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Borrowing Strength

Science

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Borrowing Strength

His bedridden mother was being poisoned by a miscalculated dose of a toxic heart drug. Driven to pull her back from the edge, a Wall Street forecaster turned his predictive models inward to forge the mathematical foundation of pharmacometrics.

In October, 2003, the scientist Lewis Sheiner sent an e-mail to Nick Holford, a former student, recalling how their field of pharmacometrics had begun. Within a few months, Sheiner was dead. The following year, Holford quoted a brief passage of the correspondence in a memorial tribute. When I reached out to him this summer for the rest of the exchange, he searched his archives and wrote back: “I cannot find the original email from Lewis that I cited.” That left only the brief scene he had already committed to print.

And it goes like this. A seminar room at the University of California, San Francisco, sometime around 1970. A young physician is up front, presenting his work on drug dosing, when an even younger economist starts interrupting from the audience — takes his math apart piece by piece, then rebuilds the field on the spot.

I spent several weeks this summer tracking the people and the institutions that grew out of that afternoon, guided by oral histories of retired clinical pharmacologists, veterans of the FDA, and a programmer who spent her career building the software that resulted from that chance encounter. The economist in the room was Barr Rosenberg. The doctor was Lewis “Lou” Sheiner. From their collision emerged pharmacometrics: the statistical scaffolding for how drugs move through populations, how doses of medicine are chosen, and how medicine attempts to learn from the sparse data of human bodies.

Barr Rosenberg was a forecaster of financial risk, and he was quite good at it. Born in Berkeley in 1942, he enrolled at the University of California at sixteen, secured a master’s degree from the London School of Economics by twenty-two, and completed a Harvard doctorate in economics at twenty-five. His dissertation carried a title only a statistician could truly appreciate: Regression with Stochastically Varying Parameters. The topic was a happy accident. He had originally intended to analyze capital markets using a pristine new stock-price database in Chicago, but when the data delivery stalled, he abandoned capital markets for pure theory, focusing entirely on how to model systems with underlying variables that continuously shifted over time.

That theoretical detour proved immensely valuable. The late 1960s and 1970s marked the dawn of quantitative finance, an era when it suddenly felt possible to quantify the invisible risks lurking inside a stock portfolio. In 1974, Rosenberg launched a consulting firm, BARRA. The reigning method scored a stock’s risk with a single number: how much it moved with the market. Rosenberg’s models pulled that risk apart across many features of the company itself. Suddenly, an oil company’s risk could ride on the price of crude and a bank’s on interest rates, a homebuilder’s to mortgage rates. The shift from one factor to many became, and remains, the working grammar of quantitative finance. It made BARRA’s tools standard equipment for institutional investors.

As Sheiner’s lost email tells it, Rosenberg’s foray into medicine began around 1967, when his mother’s heart began to fail. To keep her heart pumping, her doctors continually increased her dose of a heart medication called digoxin. First described in 1785 by the English physician William Withering, digoxin is a potent compound derived from the bell-shaped blooms of the foxglove plant. It is also a notoriously temperamental drug. It works by jamming microscopic sodium-potassium pumps in the membranes of heart muscle cells, causing calcium to pool inside. That extra calcium acts like a chemical whip, goading a weakened, flabby heart to contract with fresh intensity.

The margin for error with digoxin is perilously thin. If you underdose it, nothing happens. Make the mistake of overdoing it, and so much calcium floods the cells that the heart’s electrical system misfires, throwing the heart into a dangerous rhythm of its own. During the 1960s, doctors had no way of knowing where a patient sat within that narrow therapeutic window, because they lacked any reliable method to measure digoxin levels in a given person’s blood. So, equipped with nothing else, a doctor could only make an educated guess, tweak the dose this way and that way, and watch how their patient responded to it. A 1971 study found that about a quarter of hospitalized patients on digoxin were being poisoned by the drug. One of them was Rosenberg’s mother — who, by fate, was on the wrong side of a physician’s guesswork: every time her doctors raised her dose, she got worse.

Frustrated by the ordeal, Rosenberg began badgering his mother’s medical team with what seemed to him an obvious question. If he could use mathematics to model the volatile swings of the stock market, why couldn’t highly trained medical professionals use similar tools to chart a drug’s course through the human body?

Rosenberg saw no real difference between the stock market and human metabolism. To him, they were just two versions of the same puzzle. Both were vast, invisible systems that doctors and economists could only guess at using sparse, noisy clues — like a closing bell price or a morning blood draw. But where medicine saw missing data as a tragedy, Rosenberg saw it as a math problem waiting to be solved.

The prevailing statistical paradigm of that era treated patients as mere copies — interchangeable units stamped from a single biological template. Doctors would identify a theoretical “average” patient, calculate the statistical mean of how much of a medication would be needed to treat them, and then administer that generalized dose to everyone on the ward. They would then watch, often helplessly, as real, idiosyncratic human beings wildly diverged from that neat mathematical average.

Rosenberg’s idea was to give every patient a biology of their own: a particular rate of clearing a drug through the kidneys, a particular volume of blood to dilute it in. It did not leave them there alone. It set each one inside a larger picture, like a single, uniquely colored dot in a Pointillist painting.

On its own, a single data point doesn’t tell doctors much, but analyzing thousands of them together reveals a clear pattern. Statisticians have a homely, almost quaint name for this trick: “borrowing strength.”

In practice, you start a new patient on a dose derived from the wider population. It’s a lot like the old habit of just grabbing the “average,” but this time, you know exactly how reliable that baseline is. Then, as that patient’s own blood levels of a drug arrive, Rosenberg’s method slides the estimate off the crowd and onto them, until it describes that person and no one else.

All Rosenberg needed was a physician willing to let him test the math.

Leslie Benet has been fielding calls about the early days of pharmacometrics for a while now; the American Society of Clinical Pharmacology and Therapeutics had asked him to talk through this same history back in April. He joined the UCSF faculty in 1969, took over as chair of its Department of Pharmacy in 1978, and spent two decades around the clinical pharmacology group.

The first thing he wanted me to understand was that his chosen field was, in its early years, failing to thrive. In 1969 there were two serious centers for clinical pharmacology — how drugs interact with the human body — in the country, Vanderbilt and UCSF, and both were trying to turn it into a self-sustaining discipline of medicine. Neither managed it. “It never succeeded in doing that,” Benet said, “because it couldn’t control beds. And in a medical center, that’s what’s critical.” Infectious disease was founded in the same years and became one of the great engines of academic medicine, because infectious diseases filled wards and brought in revenue. Clinical pharmacology brought in almost nothing, and became, in Benet’s phrase, an “academic exercise.”

Without tools sensitive enough to detect microscopic traces of a drug in human blood, you cannot productively calculate an ideal, personalized dosage for a patient. For most of medical history, this was simply reality. Rosenberg’s mother’s doctors raised her digoxin half-blind, with no dependable way to see how much of it was in her blood. Benet explained that “When I started in the field, it was spectrophotometry.” This meant trying to calculate a drug’s concentration by shining a light through a fluid and measuring how much of the beam made it out the other side. The technique required large biological samples just to detect a drug in urine, and finding it in the blood was close to impossible. It took gas-liquid chromatography, then high-pressure liquid chromatography, and then finally mass spectrometers sensitive enough to count individual molecules in a vial. Rosenberg’s kind of math was useless without numbers to feed it. Those numbers only became possible to produce at the end of the 1960s — right as he came looking for a doctor to use them.

