Decision analysis

education
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I have been thinking a lot about decision analysis, the probabilistic framework for medical decision making. During my time as a statistics graduate student, I studied statistical models for medical decision making. Underlying these decision making models is the concept of expected utility.

Now that I have been back in clinic, I have thought about expected utility a lot. It comes up in nearly every medical decision.

I have been writing blog posts on my thoughts as they evolve.

If you are unfamiliar with decision analysis but have a background in probability, here is a quick intro (How to use probability to describe medical decisions). Even without any calculations, decision analysis seems to guide the decision making process (The roles assigned by decision analysis). We don’t see the decision analysis framework used too often in clinic (Decision analysis and the real world). Maybe, though, it would be better for everyone if we used it more often (The kindness of decision analysis).

I was wondering if anyone else had thought about decision analysis / expected utility in the clinic. Dr. Harrell, I know that you have generally been a proponent of expected utility, from a statistical decision theory standpoint and also from the perspective of point of care medical decision making, and your comments on the topics definitely motivated my investigation.

Responses might also inspire future blog posts, in which case I would link to the response.

I have also listed some more specific questions below.

Have there been ebbs and flows in decision analysis in medicine, and why? Are there any seminal papers or studies that influenced medicine’s view of decision analysis? I know for example there was originally a threshold method paper by Pauker that was highly influential, but it also received some criticism.

How does decision analysis interact with the statistics community, and more specifically the dynamic treatment regimes literature?

Are there any clinical problems for which decision analysis is a standard? If not, are there any clinical problems for which decision analysis should be the standard?

What are the barriers to adopting decision analysis, and what are the major criticisms?

What are the barriers to estimating the probabilities needed for a decision analysis?

Are there alternatives to expected utility, such as median utility?

What is the current state of the art in terms of eliciting and quantifying utility? Can we ever get away with just ranking preferences rather than assigning numerical utilities.

Will easy access to computing change the feasibility of integrating decision analysis into the clinical workflow? I sometimes think that the original focus on decision analysis using things like large, complex decision diagrams was too cumbersome, and this impeded adoption. However, when one thinks instead about random variables, it becomes cleaner, and also much easier to integrate into computer programs, which can be run on computers that are now ubiquitous on the floors.

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Very nice. I run a wet lab (bench work and animal modeling) where we generally formally focus more on p(s’|a,s) in your notation, i.e., in making inferences/assertions ourselves or sharing the data with the community to make their own assertions. In clinic, we also mainly focus on p(s’|a,s) although we argue here why utilities are essential for patient-specific decision making.

Our use of utilities is more extensive in designing and running clinical trials. The first trial I ever designed and ran used a proto-version of utilities for dose selection based on efficacy and toxicity. We now have multiple utility-based trial designs, many of which are easily accessible for practical use here. As described here, we advocate for the utility functions themselves to be covariate specific as in this phase I-II design and this phase II design. We provide an example of covariate specific utility function elicitation for breast cancer decision-making here.

Definitely supportive of popularizing dynamic treatment regimens in medicine. Our group designed and run what may have been the first sequential multiple assignment randomized trial (SMART) in oncology (example discussion of the trial here) and have been analyzing the first SMART in kidney cancer for years (not an easy task due to challenges such as non-compliance etc). Hopefully we will publish it in 2025. The purpose of this datamethods post was exactly to showcase the necessity of thinking in terms of treatment regimes in oncology. We accordingly just published with the Kidney Cancer Association a consensus statement on this topic.

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Thank you for this material, @Pavlos_Msaeoul. I am still making my way through it, and will likely continue to move at a slow pace.

The work on covariate-specific utility functions is interesting. It is good to see a technique that, with the help of providers, allows one to specify a family of utilities, from which the patient/provider pair can then choose one based on subjective preferences. I linked to this in my discussion as an example of a case in which the provider can help the patient specify a utility. It makes a lot of sense to have it vary by patient covariates, and to have age be a major factor, and the covariate provides even more structure. This makes me wonder if it may be possible to “adjust away” some of the variance in individual utility-preferences, making utility specification easier.

