Division of the roles into probability p(s'|a,s) and reward R(s,a,s'), where former is above a provider and latter above a patient

The roles assigned by decision analysis

Division of the roles into probability p(s'|a,s) and reward R(s,a,s'), where former is above a provider and latter above a patient

Decision analysis, as a theoretical construct, has certain implications for the roles in a medical decision, as will be described below.

As I have written in this post, a decision analysis is a way to model a medical decision as something that maximizes the expected utility of the patient. In an equation, expected utility is

E_{\pi} (R(S,A,S')|S=s) = \int_{s'}\sum_a R(s,a,s')p(s'|a,s)\pi(a|s)ds'

where p(s'|a,s) is the probability of the outcome, s', given an action, a, and an initial state, s, and where R(s,a,s') is the patient’s reward, or utility.

The equation for expected utility implies certain roles in a medical decision.

The provider’s role is to give the probabilities of outcomes, p(s'|a,s). For example, if we are considering whether to undergo a surgery for cancer, this might describe the probability of post-operative remission or complication. These probabilities are based on clinical experience or the literature.

The patient’s role is to give the utility of the outcomes, R(s,a,s'). Only they know how they will feel if they have, e.g., partial remission and a complication vs. complete remission and a complication.

The final role is that of “optimization.” Given the probabilities from the provider and the utility from the patient, one uses optimization to find the decision that maximizes the expected utility. In other words, one takes an \arg\max of E_{\pi}R over \pi.

Hence, decision analysis suggests that those involved in a medical decision have specific roles.

Decision analysis is a theoretical framework. In the real world, patients and providers do not always adhere to the roles described above. For example, in the real world, the provider sometimes helps with the patient’s task of defining the utility function. Also, the patient sometimes helps with the provider’s task of determining the probability of outcomes. Finally, either the patient, the provider, or both, usually perform (heuristically) the optimization.

Overall, however, decision analysis gives an interesting perspective, and this perspective can sometimes be useful, as I will try to describe in future posts.

6 responses to “The roles assigned by decision analysis”

  1. […] a previous post, I described how decision analysis might be viewed as a way to assign roles in a medical decision, […]

  2. TJ Avatar

    Assuming that pi(a|s) is the probability of choosing treatment a given initial covariates s, would the optimal pi(a|s) have probability 1 for a single treatment and probability 0 for all others, since there is only one choice of a that will maximize the expectation of R?

    1. Sam Weisenthal Avatar

      Yep, that is correct.

  3. […] a previous post, I described decision analysis, a framework for describing medical decision making and arriving at […]

  4. […] a recent post, I described how decision analysis defines the patient and provider roles as specifying utilities […]

  5. […] benefits of decision analysis for medical decision making. I’ve discussed how it helps define the roles in a decision, which can be easier to manage for the involved parties, and has the potential to […]

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