The doctor he needed was already down the hall. Lewis Sheiner (everyone called him Lou) had trained at the NIH and at Stanford before landing at UCSF as a clinical pharmacology fellow, and he arrived with a physician’s credentials and a mathematician’s habits of mind. He had been chewing on the same problem that pulled Rosenberg off the stock market: how to get a trustworthy prediction for one patient out of thin, noisy clinical data.

Sheiner came to Rosenberg’s aid with a computer ready. At the NIH’s Computer Systems Laboratory, the doctor had written a program run on a room-sized IBM computer to dose warfarin — a blood thinner with volatile pharmacokinetic properties. But to do so cost $12 a minute. He fitted the program to 17 patients and 199 prothrombin times, each a measure of how long that patient’s blood took to clot. But for some patients, that left only a single measurement to feed a model that demanded four. You cannot solve for four unknowns with a single data point; what Sheiner lacked was a reason to believe that his seventeen patients had anything to do with each other.

Benet was underwriting the effort via his leadership within the UCSF Department of Pharmacy. Sheiner had come in as a fellow, and his first NIH money ran through a center grant Benet controlled — one of only two such grants to support clinical pharmacology research in the country. “I basically supplied him with his initial NIH funding,” Benet told me.

The connection ran through Kenneth Melmon, the director of the UCSF clinical pharmacology group who had a rare talent for placing the right two minds in the same room. Melmon hosted a weekly seminar, and one afternoon he invited Rosenberg to sit in. This is the fabled scene from the lost email. Rosenberg patiently listened as Sheiner presented his work on drug dosing. When Sheiner finished, Rosenberg politely replied, “That was very nice, but here is how you should have done it.” Right there in the room, he sketched out the entire statistical framework. He showed how to estimate the population and the individual in tandem, allowing the vast crowd to lend its mathematical strength to the solitary patient. It was, among other things, the answer to the warfarin problem: the four parameters and the one blood draw stopped being a contradiction the moment the other 16 patients were allowed to speak for the 17th. Sheiner saw it immediately. He arranged to complete his fellowship in Melmon’s group to collaborate with Rosenberg, and he pursued the idea for the rest of his life.

While Benet didn’t know Rosenberg well, what he gave me instead was a list of people to call — including one name he kept circling back to: Carl Peck.

Carl Peck earned a bachelor’s degree in mathematics and chemistry from the University of Kansas in 1963, having spent two years as an undergraduate research assistant in a nuclear physics laboratory, and went on to win a Fulbright in chemistry. Then he went to medical school. “The way to advance your field,” he told me, “is to look over the fence into somebody else’s field and see if you can borrow something.” In 1971, a young Army physician by then, he published a paper titled “The Almighty P-value, or the Significance of Significance.”

In the early 1970s, he was chief resident at Letterman Army Medical Center in the Presidio of San Francisco, running a ward full of patients on digoxin. Calculating a patient’s dose meant walking a stack of punched cards over to the hospital’s computer center and praying the code compiled. Peck was already frustrated by the medical establishment’s grasp of statistics, “pissing and moaning about p-values” to his residents, as Peck told me. After one of these performances, a UCSF student on a clinical rotation under him told him he was “singing a song two men in the clinical pharmacology group would want to hear,” and that he ought to go meet Ken Melmon and Lou Sheiner. Peck had never heard of either. He phoned Melmon to ask whether he could sit in on a seminar, and Melmon told him to come give one instead. “I was flabbergasted, because I was very junior at the time,” Peck recalled. But he went, and sitting in the audience was Lou Sheiner.

To really put the method to the test, they turned to the obvious candidate: digoxin. At Letterman, they split 42 patients into two camps. One half received doses based purely on a doctor’s intuition, and the other half let the new computer model take the wheel. Unsurprisingly, the algorithm was much better at hitting the right blood levels. The paper that came out of it was Peck’s first, and to his own astonishment it ran in the New England Journal of Medicine.

By 1975, a follow-up study successfully executed Rosenberg’s feedback loop in clinical practice, actively recalibrating the algorithm to fit the individual parameters of each patient. Just how well the method worked, the group would pin down a few years later: for digoxin, a single blood measurement cut the error in forecasting a patient’s future levels by 40 percent, and two measurements by two-thirds — a lone draw worth more than the patient’s age, sex, and kidney readings combined.

Peck had crossed paths with Rosenberg exactly once, over at UC Berkeley. “Brilliant, fast-talking, almost charismatic,” describing a very young, front-running professor confident in his own mind. “I have to admit, the substance of what they were discussing was all over my head,” Peck said.

That was the only time. Decades later he tried to track Rosenberg down again and failed. By then, Peck said, the man had embedded himself deep in “this Eastern religious thing.”

Lou Sheiner needed a full-time statistician to push the idea further, and he found one by accident. In 1976, riding the UCSF commuter bus out to Marin County, he sat down next to Stuart Beal, a biostatistician who had come to the university a few years earlier to work in its information-systems office. Sheiner started explaining what he was after. Beal — a UCLA mathematician who had minored in logic before taking a UCSF doctorate in biostatistics — was hooked before the bus reached the county line. The friendship and the collaboration both began that afternoon, and both lasted the rest of their lives.

Melmon had to find them somewhere to sit to work on their collaboration, and what he found was a room in the Division of Laboratory Medicine, the wing that ran the clinical assays their whole method depended on. The office tiny office could barely fit two desks in it, so they they arranged them across from each other; arguing all day, for years; Sheiner grounding Beal in the clinical realities of dosing patients, and Beal walking Sheiner through the rigorous biostatistics required to make the model work. Down the hall, the Division of Laboratory Medicine was running the clinical assays — using chromatography and spectrometry to pull the exact drug concentrations from patient blood samples, generating the raw data the two men were trying to mathematically resolve.

Rosenberg, meanwhile, was orchestrating from afar as Beal became the mathematical engine Rosenberg had only hoped for. Rosenberg himself lingered in the paper trail a little longer: He was there for the 1977 study that first showed how to pull a whole population’s pharmacokinetics out of routine clinical data, and a final time in 1979, when he co-authored his final paper in medicine. Then he left medicine for good, back to BARRA and the markets.

His name stayed behind in the software. Sheiner and Beal called it NONMEM — nonlinear mixed-effects modeling — and a nonlinear mixed-effects model is the same species of mathematics as Rosenberg’s doctoral thesis, regression with parameters left free to drift from one case to the next, the tool he had carried out of economics and turned on the body. It even surfaces by name in the last paper Rosenberg ever published in medicine, in 1979: “a computer program, NONMEM, has been developed by some of us,” tucked into the appendix.

When NONMEM I shipped in April 1980, the entire software package consisted of a pale-blue instruction booklet and a single Memorex magnetic tape. The software was written in FORTRAN IV, which had strict limitations. Because early compilers capped names at six characters, the team had to abbreviate a routine like ADVANCE1 to ADVAN1. Users are still forced to use that 1980s shorthand today to advance a drug’s state to a new point in time using a one-compartment model. When NONMEM runs, only a user’s own model code is compiled; most of the FORTRAN was built into a library once, at installation, to keep the program fast. Four decades later, this foundational architecture remains untouched.

NONMEM proved its necessity in testing drugs, a necessarily artificial process. Clinical trials typically enrolled healthy, young volunteers — often medical students — who were given doses of a given drug too low to cause side effects and had their blood drawn on a perfectly rigid schedule. If a student missed a draw, his data was discarded. The numbers that finally reached the statisticians were pristine and balanced, yet divorced from the sick people who would actually take the drug. Prescribe a blood-pressure medication to an elderly population and some will react violently while others won’t respond at all; those erratic patients — not young medical students who follow instructions to the tee — are usually yanked from the study and given rescue drugs, and they are precisely the people doctors most need to understand.

