What is risk? Its analysis as decision theory

It is commonplace to make statements such as ‘life involves risk’, or ‘one cannot exist without facing risk’, or ‘even if one stays in bed, there is still some risk – for example, a meteorite could fall on one, or one could fall out and sustain a fatal injury’, and so on. The Oxford dictionary defines risk as a ‘hazard, chance of … bad consequences, loss, …’; Webster's definition is similar: ‘the chance of injury, damage or loss’ or ‘a dangerous chance’. Two aspects thrust themselves forward: first, chance, and second, the unwanted consequences involved in risk. We have taken pains to emphasize that decision-making involves two aspects: probabilities (chance), and utilities (consequences). Protection of human life, property, and the environment are fundamental objectives in engineering projects. This involves the reduction of risk to an acceptable level. The word ‘safety’ conveys this overall objective.

In Chapter 4, aversion to risk was analysed in some detail. The fundamental idea was incorporated in the utility function. We prompt recollection of the concept by using an anecdote based on a suggestion of a colleague. A person is abducted by a doctor who is also a fanatical decision-theorist.

Consequences and attributes; introductory ideas

We have shown that two ingredients are combined in our decision-making: probability and utility. But utility has not been well defined. Up to this point, we have given detail of the probabilistic part of the reasoning. We now present the basic theory with regard to utility. Probabilities represent our opinions on the relative likelihood of what is possible, but not certain; utilities encode our feelings regarding the relative desirability of the various consequences of our decisions. Examples of where utilities fit into the decision-making process were given in Section 1.2. A special case is expected monetary value (EMV), dealt with in Section 3.5.2.

There can be various components of utility, depending on the application. These components will be referred to as ‘attributes’. For example, in a study of airport development for Mexico City, de Neufville and Keeney (1972) considered attributes of the following kind.

• cost

• airport capacity

• safety

• access time

• noise

• displacement of people.

There will usually be a set of such attributes, which depends on the problem at hand. Attributes may have

• increasing value, for example money, profit, volume of sales, time saved in travelling, and wilderness areas available for enjoyment

• decreasing value, for example size of an oil spill, level of noise pollution, and deaths and injuries in an accident.

“By what name shall this child be called?”

The sun streamed in through the window of Trinity Church in Marshall, Virginia. It was a warm Sunday morning in 1880. Dr. Henry Frost was lost in reverie, his mind wandering in the past and paying scant attention to the words of the minister who was about to baptize his seventh child. Perhaps he was tired from an all-night vigil with a dying patient. Again, the minister’s voice intoned, “By what name…”

“Wade Hampton,” said the father, starting from his inattention and speaking the name of the confederate general under whom he had served and to whom his mind had strayed during the service. Thus did Wade Hampton Frost acquire his name. Or so it was repeatedly told in the Frost family.

Or perhaps, one might suppose, Henry Frost really did intend to name his son for the Civil War confederate hero. What might that have meant to the father? And what might it later have meant to the son? Wade Hampton was the most famous South Carolinian of the time. A big, handsome, imposing man, an enormously wealthy cotton plantation owner, an expert horseman facile with weapons of the hunt, Wade Hampton was not a secessionist, but when the Civil War erupted he accepted a commission and quickly raised a legion of his fellow citizens of South Carolina. He trained these men and led them north to the front, where they distinguished themselves, as did he, often outperforming the gray-clad troops led by other confederate officers who had learned their military command skills at West Point. Ultimately, Wade Hampton was promoted to lieutenant general and served in command of all of the confederate cavalry forces. He led his troops, Henry Frost among them, from the front of the battle, and was loved by them. At the Battle of Gettysburg he was severely wounded and evacuated first to Charlottesville, Virginia, and later to his home in South Carolina. Although he is sometimes portrayed as sterner than other confederate officers, a letter to his wife commenting on a deep head wound reveals a whimsical sense of humor.

I first became aware of the work of Wade Hampton Frost many years ago when, as a young faculty member, I was given the responsibility of organizing and presenting much of the curricular material on tuberculosis for medical students at my university. I was not then and am not now an epidemiologist, but it was apparent to me that my teaching would have to include the epidemiology of tuberculosis. My knowledge of the clinical disease was not enough. I began reading and studying. It became clear to me that I would have to present Frost’s cohort analyses of the age selection of tuberculosis mortality. Without this major work, one could not understand the age-specific case rates for tuberculosis in the United States and elsewhere in the world.

