Stochastic Medical Informatics

Decision Making under Uncertainty

Medical decision makers may want to answer a variety of questions about individual patients or populations. This may require comparing [Page 1077]alternative treatment strategies in terms of their cost and effectiveness or predicting the likely frequency of outcomes that have differing chances of occurrence, such as the side effects of treatments. At the level of the individual patient, such comparisons can assist in making treatment decisions. At the population level, policy decisions can be made that optimize the quality of care and allocate limited resources. Such policy decisions may also include the value of obtaining more accurate information on which to make more optimal subsequent decisions or invest in more effective implementations of policies.

Answers to such questions can be found by modeling and simulating the interactions of probable events in various treatment scenarios that may be subject to different conditional criteria over time.

All statistical models are based on observations of the real world. Uncertainty can arise in a number of ways, from the intrinsic variability of the underlying phenomena being measured through the imprecision in the measurements themselves and how they are assembled into a model. Such measurements are typically treated as “random variables,” unknown values that may be approximated by point estimate statistics, such as averages over observed values, or distributions describing the frequency of observations over a range of possible values. For example, the probability that an event occurs can be estimated by a single number between 0 and 1 (0% and 100%), while a simulation for a group of patients may be based on an average age. Alternatively, these estimates can be expressed as distributions over a range of values, reflecting the frequency of observations. Probability distributions can be represented similarly in the form of probability density functions, which may be visualized as graphs for which the area under the curve sums to a total probability of 1 (100%). For example, the probability of an event might be described using a beta function (with parameters α = 2, β = 5), whose probability density function is shown in Figure 1. Alternatively, a simpler model may use a point estimate for this probability, such as the mean (.28) or mode (.2) of this distribution. Point estimates or distributions may also be formulated as functions of other parameters in a model, such as time or age, as implemented through table lookup or function calculation.

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