Benet was coediting the Journal of Pharmacokinetics and Biopharmaceutics when Sheiner, still the junior man at the table being in his early 40s, proposed a new section for this kind of quantitative modeling and offered to run it. “Lou said, let’s create a new section in the journal called pharmacometrics,” Benet recalled. That is how the discipline now governing how the industry sets its doses got its name — a heading in a table of contents. Nobody in the room thought it was much of an occasion. “I don’t think I felt that it was really anything major happening,” Benet said. “It was just one of the developments that were going on at the time.”

The original 1980 NONMEM software was a tool built by specialists for specialists. It likely would have remained trapped in a handful of academic laboratories if not for Alison Boeckmann, a dedicated computer programmer, who joined the team around 1982. Over the following decade she wrote NM-TRAN, a control language that let pharmacologists specify their drug models in a structured script while the computer handled the calculus in the background. She also implemented PREDPP, Beal’s library of pre-packaged models, in 1984. NM-TRAN wasn’t released until 1989; it took nearly 10 years to build a version of NONMEM that a normal scientist could actually use. Boeckmann became the software’s custodian, calling NONMEM her “life’s work.” She stayed on the project for 40 years and built the email listserv that still serves as the global town square for pharmacometrics.

Through the 1980s, the technique seeped out of UCSF and into the broader pharmaceutical industry, which was beginning to suffocate under the weight of exactly the messy, sparse data NONMEM had been built to handle. In addition to publishing their research, Beal and Sheiner evangelized their software through traveling courses in Kyoto, Uppsala, and Lyon, cultivating a sprawling network of postdocs who would go on to become leaders in pharmacometrics across the world.

NONMEM became the undisputed standard for population pharmacokinetic modeling, for a reason no competitor could bear to match: its research and development was already paid for. The software, created at UCSF in the late ‘70s, was bankrolled by an NIH grant, GM26676, which ran continuously from 1977 for nearly thirty years — a MERIT award that kept paying out after both the men who built it were gone. Beal ran the operation with a proprietor’s care, personally telephoning labs that let their licenses lapse to ask for their tapes back.

Because the overhead was already covered by the government, the licensing fees UCSF charged pharmaceutical companies turned into pure departmental surplus. The software generated enough revenue, Benet told me, to fund an entire clinical wing of the department that couldn’t have sustained itself otherwise. In time the university handed distribution to a commercial firm, Globomax, who enlisted Peck and Sheiner’s frequent collaborator, Thomas Ludden, to finalize NONMEM VI. Today, ICON continues to distribute NONMEM VI, with Robert Bauer serving as the software’s modern custodian — shepherding its updates, expanding its methodology, and preserving the legacy of those who built it.

Peck was not the only one who went looking for Barr Rosenberg and came back empty-handed.

In the pharmacometrics literature Rosenberg last appears in 1979. Ask a working pharmacometrician who founded the discipline and you will hear Sheiner and Beal, which is fair. Ask who told Sheiner how to do it, and most of them will not have an answer. Alison Boeckmann, who had spent forty years building the software culminating from Sheiner and Beal’s work, did not have one either: when I asked her about Rosenberg, she wrote back that the name meant nothing to her—she had looked him up and found nothing she could tie to NONMEM.

The financial world remembered him better. After leaving BARRA, Rosenberg launched a second financial services firm in 1985 that eventually blossomed into AXA Rosenberg, managing tens of billions of dollars using his proprietary algorithms. In April 2007, a programmer at the firm accidentally introduced a flaw into the code of AXA Rosenberg’s central risk model — the very engine designed to tell clients how much financial danger they were exposed to. The error sat there for two years, disabling a component and mispricing the risk across more than 600 investment portfolios. The firm discovered it in June 2009 and left it unfixed for 10 months. They did not notify their clients until April 2010, and only after financial regulators started asking questions.

The Securities and Exchange Commission brought its first-ever enforcement action over an error in a quantitative investment model. It charged Rosenberg with hiding the flaw and ordering his staff to remain silent. He was barred from the financial industry for life. His firm paid $217 million to compensate clients, and the damage was absorbed by pension funds and university endowments. All of this was happening in the same years that the method he had handed Lewis Sheiner was taking over the Food and Drug Administration.

Digoxin had been forcing the FDA’s hand for a decade before Peck ever walked in. In 1977 the FDA wrote the first regulation in its history that was quantitative in any real sense: a bioequivalence rule, requiring that a generic tablet deliver the same amount of drug into the bloodstream as the original. Part of what forced it was digoxin. Tablets pressed by different manufacturers dissolved at different rates, and patients switched between them were being carried across the narrow window without anyone touching the dose.

It was still a shock when, in 1987, Peck — the young doctor who had run the digoxin trial — became the founding director of the FDA’s Center for Drug Evaluation and Research. Sheiner saw the opportunity immediately. “Lou was whispering in my ear: ‘My God, Carl, now you’re in a position of even more importance — let’s work together to make sure FDA gets trained up in population PK,’” Peck recalled.

Peck’s first act as director, a matter of hours into the job, was to assemble the staff of this new center. These were the reviewers and medical officers who, between them, decided which medications Americans were permitted to take. He told them, quite directly, that they were naive about pharmacology.

Peck decided to teach them himself. With Sheiner’s help, he organized regular lectures, walking the agency’s medical officers and reviewers through the mechanics of population pharmacokinetics and eventually bringing a full NONMEM short course directly to the FDA’s Rockville campus in 1993.

Not all of the staff, however, were eager students. Peck found himself fighting a two-front war against what he called “statistical dinosaurs.” On one side, entrenched biostatisticians accustomed to the old, frequentist methods of trial evaluation; on the other, medical reviewers who lacked hard-science training. The approach had always been empirical: “you give a drug, you see if it works; if it does, you accept it; if it doesn’t, you reject it,” Peck explained. “There was huge resistance... In fact, this debate still goes on — there are empiricists and there are modelers. It’s almost a worldview.” To force the issue, Peck did more than preach. He established the FDA’s first pharmacometrics group, bringing in Thomas Ludden — a pharmacokinetics expert who would eventually finalize the NONMEM VI software — to get it off the ground.

Peck constantly pushed reviewers to see the causal relationship hidden in the math. “I’ve always argued that if you have an ordinary dose-response finding, that’s prima facie evidence of effectiveness,” he said. “You give a little, you get a little response; you give a lot, you get a big response.”

Peck left the FDA in 1993, founding the Center for Drug Development Science at Georgetown University, an academic base for the same cause. But he kept campaigning after he left the FDA, only now from a witness chair. Throughout 1996 and 1997 he testified before House and Senate committees on modernizing the way the government judged drug effectiveness, and in 1997 Congress passed the FDA Modernization Act. Its Section 115a gave Peck’s principle statutory form: a single adequate, well-controlled trial, backed by “confirmatory evidence” that could include pharmacokinetic data, can establish that a drug works. He sharpened the case again in 2003, co-authoring a paper with Sheiner and the Harvard statistician Donald Rubin. Bringing in Rubin — the author of the dominant modern theory of causal inference — was yet another instance of borrowing heavy mathematical artillery from the field next door.

Peck had successfully rewritten the statute, yet the culture inside the FDA remained stubbornly tethered to the old observational empiricism. Translating this new statutory permission into actual regulatory practice would fall to a different set of scientists.

Joga Gobburu — an FDA veteran of pharmacometrics and a former postdoctoral fellow under Peck — documented the agency’s transition from traditional empiricism to model-based drug development for me in a written timeline. He joined the FDA in 1998, five years after Peck left, into a building where the law had changed and the practice had not. There was no dedicated organizational structure for the work.

