Such modeling led to Sheiner’s most important contribution, application of the “population principle” to pharmacology. According to the population principle, the behavior of drugs in individuals can be accurately predicted based on knowledge about how drugs behave in a population of patients with similar characteristics. The population principle defined drug behavior using “mixed effect” models combining the roles of “fixed effects” (e.g., dose, weight, height, age, gender), and the roles of “random effects” (things like the unexplained person-to-person differences in clearance, volume of distribution, or sensitivity to a drug) to explain drug behavior (pharmacodynamics). Further, the population principle separated the components of variability into those between individuals (interindividual variability, such as differences in clearance, which account for individual response to drugs) and those within an individual (intraindividual variability, such as assay noise). The aim was to predict drug effect as precisely as possible, taking known variables such as weight, height, gender, age, and other patient factors (e.g., genetics), to accurately predict the pharmacokinetic and pharmacodynamic factors controlling the response to a drug, factors such as clearance, volume of distribution, and potency. Thus, measurement of the right fixed effects should allow prediction of the response to a drug accurately, reducing the previously unexplained subject-to-subject variability. Reduction of residual inter-individual variability, things like assay noise, would require more precise measurements and perhaps refinement of models to more accurately describe the underlying biology.

Sheiner described the population principle in 1977 [4]. One of his insights was that pharmacokinetics in a population of patients could be estimated from routine clinical data. Sheiner’s methods allowed the design of more efficient and informative clinical trials, optimizing dosing recommendations, and, via empirical Bayesian methods, optimizing individual therapy. The work transformed clinical pharmacology [5], the pharmaceutical industry [6,7], and drug regulation [8].

Sheiner needed a statistician to develop his ideas, and a programmer to create software that would convert his concepts into research tools. In 1976, while riding on the UCSF commuter bus to Marin County, he fortuitously sat next to Stuart Beal (Fig. 40.2), an aspiring statistician recently recruited to UCSF. Sheiner explained his ideas, piquing Beal’s interest. A friendship and collaboration began that day and lasted a lifetime.

Beal expanded on Rosenberg’s concepts for dose individualization [9], leading to his developing the statistical basis for mixed-effects modeling. Beal also wrote the program NONMEM, an acronym for non-linear mixed effects modeling. It is arguably the greatest intellectual advance in the history of clinical pharmacology. NONMEM’s methodology opened the “population principle” of drug behavior to clinical pharmacologists, and became the standard modeling technique for the pharmaceutical industry. In the 1980s, Sheiner and Beal validated NONMEM against other popular approaches [10–12]. NONMEM outperformed those approaches.

In 1989, Ted Grasela approached Sheiner with a problem. Someone had sampled blood to determine theophylline concentration in neonates given theophylline to prevent apnea of prematurity. Each patient supplied a few samples. Grasela asked if a pharmacokinetic analysis could be done with such sparse sampling (compared to the standard of 10 samples or more). Sheiner realized that mixed-effects methods could be applied to Grasela’s problem: the pharmacokinetic characteristics could be determined with a sufficient number of subjects (i.e., trading fewer samples per subjects for more subjects). The analysis succeeded [13], spawning a new approach to assessing population pharmacokinetics: study many subjects (thereby learning more about the population) but obtain few samples per patient (still learning about individual characteristics because of the large number of samples). This approach is known as sparse sampling coupled with population (mixed-effects) methods.

Another novel Sheiner concept was mathematical modeling of the “effect compartment” in the context of a pharmacokinetic model. Clinicians have always known that a delay exists between drug dosing and drug effect. In 1960, Price described the time delay between thiopental concentration and drug effect [14]. Eger also provided insight into this delay or “hysteresis” for inhaled anesthetics [15]. However, this work did not link the delay to a pharmacokinetic model of the plasma drug concentration.

Stanski came to UCSF from his anesthesia residency at Massachusetts General Hospital. He wanted to develop a model explaining the delay between administration of a muscle relaxant and the resulting muscle paralysis. Immediately after receipt of a bolus dose, the plasma concentration of the muscle relaxant is at its highest concentration, but there is no drug effect. Over time the plasma concentration steadily decreases, and the level of muscle relaxation (“twitch depression”) rises, reaches a maximum, and then recedes. This leads to the curious situation where there are two different plasma concentrations associated with the same twitch: one observed while the drug effect was increasing, and the other while the effect was decreasing. How could markedly different concentrations produce the same twitch depression?

