mean risk reduction), rather than to individual patients (individual risk reduction), the relevant uncertainty  in clinical settings. We use Bayesian techniques to explore differences in uncertainty between mean and individual risk reductions.

   Methods.  With data from the NHANES I Epidemiological Followup (1971-1992), we estimated a Weibull regression relating survival duration for persons 61-74 to risk factors commonly included in risk equations: age, sex, smoking, total cholesterol, systolic blood pressure, and diagnoses of diabetes and heart disease.  We used the regression to simulate the distributions of mean and individual change in survival, ΔS_M and ΔS_I, associated with reducing systolic pressure for male smokers aged 66, total cholesterol 211, with no diabetes or heart disease.  While both distributions reflect parameter uncertainty, the individual distribution (the posterior predictive distribution) also incorporates unexplained variation represented by the error term.

   Results.  For systolic pressures of 130 or higher, there was a vanishingly small probability of loss of life expectancy at the mean level (negative ΔS_M), effectively zero, associated with reducing systolic pressure to 119.  As a specific example, for an initial pressure of 155, mean gain in life expectancy was 1.15 years (95% interval, 0.63,1.72).  By contrast, the probability of a loss in life expectancy for an individual man whose initial pressure was 155 was substantial: 0.45.  The individual's probability of harm declined as systolic pressure and the associated ΔS_I increased, from 0.49 when initial pressure was 130 to 0.35 when it was 220.

   Conclusions.  Uncertainty around estimated survival gains was, as expected, much greater for an individual patient than for groups of similar individuals.  An individual's probability of harm was greater at moderate than high risk factor levels.  The posterior predictive density represents the upper bound on true individual uncertainty since it reflects only information included in the risk equation, not additional information available to the examining physician.  To inform physicians and patients about the uncertainty in risk estimates, further work is needed on how best to model and present individual uncertainty.