The science was, in his word, nascent. Population pharmacokinetics didn’t offer much practical value on its own, and the team faced heavy pushback from reviewers acting as “preservers of the status quo.” Because Gobburu’s group lacked formal authority over these reviewers, they were forced into what he called “influencing without authority.” So, they changed their approach. Instead of trying to sell the reviewers on the math, they aimed their models squarely at the only two decisions the FDA actually makes: should this drug be approved, and what should its label say?

Gobbur is clear-eyed about the origin myths his field likes to tell about itself. Sheiner’s final seminal paper, published in 1997 when he was 57 years old, argued that traditional drug trials conflate the two distinct tasks of learning how a medication actually works, and confirming that it helps the patient. Models, Sheiner insisted, should handle the learning, observational trials should handle the confirming. “Learning versus confirming in clinical drug development” is now routinely cited as the conceptual bedrock of what the FDA calls Model-Informed Drug Development. When I asked Gobburu whether the lineage between Sheiner’s “learning versus confirming” paradigm and the MIDD framework of today was historically real or drawn in hindsight, he refused to embellish his answer. The question requires very deep reflection, he wrote, offering a quotation from Sheiner in 1991 instead: the intellectual illness of clinical drug evaluation will be cured when we restore intellectual primacy to the questions we ask, not the methods by which we answer them.

In 1989, Sheiner was presented with a handful of numbers: blood levels of theophylline, a respiratory stimulant, drawn from premature infants.

These babies were being treated for apnea of prematurity, the long pauses in breathing that can stop a newborn’s heart. There were only a few blood draws per baby, because there is a limit to how much blood you can take from a premature infant. No trial had produced the numbers necessary to do traditional pharmacokinetic modeling, and none could have — it would be unethical for doctors to risk giving a ward of ill newborns incorrect doses just to figure out the right one.

To solve this, Sheiner and his team applied the population method to the sparse data they did have, and built a functional framework for safely medicating these infants. Under this model, an infant was treated as a tiny, rapidly shifting coordinate within a massive dataset comprised mostly of adult biometrics. And by doing so, the infant essentially “borrowed statistical strength” from 10,000 strangers they would never even encounter.

That is now, more or less, how the FDA thinks. Between 2000 and 2008, the FDA evaluated 198 applications for new drugs and biologics. In over half of those cases, pharmacometric modeling directly influenced the agency’s decisions regarding approval and labeling. And for 21 of them, the agency cleared a dose of a medication that not a single Phase 3 clinical trial had ever tested directly. These figures, for what it’s worth, come from a window that closed 19 years ago. The number quoted now is that roughly 90 percent of newly approved drugs involve model-informed development in some form. Gobburu told me that “the statistic is probably accurate… Pharmacometrics has become de facto now.”

In January of this year, the FDA published a draft guidance explicitly opening the door to the broader use of Bayesian methods in clinical trials — the exact statistical philosophy of updating your beliefs as the evidence arrives that Rosenberg had sketched out in a UCSF seminar room in 1969, and that Sheiner and Peck spent their careers pressing on a reluctant agency. “This guidance published earlier this year is almost too good to be true,” Peck said. The paper trail of that long campaign dominates his CV: Bayesian bioequivalence in 2019, again in 2022, and in 2024; a piece in The American Statistician on inference and decision-making for 21st century drug approval; a paper this year on expanding the role of modeling in regulatory decisions.

Peck has lived long enough to see the work take its final, codified form, but he stands almost entirely alone. Kenneth Melmon, the architect of both Rosenberg and Peck’s initial meetings with Sheiner, had carried his life to Stanford in 1978 to oversee its Department of Medicine, before his death in 2002. Lewis Sheiner died on April 22, 2004, at the age of 63. By Peck’s telling, Sheiner’s heart had been fragile his whole life. His father died before 50; Sheiner had his first heart attack in his late 30s, and colleagues visited him in the hospital not sure he would walk out. He did, and worked another quarter century. He was riding a train down through the Swiss Alps after a pharmacokinetics workshop when his heart gave out. A week earlier, he had received the highest honor his discipline could bestow, the Oscar B. Hunter Career Award in Therapeutics.

Stuart Beal died 21 months after that, in January 2006. Peck has a theory about the timing. “He died, I think in part, of a broken heart.” They had been inseparable, Sheiner and Beal. Beal had spent those last months of his life pushing to modernize NONMEM to handle parallel processing. On Friday, January 6, he left instructions with Boeckmann: no more code changes, let’s work on the release of NONMEM VI as soon as possible. He died that weekend. On the afternoon the team received the news, the new Sun workstation Beal had ordered finally arrived.

Barr Rosenberg outlived most of them by two decades, spending his last years a long way from Wall Street. He taught for years at a Buddhist institute tucked into the Berkeley hills, the Nyingma Institute, eventually serving as its co-dean. He died in February 2025, at a quiet retreat center on the Sonoma coast.

The world remembers Barr Rosenberg primarily for the money. His obituaries record the factor models and portfolio risk, the companies, the SEC actions, the ban. Such details are accurate, yes — but none of them mention the profound grace of his earlier life. They do not record that because of his mind, a premature infant trembling in a NICU ward can be given the exact measure of a medicine that was never tested on such fragile flesh. A Financial Times obituary noted that he never bragged about what he had built, in finance or out of it, which may be why so little of it was ever written down. It is a strange and heavy thing to gather the remnants of such a history — to hold this son’s brilliant mathematics in one hand, and his mother’s fading breath in the other.

Her name was Dorothy Sargent Rosenberg. She was a poet, leaving behind a volume of verse called Look Again. She was loved by a man named Marvin Rosenberg, Barr’s father and a scholar at Berkeley who devoted his life to understanding how three centuries of actors had breathed life into the lines of Shakespeare. When Dorothy’s health began to fail, Marvin nursed her through those long, shadowed years of her illness, until she died in the autumn of 1969.

What finally killed her is not a matter of public record. Sheiner’s email to his former student, typed from memory 36 years later, says congestive heart failure, mitral insufficiency, and a dose that kept climbing. The Berkeley memorial for her husband says only that she was in ill health. Whether the drug that started all of this is the drug that finished her is not recorded.

The field’s memory of her has drifted in any case. In the rare places where her story surfaces, the delicate facts slip and blur, suffering the inevitable distortions of a tale passed from hand to hand. Was it Lou’s mother, rather than Rosenberg’s? Warfarin, not digoxin? One posted history of the field, a chapter on modeling in anesthesia, opens by attributing the failing heart to Sheiner’s mother.

Marvin Rosenberg spent the rest of his life putting her name on things. He founded poetry prizes in her memory, and when he died in 2003, he left money behind to keep them going. Barr Rosenberg and his father’s widow (he remarried) ran them for nine years out of a post office box in Orinda, giving away as much as $200,000 a year to poets under 40. Then, in 2013 — two years after the SEC barred him from finance for the rest of his life — Barr Rosenberg signed the remaining $1.2 million of his fortune over to the Poetry Foundation in Chicago. The money endowed a fellowship of $27,000 each awarded to five American poets a year, one of the largest prizes a young writer in this country can win. The fellowship carries Dorothy’s name. The first class, in 2014, included Ocean Vuong.

Peck’s 42 patients — the trial that proved a computer could dose the drug better than a physician — ran in 1973. By then, Dorothy had been at rest for four years, having left this world just before it learned how to keep her.