Sheiner argued that the relevant concentration is the one at the neuromuscular junction (Sheiner chose the general term “effect site”). He linked it to the plasma concentration by simple “first order” diffusion down the concentration gradient. Sheiner and Stanski introduced the concept of the effect site” in a manuscript describing the time course of d-tubocurarine [16]. It became Stanski’s most cited manuscript. Interestingly, using the same principle of first order diffusion down the concentration gradient, Chris Hull, a British anesthesiologist in Newcastle, UK, developed an effect compartment model for pancuronium [17]. Although Hull’s publication preceded Sheiner’s, Hull did little to popularize his work, and the Sheiner-Stanski contribution is considered pivotal.

Sheiner pursued other issues: nonparametric approaches making minimal assumptions [18], therapeutic drug monitoring [19], how to handle missing dose data [20], and modeling drug compliance [21,22]. He was a formidable intellect engaging anyone having interesting questions. He loved data. He was never just the visionary. Sheiner formatted the data, wrote NONMEM control streams, fitted the data to models, created the graphs, and analyzed the outputs. Fisher or Shafer would call Sheiner with a question, and his answer was often “Let me see the data, and I’ll get back to you.” He rarely looked anything up in books. It might be faster, but if he forced himself to do the derivation, he would then understand it better. Besides, it was more fun.

Sheiner mentored more than a generation of investigators and clinical pharmacologists. Most clinical pharmacology papers continue to reflect his work. He mentored Carl Peck, former Director of the FDA Center for Drug Evaluation and Research which incorporated Sheiner’s concepts into FDA work. Sheiner was Stanski’s mentor and greatest friend. He mentored Fisher whose papers in the 1990s benefited from Sheiner’s insights.

Beal’s education at UCLA included a BA degree in mathematics with a minor in Logic and Fine Arts, and MS and PhD degrees in biostatistics. He started at UCSF in 1973 as a Senior Statistician in the Office of Information Systems, joining the faculty in 1976, the year of his bus ride with Sheiner.

Sheiner was the front man’meeting people, giving lectures, looking for good questions and informative data, and raising new ideas. Beal was the implementer, the developer of statistics, translating Sheiner’s grand ideas into NONMEM. NONMEM was Beal’s life. He created new methods in NONMEM to handle the challenges raised by Sheiner and others. NONMEM came to encompass all of statistics to Beal.

In 2001, Shafer asked Beal how to perform a repeated measures ANOVA. Not trained as a statistician, Shafer had no idea about the “right” way to approach it, but had coded the problem using NONMEM. Beal laughed. Like Shafer, he could perform a repeated measures ANOVA using NONMEM, but had forgotten how to do it with conventional approaches. Indeed, Beal used NONMEM for t-tests. That conversation speaks volumes about NONMEM’s versatility. Why use anything else, if NONMEM can provide any statistical test?

Beal and Sheiner offered NONMEM for a modest user fee to colleagues in academia and industry. If you didn’t renew your license, then Beal (yes, the same Beal who developed the code) would personally call and ask you to return your magnetic tape or, once that was obsolete, the floppy disks. A week later you got another call, again from Beal.

Sheiner’s colleague, Malcolm Rowland, thought that making NONMEM available inexpensively was a terrible idea: if Sheiner and Beal didn’t make NONMEM profitable, then there would be no posthumous support structure for NONMEM. Eventually Sheiner and Beal accepted Rowland’s wisdom and turned over NONMEM distribution to Globomax (now ICON Development Systems). Rowland’s suggestion proved prescient. Despite Sheiner’s and Beal’s premature deaths, NONMEM has grown in popularity, usability, and statistical power.

Although many found Beal to be distant and reserved, he and Shafer were unusually close. Their friendship grew from a 1990s disagreement about modeling. Shafer, whose research was in target controlled drug delivery, had numerous reservations about NONMEM. NONMEM could not be used for TCI, which required changing infusion rate every 10 seconds. Shafer had modeled all patients’ responses simultaneously, ignoring inter-subject variability [23]. Beal dismissed the approach as “naïve” but allowed Shafer to deluge him with data, graphs, and analyses. Eventually Beal agreed that the naïve approach had merits, and was sometimes powerful. In the process, Beal showed Shafer how data settle scientific debates. Beal’s patient mentorship led to Shafer’s interest in the role of data in evidential reasoning [24]. Their relationship is evident in a letter Shafer sent to Beal in January, 1995:

“I’m a physician with no formal training in mathematics or statistics. My role in clinical pharmacology is to bring the tools developed by your group to bear on questions important to me as a clinician. Your mentoring has allowed me to perform my work at a more sophisticated level than would otherwise be possible.