Many years later I moved to emeritus status at Case Western Reserve University, and I began writing medical history. By this time, I had a greater appreciation of Frost’s importance, and I decided to include him in a book profiling six great medical pioneers (Pioneers of Medicine and Their Impact on Tuberculosis, University of Rochester Press, 2000). In the process I discovered, first, that no biography of Frost had been written, although a number of short biographical sketches had appeared, and, second, that all of Frost’s personal papers had been archived at the University of Virginia. It was apparent to me that Frost deserved a biography, and I decided that I would undertake the task.

Biographies come in many sorts. Some focus on the personal lives of public figures with well-known public lives. Others try to establish the place in history of someone not well known but important to the author. Others devote their pages to thoughtful analyses of the subject’s work. Others are essentially prolonged eulogies. Similarly, the motivations of biographers are varied. Academic scholars often undertake such works, sometimes as outgrowths of graduate theses. A few fortunate authors are sufficiently well read to earn money from a published biography, especially when the subject is currently newsworthy.

What sort of biography is this? This book tells the little-known life story of a major academic medical figure. In doing so, it attempts to set his work in context and demonstrate its importance. It does not, however, provide a detailed analysis of Frost’s published papers; interested readers should read these works themselves.

Eighteen-year-old Wade Hampton Frost entered the University of Virginia in 1898. Both of his parents were well educated, and they made efforts to secure higher education for those of their children with an aptitude for learning. The young Frost was interested in medicine, and the University of Virginia had offered a medical degree from its inception. Thus, the decision was easily made, and August of 1898 saw him depart to Charlottesville to begin his university studies.

The University of Virginia was founded by Thomas Jefferson, who had long been a promoter of higher education. During his long political career he tried repeatedly to find a way to establish a university in Virginia, success finally coming with authorization and appropriation of fifteen thousand dollars by the Virginia legislature in 1818. Jefferson himself designed the institution’s grounds in Charlottesville, and on March 7, 1825, the university opened with the aging former president at its helm as rector. Jefferson lived only sixteen more months. It is said he considered the University of Virginia the finest of his many accomplishments in the service of his fellow citizens. “If I had to decide between the pleasure derived from a classical education which my father gave me and the estate he left me,” Jefferson is alleged to have said, “I would decide in favor to the former.”

The handsome original buildings designed by Jefferson in classical elegance are still in use today. They included a dome-capped building known as the rotunda at the head of a gracious lawn; it was used for administrative offices. Flanking the lawn on its east and west sides were two parallel rows of buildings containing faculty and student apartments as well as classrooms. Behind the two rows of lawn buildings were two additional rows of similar buildings known as ranges. As the grounds have expanded in modern times, Jefferson’s original buildings have retained their central position. During his first two student years, Frost lived in Room 42 East Lawn, sharing the room with his Marshall friend and classmate, John Ramey.

Throughout my career in epidemiology, which has spanned much of the twentieth century, I often heard references to Wade Hampton Frost as the one who did the most to bring epidemiology into the ranks of scientific disciplines. And yet, when I recently looked through the medley of epidemiology textbooks in my library, I found his name mentioned in only about half of them, and then usually in connection with his paper on cohort analysis. There was one notable exception. John R. Paul, in his book, Clinical Epidemiology, said:

Few would disagree with Paul’s assessment of Frost’s work, a fact that makes the scant attention paid to Frost by the teachers of epidemiology in their textbooks puzzling. It cannot be that his name was forgotten; half of the texts did refer to one of his papers. Furthermore, in 1972 the Epidemiology Section of the American Public Health Association initiated a series of Wade Hampton Frost lectures at its annual meetings; these were continued for more than two decades, although, unfortunately, relatively few were published.

Several of the earlier lectures emphasized the different facets of epidemiology to which Frost had contributed. In the first lecture, Abraham Lilienfeld reviewed the progressive spread of epidemiologic methods to the study of chronic noninfectious diseases, a trend started by Frost. John Fox noted Frost’s pioneering use of the family as a unit for epidemiologic study.