Science

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Borrowing Strength

His bedridden mother was being poisoned by a miscalculated dose of a toxic heart drug. Driven to pull her back from the edge, a Wall Street forecaster turned his predictive models inward to forge the mathematical foundation of pharmacometrics.

In October, 2003, the scientist Lewis Sheiner sent an e-mail to Nick Holford, a former student, recalling how their field of pharmacometrics had begun. Within a few months, Sheiner was dead. The following year, Holford quoted a brief passage of the correspondence in a memorial tribute. When I reached out to him this summer for the rest of the exchange, he searched his archives and wrote back: “I cannot find the original email from Lewis that I cited.” That left only the brief scene he had already committed to print.

And it goes like this. A seminar room at the University of California, San Francisco, sometime around 1970. A young physician is up front, presenting his work on drug dosing, when an even younger economist starts interrupting from the audience — takes his math apart piece by piece, then rebuilds the field on the spot.

I spent several weeks this summer tracking the people and the institutions that grew out of that afternoon, guided by oral histories of retired clinical pharmacologists, veterans of the FDA, and a programmer who spent her career building the software that resulted from that chance encounter. The economist in the room was Barr Rosenberg. The doctor was Lewis “Lou” Sheiner. From their collision emerged pharmacometrics: the statistical scaffolding for how drugs move through populations, how doses of medicine are chosen, and how medicine attempts to learn from the sparse data of human bodies.

Barr Rosenberg was a forecaster of financial risk, and he was quite good at it. Born in Berkeley in 1942, he enrolled at the University of California at sixteen, secured a master’s degree from the London School of Economics by twenty-two, and completed a Harvard doctorate in economics at twenty-five. His dissertation carried a title only a statistician could truly appreciate: Regression with Stochastically Varying Parameters. The topic was a happy accident. He had originally intended to analyze capital markets using a pristine new stock-price database in Chicago, but when the data delivery stalled, he abandoned capital markets for pure theory, focusing entirely on how to model systems with underlying variables that continuously shifted over time.

That theoretical detour proved immensely valuable. The late 1960s and 1970s marked the dawn of quantitative finance, an era when it suddenly felt possible to quantify the invisible risks lurking inside a stock portfolio. In 1974, Rosenberg launched a consulting firm, BARRA. The reigning method scored a stock’s risk with a single number: how much it moved with the market. Rosenberg’s models pulled that risk apart across many features of the company itself. Suddenly, an oil company’s risk could ride on the price of crude and a bank’s on interest rates, a homebuilder’s to mortgage rates. The shift from one factor to many became, and remains, the working grammar of quantitative finance. It made BARRA’s tools standard equipment for institutional investors.

As Sheiner’s lost email tells it, Rosenberg’s foray into medicine began around 1967, when his mother’s heart began to fail. To keep her heart pumping, her doctors continually increased her dose of a heart medication called digoxin. First described in 1785 by the English physician William Withering, digoxin is a potent compound derived from the bell-shaped blooms of the foxglove plant. It is also a notoriously temperamental drug. It works by jamming microscopic sodium-potassium pumps in the membranes of heart muscle cells, causing calcium to pool inside. That extra calcium acts like a chemical whip, goading a weakened, flabby heart to contract with fresh intensity.

The margin for error with digoxin is perilously thin. If you underdose it, nothing happens. Make the mistake of overdoing it, and so much calcium floods the cells that the heart’s electrical system misfires, throwing the heart into a dangerous rhythm of its own. During the 1960s, doctors had no way of knowing where a patient sat within that narrow therapeutic window, because they lacked any reliable method to measure digoxin levels in a given person’s blood. So, equipped with nothing else, a doctor could only make an educated guess, tweak the dose this way and that way, and watch how their patient responded to it. A 1971 study found that about a quarter of hospitalized patients on digoxin were being poisoned by the drug. One of them was Rosenberg’s mother — who, by fate, was on the wrong side of a physician’s guesswork: every time her doctors raised her dose, she got worse.

Frustrated by the ordeal, Rosenberg began badgering his mother’s medical team with what seemed to him an obvious question. If he could use mathematics to model the volatile swings of the stock market, why couldn’t highly trained medical professionals use similar tools to chart a drug’s course through the human body?

Rosenberg saw no real difference between the stock market and human metabolism. To him, they were just two versions of the same puzzle. Both were vast, invisible systems that doctors and economists could only guess at using sparse, noisy clues — like a closing bell price or a morning blood draw. But where medicine saw missing data as a tragedy, Rosenberg saw it as a math problem waiting to be solved.

The prevailing statistical paradigm of that era treated patients as mere copies — interchangeable units stamped from a single biological template. Doctors would identify a theoretical “average” patient, calculate the statistical mean of how much of a medication would be needed to treat them, and then administer that generalized dose to everyone on the ward. They would then watch, often helplessly, as real, idiosyncratic human beings wildly diverged from that neat mathematical average.

Rosenberg’s idea was to give every patient a biology of their own: a particular rate of clearing a drug through the kidneys, a particular volume of blood to dilute it in. It did not leave them there alone. It set each one inside a larger picture, like a single, uniquely colored dot in a Pointillist painting.

On its own, a single data point doesn’t tell doctors much, but analyzing thousands of them together reveals a clear pattern. Statisticians have a homely, almost quaint name for this trick: “borrowing strength.”

In practice, you start a new patient on a dose derived from the wider population. It’s a lot like the old habit of just grabbing the “average,” but this time, you know exactly how reliable that baseline is. Then, as that patient’s own blood levels of a drug arrive, Rosenberg’s method slides the estimate off the crowd and onto them, until it describes that person and no one else.

All Rosenberg needed was a physician willing to let him test the math.

Leslie Benet has been fielding calls about the early days of pharmacometrics for a while now; the American Society of Clinical Pharmacology and Therapeutics had asked him to talk through this same history back in April. He joined the UCSF faculty in 1969, took over as chair of its Department of Pharmacy in 1978, and spent two decades around the clinical pharmacology group.

The first thing he wanted me to understand was that his chosen field was, in its early years, failing to thrive. In 1969 there were two serious centers for clinical pharmacology — how drugs interact with the human body — in the country, Vanderbilt and UCSF, and both were trying to turn it into a self-sustaining discipline of medicine. Neither managed it. “It never succeeded in doing that,” Benet said, “because it couldn’t control beds. And in a medical center, that’s what’s critical.” Infectious disease was founded in the same years and became one of the great engines of academic medicine, because infectious diseases filled wards and brought in revenue. Clinical pharmacology brought in almost nothing, and became, in Benet’s phrase, an “academic exercise.”

Without tools sensitive enough to detect microscopic traces of a drug in human blood, you cannot productively calculate an ideal, personalized dosage for a patient. For most of medical history, this was simply reality. Rosenberg’s mother’s doctors raised her digoxin half-blind, with no dependable way to see how much of it was in her blood. Benet explained that “When I started in the field, it was spectrophotometry.” This meant trying to calculate a drug’s concentration by shining a light through a fluid and measuring how much of the beam made it out the other side. The technique required large biological samples just to detect a drug in urine, and finding it in the blood was close to impossible. It took gas-liquid chromatography, then high-pressure liquid chromatography, and then finally mass spectrometers sensitive enough to count individual molecules in a vial. Rosenberg’s kind of math was useless without numbers to feed it. Those numbers only became possible to produce at the end of the 1960s — right as he came looking for a doctor to use them.

The doctor he needed was already down the hall. Lewis Sheiner (everyone called him Lou) had trained at the NIH and at Stanford before landing at UCSF as a clinical pharmacology fellow, and he arrived with a physician’s credentials and a mathematician’s habits of mind. He had been chewing on the same problem that pulled Rosenberg off the stock market: how to get a trustworthy prediction for one patient out of thin, noisy clinical data.

