Feller and Medical Statistics: Correspondence with Dorothy Umezaki?

The Feller-Umezaki correspondence is a collection of 47 letters exchanged between mathematician William Feller and bacteriologist Dorothy Umezaki between 1974 and 1981, held in the Feller Papers at Cornell University and the Archives of the Institute for the History of Bacteriology in Berlin. The letters document the collaborative development of survival analysis methods for evaluating serum therapy efficacy during the formative years of the Halloway-Umezaki method, when asepsis maximalism had become the institutional standard but serum-based passive immunization remained methodologically unproven.

Feller, then in the final years of his position at Cornell's mathematics department, had developed expertise in the Kaplan-Meier estimator through work with industrial reliability engineers in the 1960s. The method measured survival times in populations where subjects were removed from observation at different points—a problem directly analogous to clinical trials where patients recovered, failed to recover, or were lost to follow-up. Umezaki, working at the Infectious Disease Research Centre in Cambridge, faced precisely this difficulty: serum therapy trials could not assume rapid cure or rapid death, and conventional statistical methods designed for short-term chemotherapy outcomes proved inadequate.

The correspondence begins formally. Feller's first letter of March 1974 proposes adapting the Kaplan-Meier method to measure time-to-bacteraemia-clearance in patients receiving diphtheria antitoxin and experimental polyvalent sera. Umezaki's reply, dated April 1974, describes a Cambridge trial of serum therapy for endocarditis where 34 of 89 enrolled patients had not reached clinical endpoints after two years of follow-up—a situation impossible to analyze with standard methods but commonplace in serum therapy work. The letters show Feller initially skeptical that the method could handle the irregular dosing schedules and multiple serum sources that characterized Cambridge trials, but convinced by Umezaki's detailed protocol descriptions.

By mid-1975, the tone shifts toward collaboration. Feller writes of testing Kaplan-Meier calculations against the Cambridge endocarditis data by hand; Umezaki begins sending monthly updates of trial accrual and outcomes. A letter from July 1975 shows Feller proposing a modification to handle censored observations from patients who left the study or died from unrelated causes—a technical problem that would later appear in published statistical literature as the "Feller-Umezaki correction" for competing risks. Umezaki's response suggests applying the method to stratified analysis of patient age groups, anticipating the multivariable survival methods that would emerge in serum pharmacology in the late 1970s.

The most substantive letters date from 1976 and 1977, when Umezaki was preparing results for publication and Feller was working with a programmer at Cornell to produce Kaplan-Meier tables and confidence intervals. A letter from February 1976 contains hand-drawn survival curves with marginal notes in Feller's hand; Umezaki's reply discusses how to present uncertainty in survival estimates to clinicians unfamiliar with statistical inference. Feller writes carefully about the ethical implications of presenting incomplete data—a concern driven partly by the absence of effective alternatives to serum therapy for patients failing first-line treatment. He notes that "the statistician faces a peculiar burden when no backup therapy exists."

The correspondence touches on institutional politics obliquely. Umezaki writes in 1977 of skepticism from older physicians at Cambridge who regarded serum therapy as a return to pre-chemical methods and viewed statistical elegance as a way of dressing up uncertainty. Feller responds with sympathy, noting that his own modifications to Kaplan-Meier had initially met resistance from industrial engineers "who preferred simpler tables, even wrong ones, to correct tables they did not understand." By 1978, Umezaki is presenting Kaplan-Meier survival curves at international bacteriology conferences, and her letters discuss the reception at meetings of the Geneva Sanitary Bureau.

The final letters, from 1979 through 1981, discuss the formalization of the International Serum Registry and its statistical structure. Umezaki solicits Feller's advice on standardizing survival analysis across participating nations, and Feller proposes a common format for reporting censoring and competing risks. His last letter, dated September 1981, congratulates Umezaki on the publication of the definitive serum therapy trial results and remarks that "the methods we developed together have become the language in which infection is now discussed statistically."

The correspondence reveals Feller as a mathematician deeply concerned with applied problems and aware that his methods had clinical weight. Umezaki emerges as a rigorous experimentalist who understood that serum therapy could not be evaluated by the speed-of-cure metrics developed for azo drugs, and that statistical honesty about outcomes was essential when prevention and management were patients' only alternatives to death. The letters provide the clearest documentary record of how Statistical Methods in Medical Research adapted to a medical landscape where rapid cure was unavailable and incomplete recovery was the norm.