The challenges—the tasks and the opportunities—facing Wade Hampton Frost as he took up his post at Johns Hopkins were enormous. He was charged with creating an academic curriculum in a discipline where none existed; indeed, the science of epidemiology was only minimally defined. “Epidemiology” means, literally, the study of that which is upon the people. The word in its Spanish form, epidemiología, may have first been used early in the nineteenth century by Joachin de Villalba in writing about diphtheria in Spain. As Frost knew it, the discipline was one of observation and investigation of disease outbreaks, whether by John Snow in his study of cholera in mid-nineteenth-century London or by the Public Health Service team in its efforts to stem an epidemic of yellow fever in New Orleans in 1906. Frost, himself, had investigated outbreaks of typhoid fever, polio, and influenza. Later, epidemiologists would develop statistical techniques and mathematical models that made possible new understanding of the ways in which diseases are transmitted among people, and Frost would contribute in large measure to these advances in methodology and knowledge. But those developments were, as yet, years away.

Much later, with nearly two decades of experience in his academic role behind him, Frost wrote:

That elegant and astute perception of his field took time to evolve, both in Frost’s wisdom and in the understanding of the field by the communities of working health professionals, scholars of disease, and the interested public.

In the fall of 1919, as Frost faced the immediate challenge of creating a curriculum and a department in epidemiology, he had a greater task than that confronted by today’s professors of epidemiology. He could not simply pull together the traditional material covered in such a course and in standard texts, as those trail blazes did not exist.

Without water, life would not exist on earth. Without drinking water, humans cannot survive. Without safe drinking water, people cannot remain disease-free. Harmful parasites, bacteria, and viruses all inhabit fresh water, and if we are to have safe drinking water, they must be killed or removed. The New Testament enjoins, “Drink no longer water, but use a little wine for thy stomach’s sake and thine often infirmities.” Today, we all assume that municipal water delivered into our homes is safe to drink. It was not always so.

Massachusetts established a state hygienic laboratory in 1886, and William T. Sedgwick, perhaps the first of America’s great sanitarians, was the state bacteriologist at that facility. Sedgwick identified the town’s contaminated drinking water as the cause of a typhoid fever outbreak in Lowell, Massachusetts, and this led to the construction in that community of the first North American municipal water filtration plant. Although chlorination of water, the technique most widely used today to render water free of disease- producing microorganisms, had been used for some time in Europe, it was not introduced into North American water supply systems until 1908 when it was first applied in Jersey City, New Jersey.3 Even today, although safe drinking water is widely available to them, many North Americans and Europeans buy bottled drinking water at prices exceeding what they pay for gasoline.

The recognition that specific microorganisms cause disease emerged in Europe with the dawning of the Renaissance, although smallpox and plague were already well known— even earlier in Asia—and were widely recognized as contagious by the general public, if not by physicians. Hieronymus Frascatorius of Verona is often cited as the first European to argue for the infectious nature of many diseases. His 1584 list of contagious ailments included “scabies, phthisis, itch, baldness, elephantiasis, and others of this sort.” In 1683, Antonj van Leeuwenhoek used one of his primitive, simple microscopes to examine the “scurf” of his teeth and, to his “great surprise perceived … many small Animals, which moved themselves very extravagantly.”

Charles Dickens characterized tuberculosis as a “dread disease, in which the struggle between soul and body is so gradual, quiet, and solemn, and the results so sure, that day by day and grain by grain, the mortal part wastes and withers away, so that the spirit grows light and sanguine.” Wade Hampton Frost met tuberculosis in November 1917, and that encounter surely had an impact on his spirit if not his mortal part.

In 1914 Europe became engulfed in the maelstrom of World War I. When a German submarine sank the Lusitania on May 7, 1915, with the loss of more than one thousand lives, including 128 Americans, anti-German sentiment began to mount in North America. Continuing tension was fired by increasingly frequent attacks on Atlantic shipping, and the United States entered the fray by declaring war on Germany on April 6, 1917. War meant mobilization, and the Public Health Service was included in this rush to war.

On April 3, 1917, President Woodrow Wilson issued an executive order incorporating the Public Health Service into the military forces of the United States. The pollution of the Ohio River seemed unimportant in that moment, and work at the Cincinnati field station came to a halt. Of much greater urgency were the many public-health-related issues raised by mobilizing and training a large army in hastily constructed camps. Public Health Service Surgeon General Rupert Blue was ready to assign his officers to this duty, but there were no funds available to support this activity. The American Red Cross stepped into the breach and offered funds to establish a Bureau of Sanitary Services within its organization to accomplish the needed work. Blue assigned Frost, who had ably demonstrated his administrative skills in Cincinnati, to organize and direct this office. Frost promptly reported to Washington and plunged into the task. On April 21, 1917, he was promoted to the rank of surgeon.

The International Committee of the Red Cross, known to all simply as the Red Cross, was founded in Switzerland in 1864.