Sheiner came to Rosenberg’s aid with a computer ready. At the NIH’s Computer Systems Laboratory, the doctor had written a program run on a room-sized IBM computer to dose warfarin — a blood thinner with volatile pharmacokinetic properties. But to do so cost $12 a minute. He fitted the program to 17 patients and 199 prothrombin times, each a measure of how long that patient’s blood took to clot. But for some patients, that left only a single measurement to feed a model that demanded four. You cannot solve for four unknowns with a single data point; what Sheiner lacked was a reason to believe that his seventeen patients had anything to do with each other.

Benet was underwriting the effort via his leadership within the UCSF Department of Pharmacy. Sheiner had come in as a fellow, and his first NIH money ran through a center grant Benet controlled — one of only two such grants to support clinical pharmacology research in the country. “I basically supplied him with his initial NIH funding,” Benet told me.

The connection ran through Kenneth Melmon, the director of the UCSF clinical pharmacology group who had a rare talent for placing the right two minds in the same room. Melmon hosted a weekly seminar, and one afternoon he invited Rosenberg to sit in. This is the fabled scene from the lost email. Rosenberg patiently listened as Sheiner presented his work on drug dosing. When Sheiner finished, Rosenberg politely replied, “That was very nice, but here is how you should have done it.” Right there in the room, he sketched out the entire statistical framework. He showed how to estimate the population and the individual in tandem, allowing the vast crowd to lend its mathematical strength to the solitary patient. It was, among other things, the answer to the warfarin problem: the four parameters and the one blood draw stopped being a contradiction the moment the other 16 patients were allowed to speak for the 17th. Sheiner saw it immediately. He arranged to complete his fellowship in Melmon’s group to collaborate with Rosenberg, and he pursued the idea for the rest of his life.

While Benet didn’t know Rosenberg well, what he gave me instead was a list of people to call — including one name he kept circling back to: Carl Peck.

Carl Peck earned a bachelor’s degree in mathematics and chemistry from the University of Kansas in 1963, having spent two years as an undergraduate research assistant in a nuclear physics laboratory, and went on to win a Fulbright in chemistry. Then he went to medical school. “The way to advance your field,” he told me, “is to look over the fence into somebody else’s field and see if you can borrow something.” In 1971, a young Army physician by then, he published a paper titled “The Almighty P-value, or the Significance of Significance.”

In the early 1970s, he was chief resident at Letterman Army Medical Center in the Presidio of San Francisco, running a ward full of patients on digoxin. Calculating a patient’s dose meant walking a stack of punched cards over to the hospital’s computer center and praying the code compiled. Peck was already frustrated by the medical establishment’s grasp of statistics, “pissing and moaning about p-values” to his residents, as Peck told me. After one of these performances, a UCSF student on a clinical rotation under him told him he was “singing a song two men in the clinical pharmacology group would want to hear,” and that he ought to go meet Ken Melmon and Lou Sheiner. Peck had never heard of either. He phoned Melmon to ask whether he could sit in on a seminar, and Melmon told him to come give one instead. “I was flabbergasted, because I was very junior at the time,” Peck recalled. But he went, and sitting in the audience was Lou Sheiner.

To really put the method to the test, they turned to the obvious candidate: digoxin. At Letterman, they split 42 patients into two camps. One half received doses based purely on a doctor’s intuition, and the other half let the new computer model take the wheel. Unsurprisingly, the algorithm was much better at hitting the right blood levels. The paper that came out of it was Peck’s first, and to his own astonishment it ran in the New England Journal of Medicine.

By 1975, a follow-up study successfully executed Rosenberg’s feedback loop in clinical practice, actively recalibrating the algorithm to fit the individual parameters of each patient. Just how well the method worked, the group would pin down a few years later: for digoxin, a single blood measurement cut the error in forecasting a patient’s future levels by 40 percent, and two measurements by two-thirds — a lone draw worth more than the patient’s age, sex, and kidney readings combined.

Peck had crossed paths with Rosenberg exactly once, over at UC Berkeley. “Brilliant, fast-talking, almost charismatic,” describing a very young, front-running professor confident in his own mind. “I have to admit, the substance of what they were discussing was all over my head,” Peck said.

That was the only time. Decades later he tried to track Rosenberg down again and failed. By then, Peck said, the man had embedded himself deep in “this Eastern religious thing.”

Lou Sheiner needed a full-time statistician to push the idea further, and he found one by accident. In 1976, riding the UCSF commuter bus out to Marin County, he sat down next to Stuart Beal, a biostatistician who had come to the university a few years earlier to work in its information-systems office. Sheiner started explaining what he was after. Beal — a UCLA mathematician who had minored in logic before taking a UCSF doctorate in biostatistics — was hooked before the bus reached the county line. The friendship and the collaboration both began that afternoon, and both lasted the rest of their lives.

Melmon had to find them somewhere to sit to work on their collaboration, and what he found was a room in the Division of Laboratory Medicine, the wing that ran the clinical assays their whole method depended on. The office tiny office could barely fit two desks in it, so they they arranged them across from each other; arguing all day, for years; Sheiner grounding Beal in the clinical realities of dosing patients, and Beal walking Sheiner through the rigorous biostatistics required to make the model work. Down the hall, the Division of Laboratory Medicine was running the clinical assays — using chromatography and spectrometry to pull the exact drug concentrations from patient blood samples, generating the raw data the two men were trying to mathematically resolve.

Rosenberg, meanwhile, was orchestrating from afar as Beal became the mathematical engine Rosenberg had only hoped for. Rosenberg himself lingered in the paper trail a little longer: He was there for the 1977 study that first showed how to pull a whole population’s pharmacokinetics out of routine clinical data, and a final time in 1979, when he co-authored his final paper in medicine. Then he left medicine for good, back to BARRA and the markets.

His name stayed behind in the software. Sheiner and Beal called it NONMEM — nonlinear mixed-effects modeling — and a nonlinear mixed-effects model is the same species of mathematics as Rosenberg’s doctoral thesis, regression with parameters left free to drift from one case to the next, the tool he had carried out of economics and turned on the body. It even surfaces by name in the last paper Rosenberg ever published in medicine, in 1979: “a computer program, NONMEM, has been developed by some of us,” tucked into the appendix.

When NONMEM I shipped in April 1980, the entire software package consisted of a pale-blue instruction booklet and a single Memorex magnetic tape. The software was written in FORTRAN IV, which had strict limitations. Because early compilers capped names at six characters, the team had to abbreviate a routine like ADVANCE1 to ADVAN1. Users are still forced to use that 1980s shorthand today to advance a drug’s state to a new point in time using a one-compartment model. When NONMEM runs, only a user’s own model code is compiled; most of the FORTRAN was built into a library once, at installation, to keep the program fast. Four decades later, this foundational architecture remains untouched.

NONMEM proved its necessity in testing drugs, a necessarily artificial process. Clinical trials typically enrolled healthy, young volunteers — often medical students — who were given doses of a given drug too low to cause side effects and had their blood drawn on a perfectly rigid schedule. If a student missed a draw, his data was discarded. The numbers that finally reached the statisticians were pristine and balanced, yet divorced from the sick people who would actually take the drug. Prescribe a blood-pressure medication to an elderly population and some will react violently while others won’t respond at all; those erratic patients — not young medical students who follow instructions to the tee — are usually yanked from the study and given rescue drugs, and they are precisely the people doctors most need to understand.