The proposed utility function also allows one to deal with a continuous toxicity burden and continuous survival time, which is great. Dealing with continuous outcomes makes for a very complex medical-decision-making scenario. This makes me think that decision analysis might be useful not just for the reasons I had outlined here, such as encouraging the incorporation of patient preferences and freeing the provider to focus on probabilities, but also because, fundamentally, most of the outcomes in medicine fall on a continuum, and continuums are so challenging to deal with (I have now noted this in that post and added a link to the paper).

I can’t imagine the difficulty of trying to discuss something like the probability of a toxicity burden when there is an infinite number of possibilities between 0 and 1. If we can offload some of this cognitive challenge to a calculator, it would help (like offloading multiplication to a calculator). Maybe also this points us to an example of a set of problems for which decision analysis might be really useful —- problems for which there are continuous outcomes.

I also see that this paper describes a way to sample from the posterior of utility. With a posterior, one can take any function of the p(s’|a,s) rather than the mean, which addresses my question about decision analysis using anything besides the expectation. Perhaps the historical emphasis on expected utility was based on the fact that much of decision theory was developed in the pre-computing era, and expected utility can in theory be hand-calculated. Modern computing helps with Monte-Carlo and sampling though, so maybe we are no longer constrained to expectations.

Also very nice to see nonparametric Bayes here; one of my concerns about decision analysis is that a specification of the joint distribution p(s’|a,s) might be incorrect, and nonparametric Bayes should cover this.

Thank you again, I hope to make my way through the other papers over time.

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Exactly, you hit the nail on the head in all of the above. Including why our group likes using posterior sampling so much: it provides more flexibility, which can be coupled with the robustness of non-parametric Bayes. Keep it up - very much looking forward to how your efforts and blog posts will continue evolve!

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I would appreciate your perspective on estimating the relative benefit of making effects covariate specific (absolute risk scale) vs. making utilities covariate-specific. I think that the form is maybe 10 times more important than the latter. Do you agree?

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Both are important but I personally absolutely agree that the effects are the primary focus. In fact, this is why we we focused only on covariate-specific effects in this explainer. In my mind this is the key starting point. However, once we estimate the covariate-specific effects there are scenarios where different covariates can yield the same efficacy / toxicity balance but the decisions made should use different trade-off considerations. In the breast cancer paper, we made the plausible assumption that older women (the covariate being “age”) would be less tolerant of higher toxicity for the same efficacy benefit. Thus their covariate-specific utility functions should reflect this.

One difference between covariate-specific effects versus utilities is that we could in theory use modern tools to elicit the latter for each individual patient. They are in theory computable and can be understood as an inference moving from “individual to group”. Conversely, covariate-specific effects will always be based on inferences moving from “group to individual” and truly individualized risk values are typically uncomputable.

Having said that, covariate-specific utilities may also be used to incorporate objective constraints that may not be as easily incorporated (at least not currently) by covariate-specific effects. An example is this dose-finding design which uses covariate-specific utilities to incorporate the general knowledge that cancer therapy dosage should be escalated for more aggressive disease. That inference could in theory be computable with larger sample sizes and measurement of long-term outcomes (see here our advocacy for moving towards the latter in dose-finding) but as it stands, most dose-finding trials today will base their cohort-specific decisions (typically in cohorts of 3 patients) on early efficacy/toxicity outcomes. The subgroup-specific utility functions can be used as pragmatic tool to incorporate our expectations of the dose-effect on long-term outcomes in currently available designs.

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This is so far ahead of what is being taught in biostatistics and in clinical investigator training courses that I’m worried about what budding investigators are missing out on. Great work!

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Thank you for reading my response! Thank you, looking forward to reading through more of the linked work as well!

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This is an interesting question, because a covariate in the reward R(s,a,s’), where s is pre-treatment covariates, s’ is post-treatment covariates, a is the treatment, is a true constraint (if the utility is nonrandom), whereas a covariate in P(s’|a,s), the distribution of the outcome (of which the effect is a function), impacts S’ randomly.

Note that one can also give utility a distribution P(R|s,a,s’), to account for random variation, except our individual preferences are not really random… I can see it accounting for one individual’s variation in preference, but I have to think more about the variation between two individuals.

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