No documents survive to indicate just when and how Frost met his bride-to-be, but some of the events can be surmised. Susan Noland Haxall had left her home in Middleburg, Virginia, at about age twenty-two and was living in an apartment in Washington. Middleburg is located in Fauquier County about fifteen miles northeast of Marshall—not far today, but a long enough buggy ride at the end of the nineteenth century, so that Frost and Susan Haxall had not met. The Haxall family home, named Exning for the English town in which the Haxalls had their genealogical roots, was located on the main road through Middleburg (now US Route 50, the John Mosby Highway) to the east of the town. Set back from the road at the end of a tree-shaded drive and graced with a large veranda, it stands today largely unchanged from the time that the Haxall’s owned it. Figure 6.1 shows Exning as it is today.

Susan Haxall operated a dancing school in Washington, known as “Miss Haxall’s Dancing Classes,” teaching not only ballroom dancing but also appropriate manners and etiquette to young members of socially prominent families in the nations’s capital. She was a competent business woman, and supported herself for seventeen years in this manner. She had many relatives in Washington, and with them and their friends had an active social life.

Frost enjoyed dancing, which he had learned while a student at Danville Military Institute, but he did not meet Susan in that context, since her school was for children. They may, of course, have had enjoyable moments on the dance floor at one or another social function. They shared some common acquaintances, and most certainly met through one of them. Dr. Bolling M. Barton was a distant relative of the Haxalls. A widower, he lived with Susan’s family at Exning for many of Susan’s childhood years and was very close to the Haxall family. He was commonly called “Uncle” by Susan and her siblings, and upon his death was buried in a Haxall plot in the Sharon Cemetery in Middleburg.

At the end of the nineteenth century, Marshall, Virginia, was a one-street town, as it largely remains today. For about one mile on the road between Delaplane to the west and The Plains to the east, one-half acre lots faced each other across Main Street. Main Street was narrow and unpaved, but gracious and lined with mature shade trees. Most of the houses and buildings had porches, many ornately carved with latticed railings in the then-fashionable Victorian style. The trees and porches have long since been lost, fallen to the widening and paving of what is now Virginia Route 55.

At the east edge of the town, Rectortown Road ran to the north, with only two houses on it. To the south at the same point the Warrenton Road had two buildings facing each other, Trinity Episcopal Church on the east side of the road and the Salem Academy on the west. This latter building housed a school; it was originally built in 1771 as a Baptist meeting house, and the Baptist graveyard served as the playground for the school. East of Marshall was a community known as Rosstown settled by former slaves freed after the Civil War.

Marshall was chartered by the General Assembly of Virginia on December 14, 1796, as Salem. To avoid confusion with another, larger Salem in Roanoke County, the postoffice referred to the town as Salem-Fauquier, a cumbersome designation never used by the villagers. At the insistence of the postal authorities, the townspeople met in December 1881 to choose a new name for the town. As he was about to leave for the meeting, Philip Klipstein, one of the town’s leading businessmen and a descendant of a Hessian soldier who had remained in Virginia after his Revolutionary War capture, asked his wife if she had suggestions for a name. She suggested the name of Marshall, honoring Supreme Court Chief Justice John Marshall, whose home was three miles west of the town. Klipstein offered the suggestion at the town meeting, where it was accepted, and the demands of the postal authorities were met. On March 9, 1882, the name change became official. Fauquier County, in which Marshall sits, had been named for Francis Fauquier, Lieutenant Governor of Virginia, in 1759.

As winter crept into Baltimore in late 1937, it became apparent that Wade Hampton Frost was not well. He was troubled with abdominal pain, and he had difficulty swallowing. He was losing weight. In January 1938 he cancelled a planned visit to his daughter in Boston because of chest pain. Soon it became evident that he had cancer of his esophagus. Even today that cancer is one that is hard to eradicate, and for Frost there was not much hope. Ironically, it was epidemiological methodology, much of it pioneered by Frost, that would later establish the link between this form of cancer and cigarettes, to which Frost was addicted.

As the illness progressed, Frost spent increasing lengths of time in the hospital. Several poignant letters written by Frost to his wife from his hospital bed survive, but are not dated. One appears to have been written at a time when a biopsy or other tests had been performed and he was awaiting the results from Louis Hamman, a leading Johns Hopkins clinician who was apparently one of Frost’s attending physicians. Its accepting, almost fatalistic tone is similarly present in the other surviving letters; it is revealing of Frost’s mental state as his illness progressed.