Benet was coediting the Journal of Pharmacokinetics and Biopharmaceutics when Sheiner, still the junior man at the table being in his early 40s, proposed a new section for this kind of quantitative modeling and offered to run it. “Lou said, let’s create a new section in the journal called pharmacometrics,” Benet recalled. That is how the discipline now governing how the industry sets its doses got its name — a heading in a table of contents. Nobody in the room thought it was much of an occasion. “I don’t think I felt that it was really anything major happening,” Benet said. “It was just one of the developments that were going on at the time.”

The original 1980 NONMEM software was a tool built by specialists for specialists. It likely would have remained trapped in a handful of academic laboratories if not for Alison Boeckmann, a dedicated computer programmer, who joined the team around 1982. Over the following decade she wrote NM-TRAN, a control language that let pharmacologists specify their drug models in a structured script while the computer handled the calculus in the background. She also implemented PREDPP, Beal’s library of pre-packaged models, in 1984. NM-TRAN wasn’t released until 1989; it took nearly 10 years to build a version of NONMEM that a normal scientist could actually use. Boeckmann became the software’s custodian, calling NONMEM her “life’s work.” She stayed on the project for 40 years and built the email listserv that still serves as the global town square for pharmacometrics.

Through the 1980s, the technique seeped out of UCSF and into the broader pharmaceutical industry, which was beginning to suffocate under the weight of exactly the messy, sparse data NONMEM had been built to handle. In addition to publishing their research, Beal and Sheiner evangelized their software through traveling courses in Kyoto, Uppsala, and Lyon, cultivating a sprawling network of postdocs who would go on to become leaders in pharmacometrics across the world.

NONMEM became the undisputed standard for population pharmacokinetic modeling, for a reason no competitor could bear to match: its research and development was already paid for. The software, created at UCSF in the late ‘70s, was bankrolled by an NIH grant, GM26676, which ran continuously from 1977 for nearly thirty years — a MERIT award that kept paying out after both the men who built it were gone. Beal ran the operation with a proprietor’s care, personally telephoning labs that let their licenses lapse to ask for their tapes back.

Because the overhead was already covered by the government, the licensing fees UCSF charged pharmaceutical companies turned into pure departmental surplus. The software generated enough revenue, Benet told me, to fund an entire clinical wing of the department that couldn’t have sustained itself otherwise. In time the university handed distribution to a commercial firm, Globomax, who enlisted Peck and Sheiner’s frequent collaborator, Thomas Ludden, to finalize NONMEM VI. Today, ICON continues to distribute NONMEM VI, with Robert Bauer serving as the software’s modern custodian — shepherding its updates, expanding its methodology, and preserving the legacy of those who built it.

Peck was not the only one who went looking for Barr Rosenberg and came back empty-handed.

In the pharmacometrics literature Rosenberg last appears in 1979. Ask a working pharmacometrician who founded the discipline and you will hear Sheiner and Beal, which is fair. Ask who told Sheiner how to do it, and most of them will not have an answer. Alison Boeckmann, who had spent forty years building the software culminating from Sheiner and Beal’s work, did not have one either: when I asked her about Rosenberg, she wrote back that the name meant nothing to her—she had looked him up and found nothing she could tie to NONMEM.

The financial world remembered him better. After leaving BARRA, Rosenberg launched a second financial services firm in 1985 that eventually blossomed into AXA Rosenberg, managing tens of billions of dollars using his proprietary algorithms. In April 2007, a programmer at the firm accidentally introduced a flaw into the code of AXA Rosenberg’s central risk model — the very engine designed to tell clients how much financial danger they were exposed to. The error sat there for two years, disabling a component and mispricing the risk across more than 600 investment portfolios. The firm discovered it in June 2009 and left it unfixed for 10 months. They did not notify their clients until April 2010, and only after financial regulators started asking questions.

The Securities and Exchange Commission brought its first-ever enforcement action over an error in a quantitative investment model. It charged Rosenberg with hiding the flaw and ordering his staff to remain silent. He was barred from the financial industry for life. His firm paid $217 million to compensate clients, and the damage was absorbed by pension funds and university endowments. All of this was happening in the same years that the method he had handed Lewis Sheiner was taking over the Food and Drug Administration.

Digoxin had been forcing the FDA’s hand for a decade before Peck ever walked in. In 1977 the FDA wrote the first regulation in its history that was quantitative in any real sense: a bioequivalence rule, requiring that a generic tablet deliver the same amount of drug into the bloodstream as the original. Part of what forced it was digoxin. Tablets pressed by different manufacturers dissolved at different rates, and patients switched between them were being carried across the narrow window without anyone touching the dose.

It was still a shock when, in 1987, Peck — the young doctor who had run the digoxin trial — became the founding director of the FDA’s Center for Drug Evaluation and Research. Sheiner saw the opportunity immediately. “Lou was whispering in my ear: ‘My God, Carl, now you’re in a position of even more importance — let’s work together to make sure FDA gets trained up in population PK,’” Peck recalled.

Peck’s first act as director, a matter of hours into the job, was to assemble the staff of this new center. These were the reviewers and medical officers who, between them, decided which medications Americans were permitted to take. He told them, quite directly, that they were naive about pharmacology.

Peck decided to teach them himself. With Sheiner’s help, he organized regular lectures, walking the agency’s medical officers and reviewers through the mechanics of population pharmacokinetics and eventually bringing a full NONMEM short course directly to the FDA’s Rockville campus in 1993.

Not all of the staff, however, were eager students. Peck found himself fighting a two-front war against what he called “statistical dinosaurs.” On one side, entrenched biostatisticians accustomed to the old, frequentist methods of trial evaluation; on the other, medical reviewers who lacked hard-science training. The approach had always been empirical: “you give a drug, you see if it works; if it does, you accept it; if it doesn’t, you reject it,” Peck explained. “There was huge resistance... In fact, this debate still goes on — there are empiricists and there are modelers. It’s almost a worldview.” To force the issue, Peck did more than preach. He established the FDA’s first pharmacometrics group, bringing in Thomas Ludden — a pharmacokinetics expert who would eventually finalize the NONMEM VI software — to get it off the ground.

Peck constantly pushed reviewers to see the causal relationship hidden in the math. “I’ve always argued that if you have an ordinary dose-response finding, that’s prima facie evidence of effectiveness,” he said. “You give a little, you get a little response; you give a lot, you get a big response.”

Peck left the FDA in 1993, founding the Center for Drug Development Science at Georgetown University, an academic base for the same cause. But he kept campaigning after he left the FDA, only now from a witness chair. Throughout 1996 and 1997 he testified before House and Senate committees on modernizing the way the government judged drug effectiveness, and in 1997 Congress passed the FDA Modernization Act. Its Section 115a gave Peck’s principle statutory form: a single adequate, well-controlled trial, backed by “confirmatory evidence” that could include pharmacokinetic data, can establish that a drug works. He sharpened the case again in 2003, co-authoring a paper with Sheiner and the Harvard statistician Donald Rubin. Bringing in Rubin — the author of the dominant modern theory of causal inference — was yet another instance of borrowing heavy mathematical artillery from the field next door.

Peck had successfully rewritten the statute, yet the culture inside the FDA remained stubbornly tethered to the old observational empiricism. Translating this new statutory permission into actual regulatory practice would fall to a different set of scientists.

Joga Gobburu — an FDA veteran of pharmacometrics and a former postdoctoral fellow under Peck — documented the agency’s transition from traditional empiricism to model-based drug development for me in a written timeline. He joined the FDA in 1998, five years after Peck left, into a building where the law had changed and the practice had not. There was no dedicated organizational structure for the work.

