Sequential decision making with continuous disease states and measurements: I. theory

The question of whether to perform a continuous valued test to assess a continuous valued health state such as blood pressure or serum cholesterol is explored by decision analysis. Principal assumptions are that the underlying health state and measurement variability are both normally distributed, and that the impact of treatment on the utility of outcomes varies linearly with the underlying health state. Using Bayes’ theorem, an expression for the ex pected utility of performing the test is derived and compared with immediate treatment or decision to withhold treatment. The calculations can be carried out with a pocket calculator and a table of the normal distribution. Iterating the analysis, a sequential decision making process is developed, leading to a series of no treat/test again and test again/treat thresholds with which a running average of independently obtained measurements can be compared to produce stepwise optimal results. The thresholds are readily calculated on a microcom puter. Finally, the conjugate-normal-linear model is extended to encompass the correlated observations that may be made on a single visit. This paper concentrates on the mathematics of decision making with continuous variables. The companion paper illustrates its application to diastolic blood pressure.