“Mentoring takes time and patience, and God knows I’ve sorely tested your store of each. You have been patient with me, careful in your explanations, and considerate of my lack of formal training in mathematics and statistics. With your permission, I’ll continue to pester you with problems, bother you with bugs, quiz you with questions, and irritate you with irreverent e-mail.”

Fisher (Fig. 40.3) arrived in San Francisco in 1980, his interests quickly attracting him to Sheiner’s circle. A pediatric anesthesiologist, Fisher initially studied pharmacokinetics and pharmacodynamics of muscle relaxants and intravenous anesthetic drugs in children, infants, and neonates. He developed a model describing the kinetics of drugs like atracurium that were degraded in plasma [25]. Burroughs Wellcome (now GSK) repeatedly challenged the model without explaining their rationale. Their stance galled Fisher because they adopted a similar model for cisatracurium, and claimed that they developed the model [26].

Francois Donati obtained simultaneous measurements of twitch depression at the thumb (adductor pollicis) and the laryngeal muscles, leading Fisher to a remarkable insight: with two different rates of onset, both driven by the same plasma drug concentrations, he could estimate the relative potency of the two drugs, and the rate of plasma-effect site equilibration for each with no measurement of plasma concentrations. The manuscript [27] prompted a suggestion by “an anonymous reviewer” (Shafer) to validate the model by repeating the study with plasma sampling and computing the outcome with and without those data. Fisher did, the results confirming his thesis [28].

Fisher presently evaluates many new drugs, most having nothing to do with anesthesia. His software, PLT Tools (in which Shafer also has a commercial interest) provides a powerful environment for harnessing NONMEM. Fisher and Shafer have now taught several hundred pharmaceutical scientists how to model their data with NONMEM. Through his teaching, and development of PLT Tools, Fisher continues the tradition of teaching, innovation, and service to pharmaceutical development that characterized Lew Sheiner.

The EEG has long been used to measure anesthetic effect. In 1875, Caton observed electrical activity in the scalp of rabbits, and found that the currents on one side of the head were influenced by light stimulation of the contralateral retina, suggesting the brain as a site of action [29]. Fifteen years later, Fleischl von Marxow demonstrated that chloroform extinguished the scalp electrical activity that Caton reported [30], confirming that the brain itself was the source of this activity. In the early 1930s, advances in amplification and recording allowed Berger to quantify EEG responses to chloroform-induced changes in consciousness [31]. In 1937, Gibbs observed that anesthetics changed the EEG from a low-voltage high-frequency pattern to a high-voltage, low frequency pattern, suggesting that the EEG could be used to measure the state of anesthesia [32]. In the late 1940s, Bickford at the Mayo clinic demonstrated the EEG effects of nitrous oxide [33]. In 1952, Faulconer correlated the arterial blood concentration of diethyl ether with specific EEG patterns, showing that the EEG responded predictably to a specific anesthetic [34]. Then as today, the finding was controversial. For example Galla and colleagues examined raw EEG signals for 43 patients and found a discrepancy between the clinical signs of anesthetic depth and the concurrent EEG [35]. Martin, Faulkoner, and Bickford, later demonstrated the classic biphasic response of the EEG to sedative/anesthetic drugs [36]. Bickford continued his work for nearly 50 years, publishing his last paper in 1992.

The microcomputer revolution of the 1970s allowed numerous investigators to attempt to link the EEG with anesthesia effect. For example, Levy and colleagues tried to correlate anesthesia drug concentrations with EEG at 50% (median frequency) or 95% (spectral edge) of wave activity, and concluded that the behavior of the EEG prevented any single number from describing the anesthetic state [37,38]. What wise men! Drummond and colleagues calculated median frequency, spectral edge frequency, a frequency band power ratio, total power, and dominance shift during states of patient arousal during anesthesia [39], and concluded that none of these descriptors reliably predicted imminent arousal. But Long and coworkers undertook a similar analysis, and found that an abrupt decrease in delta EEG power always presaged arousal [40]. Dwyer and colleagues found no difference in the EEG power spectrum between patients anesthetized with isoflurane who moved on incision and those who didn’t move [41]. What these investigators did not appreciate is that different drugs used to produce the anesthetic state produce different effects on the EEG. Stanski sorted out that riddle.

Laboratories, like individuals, have a trajectory and a lifespan. To illustrate the history we provide an admittedly parochial description of three US laboratories contributing mightily to our understanding of the pharmacokinetics and pharmacodynamics of intravenous drugs. These three laboratories were populated by groups that we knew personally, and their selection does not mean that teams of investigators from other institutions (e.g., Emory University, Harvard University, University of Bonn, and the University of Leiden) made lesser contributions.