The science was, in his word, nascent. Population pharmacokinetics didn’t offer much practical value on its own, and the team faced heavy pushback from reviewers acting as “preservers of the status quo.” Because Gobburu’s group lacked formal authority over these reviewers, they were forced into what he called “influencing without authority.” So, they changed their approach. Instead of trying to sell the reviewers on the math, they aimed their models squarely at the only two decisions the FDA actually makes: should this drug be approved, and what should its label say?

Gobbur is clear-eyed about the origin myths his field likes to tell about itself. Sheiner’s final seminal paper, published in 1997 when he was 57 years old, argued that traditional drug trials conflate the two distinct tasks of learning how a medication actually works, and confirming that it helps the patient. Models, Sheiner insisted, should handle the learning, observational trials should handle the confirming. “Learning versus confirming in clinical drug development” is now routinely cited as the conceptual bedrock of what the FDA calls Model-Informed Drug Development. When I asked Gobburu whether the lineage between Sheiner’s “learning versus confirming” paradigm and the MIDD framework of today was historically real or drawn in hindsight, he refused to embellish his answer. The question requires very deep reflection, he wrote, offering a quotation from Sheiner in 1991 instead: the intellectual illness of clinical drug evaluation will be cured when we restore intellectual primacy to the questions we ask, not the methods by which we answer them.

In 1989, Sheiner was presented with a handful of numbers: blood levels of theophylline, a respiratory stimulant, drawn from premature infants.

These babies were being treated for apnea of prematurity, the long pauses in breathing that can stop a newborn’s heart. There were only a few blood draws per baby, because there is a limit to how much blood you can take from a premature infant. No trial had produced the numbers necessary to do traditional pharmacokinetic modeling, and none could have — it would be unethical for doctors to risk giving a ward of ill newborns incorrect doses just to figure out the right one.

To solve this, Sheiner and his team applied the population method to the sparse data they did have, and built a functional framework for safely medicating these infants. Under this model, an infant was treated as a tiny, rapidly shifting coordinate within a massive dataset comprised mostly of adult biometrics. And by doing so, the infant essentially “borrowed statistical strength” from 10,000 strangers they would never even encounter.

That is now, more or less, how the FDA thinks. Between 2000 and 2008, the FDA evaluated 198 applications for new drugs and biologics. In over half of those cases, pharmacometric modeling directly influenced the agency’s decisions regarding approval and labeling. And for 21 of them, the agency cleared a dose of a medication that not a single Phase 3 clinical trial had ever tested directly. These figures, for what it’s worth, come from a window that closed 19 years ago. The number quoted now is that roughly 90 percent of newly approved drugs involve model-informed development in some form. Gobburu told me that “the statistic is probably accurate… Pharmacometrics has become de facto now.”

In January of this year, the FDA published a draft guidance explicitly opening the door to the broader use of Bayesian methods in clinical trials — the exact statistical philosophy of updating your beliefs as the evidence arrives that Rosenberg had sketched out in a UCSF seminar room in 1969, and that Sheiner and Peck spent their careers pressing on a reluctant agency. “This guidance published earlier this year is almost too good to be true,” Peck said. The paper trail of that long campaign dominates his CV: Bayesian bioequivalence in 2019, again in 2022, and in 2024; a piece in The American Statistician on inference and decision-making for 21st century drug approval; a paper this year on expanding the role of modeling in regulatory decisions.

Peck has lived long enough to see the work take its final, codified form, but he stands almost entirely alone. Kenneth Melmon, the architect of both Rosenberg and Peck’s initial meetings with Sheiner, had carried his life to Stanford in 1978 to oversee its Department of Medicine, before his death in 2002. Lewis Sheiner died on April 22, 2004, at the age of 63. By Peck’s telling, Sheiner’s heart had been fragile his whole life. His father died before 50; Sheiner had his first heart attack in his late 30s, and colleagues visited him in the hospital not sure he would walk out. He did, and worked another quarter century. He was riding a train down through the Swiss Alps after a pharmacokinetics workshop when his heart gave out. A week earlier, he had received the highest honor his discipline could bestow, the Oscar B. Hunter Career Award in Therapeutics.

Stuart Beal died 21 months after that, in January 2006. Peck has a theory about the timing. “He died, I think in part, of a broken heart.” They had been inseparable, Sheiner and Beal. Beal had spent those last months of his life pushing to modernize NONMEM to handle parallel processing. On Friday, January 6, he left instructions with Boeckmann: no more code changes, let’s work on the release of NONMEM VI as soon as possible. He died that weekend. On the afternoon the team received the news, the new Sun workstation Beal had ordered finally arrived.

Barr Rosenberg outlived most of them by two decades, spending his last years a long way from Wall Street. He taught for years at a Buddhist institute tucked into the Berkeley hills, the Nyingma Institute, eventually serving as its co-dean. He died in February 2025, at a quiet retreat center on the Sonoma coast.

The world remembers Barr Rosenberg primarily for the money. His obituaries record the factor models and portfolio risk, the companies, the SEC actions, the ban. Such details are accurate, yes — but none of them mention the profound grace of his earlier life. They do not record that because of his mind, a premature infant trembling in a NICU ward can be given the exact measure of a medicine that was never tested on such fragile flesh. A Financial Times obituary noted that he never bragged about what he had built, in finance or out of it, which may be why so little of it was ever written down. It is a strange and heavy thing to gather the remnants of such a history — to hold this son’s brilliant mathematics in one hand, and his mother’s fading breath in the other.

Her name was Dorothy Sargent Rosenberg. She was a poet, leaving behind a volume of verse called Look Again. She was loved by a man named Marvin Rosenberg, Barr’s father and a scholar at Berkeley who devoted his life to understanding how three centuries of actors had breathed life into the lines of Shakespeare. When Dorothy’s health began to fail, Marvin nursed her through those long, shadowed years of her illness, until she died in the autumn of 1969.

What finally killed her is not a matter of public record. Sheiner’s email to his former student, typed from memory 36 years later, says congestive heart failure, mitral insufficiency, and a dose that kept climbing. The Berkeley memorial for her husband says only that she was in ill health. Whether the drug that started all of this is the drug that finished her is not recorded.

The field’s memory of her has drifted in any case. In the rare places where her story surfaces, the delicate facts slip and blur, suffering the inevitable distortions of a tale passed from hand to hand. Was it Lou’s mother, rather than Rosenberg’s? Warfarin, not digoxin? One posted history of the field, a chapter on modeling in anesthesia, opens by attributing the failing heart to Sheiner’s mother.

Marvin Rosenberg spent the rest of his life putting her name on things. He founded poetry prizes in her memory, and when he died in 2003, he left money behind to keep them going. Barr Rosenberg and his father’s widow (he remarried) ran them for nine years out of a post office box in Orinda, giving away as much as $200,000 a year to poets under 40. Then, in 2013 — two years after the SEC barred him from finance for the rest of his life — Barr Rosenberg signed the remaining $1.2 million of his fortune over to the Poetry Foundation in Chicago. The money endowed a fellowship of $27,000 each awarded to five American poets a year, one of the largest prizes a young writer in this country can win. The fellowship carries Dorothy’s name. The first class, in 2014, included Ocean Vuong.

Peck’s 42 patients — the trial that proved a computer could dose the drug better than a physician — ran in 1973. By then, Dorothy had been at rest for four years, having left this world just before it learned how to keep her.

About the Author

Alex Kesin is a biotech strategist and writer focused on the incentives, institutions, and policies shaping drug development. He is on X @alexkesin