Susan Murphy

Life and career

Most statisticians who study causal inference work on data someone else collected. Susan Murphy's distinguishing move was to go the other way: if you want to know what a sequence of treatment decisions does to a person, design the experiment that can answer it, then build the machine that runs it — and then, because the machine is a phone in someone's pocket, learn on the fly.

Murphy trained in statistics at the University of North Carolina at Chapel Hill and spent the long middle of her career at the University of Michigan, where she held appointments in statistics and in the Institute for Social Research, an unusual pairing that put her in daily contact with the people who actually run behavioral interventions: addiction researchers, psychiatrists, mental health clinicians. That contact shaped everything. The questions she took up were not abstractions about identification; they were the questions a substance-abuse trialist genuinely could not answer with the tools on hand. If a patient does not respond to the first-line treatment after eight weeks, should you augment or switch? How do you *design a trial* whose output is an answer to that question rather than an answer to "does drug A beat drug B on average"?

She was named a MacArthur Fellow in 2013, an unusual honor for a statistician, and one that recognized precisely this: methodology built in contact with the clinic rather than in retreat from it. She has been elected to the National Academy of Sciences and the National Academy of Medicine, and has held senior leadership roles in her professional societies.

In 2017 she moved to Harvard, where she is a professor of statistics and of computer science — again the double appointment, and again not an accident. By then her work had migrated from trial design toward online reinforcement learning, because the intervention had migrated from a clinic visit to a smartphone notification. When the decision points number in the thousands per participant rather than two or three, the sequential-decision problem stops being a statistics problem with a small discrete policy space and becomes a bandit problem that also has to survive a regulator's scrutiny. Her group's projects — activity coaching, oral health, substance use recovery — are real deployed studies with real participants, and the algorithms in them are hers.

The unifying commitment across four decades is that adaptive, personalized treatment is not a slogan but an estimand: something you can define precisely, design an experiment to identify, estimate with a stated uncertainty, and defend to a skeptical review board. She has spent her career making sure that the flexibility people want from "personalized medicine" does not cost them the inferential guarantees that made medicine trustworthy in the first place.

Key contributions

**Dynamic treatment regimes.** A dynamic treatment regime is a sequence of decision rules: at each stage, map the patient's accumulated history to the next treatment. The clinical question is which regime is optimal. Murphy's contributions here are both conceptual and technical. Her work in the early 2000s formalized estimation of optimal regimes from sequential data using backward induction — solve the last stage, plug the resulting optimal value back in, solve the previous stage — with methods related to but distinct from Robins' g-estimation, and with an eye on what happens when the model for the intermediate stage is misspecified.

The subtle part, and the part graduate students should notice, is **non-regular inference**. The parameter "the effect of treating at stage one" depends on what you will do at stage two, which depends on a maximum over stage-two actions. Maxima are not differentiable. When the true stage-two effect is exactly zero — when it genuinely does not matter what you do next — the estimator's asymptotic distribution is not normal and the standard bootstrap fails. Murphy and collaborators characterized this failure and developed procedures (adaptive confidence intervals, projection and thresholding approaches) that produce honest coverage anyway. This is the kind of problem that only surfaces if you are serious about giving people confidence intervals, and it is a signature of her work that she treated it as a blocker rather than a footnote.

**SMART designs.** The sequential multiple assignment randomized trial re-randomizes participants at each decision stage, conditional on their response so far. The point is that a SMART is powered to compare *regimes*, not just treatments — it delivers, from a single trial, the data needed to construct and compare adaptive strategies. Murphy laid out the design principles, the sample-size calculations, and the analysis, and SMARTs subsequently ran in addiction, ADHD, autism, and cancer research.

**Micro-randomized trials and just-in-time adaptive interventions.** This is the contribution that defines her modern reputation. On a phone or wearable, you can randomize hundreds or thousands of times per participant: send the activity prompt or don't, right now. The MRT formalizes this. The estimand is the *causal excursion effect* — the effect of a prompt at a decision point on a proximal outcome (say, step count over the next thirty minutes), averaged over the population and possibly modified by context: is it raining, is the person at work, did they just get a prompt an hour ago. Weighted and centered least-squares estimators recover these time-varying effects with valid inference under the randomization, and the design carries explicit notions of *availability* (you must not prompt someone who is driving) and *burden* (habituation is real; people disable notifications). The HeartSteps studies deployed exactly this on real phones with real participants.

**Online RL with inferential guarantees.** The natural next step — let a bandit algorithm choose the randomization probabilities and adapt — breaks classical inference, because the data are no longer independently randomized and the sampling probabilities are themselves random. Murphy's recent program addresses this head on: algorithms that pool information across users while remaining conservative enough that after-study statistical inference remains valid, and that degrade gracefully when a user's data is too sparse to personalize on at all. This is the honest boundary of her method, and she has been the one to mark it.

In battle

Murphy's profile is that of a strong specialist with a broad statistical base: mean around 40 over a hundred problems, but eight problems where she scores 80 or above, and a category table with an unmistakable top.

`experimental-design` at 69.0 across fifteen problems is her fortress, and `rl` at 67.0 is the modern extension of it. She scores **98 on P011 — Just-in-time on the phone**, which is not so much a problem she is good at as a description of her research program handed back to her as an exam question: randomize at thousands of decision points, recover context-specific proximal effects from a mountain of noise, and handle habituation and burden as first-class design constraints. **P228 — The policy learned from old charts** also scores 98: learning a treatment policy from observational sequential data is dynamic treatment regimes in their original form, including the awkward non-regularity that makes the confidence intervals hard.

Her other dominant problems fan out predictably from those two. **P008 — A/B test with a twist** (95) and **P010 — The adaptive dose-finder** (94) are adaptive experimental design; **P120 — Play the winner** (80) is the classical response-adaptive randomization ancestor of her own work, and note that this is a problem John Lafferty scores 8 on — it *sounds* statistical, but only a sequential-design specialist owns it. **P129 — How big must the study be?** (84) is trial power calculation, unglamorous and exactly her craft. **P121 — When treatment leaks across friends** (85) is interference, where her design instincts carry her further than her network-modeling background would. And **P299 — The proxy that rationed care** (80) reflects the `fairness` strength of 60.5: someone who has spent decades asking what a treatment decision actually does to a person is well positioned to notice when an algorithm's outcome variable is a proxy that encodes access rather than need.

Her losses are the crisp complement. `information` at 6.0 is her floor: **P165 — The optimal codebook** (6) and **P170 — The message no eavesdropper can read** (6) are coding and cryptography, and her randomization is an identification device, not a cryptographic primitive — a nice trap for players who see "randomized" and assume transfer. **P076 — Index the entire web** (8) and **P179 — A good-enough tour of a thousand cities** (8) are systems engineering and combinatorial approximation; **P163 — The fastest-growing function** (7) is computability; **P242 — The memory that completes the pattern** (8) is associative-memory neural modeling. `perception` at 11.5, `nlp` at 15.0, `optimization` at 15.0, and `high-dim` at 18.5 mark the whole territory she does not cover: she is not a p >> n person, not a representation-learning person, and not an algorithms person.

The tactical read is straightforward. Any problem whose difficulty is *what should we do next, and how will we know it worked* belongs to Murphy, and she will beat the field on it decisively. Any problem whose difficulty is representation, scale, or computation belongs to almost anyone else.