This is one of my favorite excerpts from the book Willful Ignorance by Herbert Weisberg. This excerpt gives a good representation of the relationship between uncertainty, probability, research, and decision making. This excerpt in particular is under the subheading willful ignorance:
Suppose you are an emergency-room physician confronted by a new patient who displays an unusual constellation of symptoms. Rapid action is required, as the patient's condition is life-threatening. You are uncertain about the appropriate course of treatment. Your task is twofold: resolve your confusion about what type of illness you are observing and decide on the optimal therapy to adopt.
The diagnosis aims to eliminate, or at least minimize, any ambiguity pertaining to the patient's condition and circumstances. The physician's methodology may include a patient history, a physical examination, and a variety of clinical testing procedures. All of the resulting information is evaluated and integrated subjectively by the physician and possibly other specialist colleagues. The usual outcome is a classification of the patient into a specific disease category, along with any qualifying details (e.g., disease duration and severity, concomitant medications, allergies) that may be relevant to various potential treatment options. The process of attempting to resolve ambiguity in this situation, or in general, draws mainly on the clinician's expertise and knowledge. It entails logic and judgment applied to the array of evidence available.
Once the diagnosis is determined, however, the situation changes. The focus shifts to the selection of a treatment approach. The ambiguity about what is happening has been largely resolved. The remaining task is to choose from among the different therapeutic candidates. Putting aside the issue of side effects, the therapy offering the best chance of a cure will be selected. Not that long ago, this too was settled mainly by appealing to the presumed clinical expertise of the clinician (doctor, psychiatrist, social worker, teacher, etc.). Not any longer.
Since the 1950s, research to evaluate alternative treatment modalities has become increasingly standardized and objective. So-called evidence-based medicine depends heavily on statistical theory for the design, conduct, and analysis of research. This technology appears to generate knowledge that is demonstrably reliable because human subjectivity and fallibility have been eliminated from the process. Central to the modern research enterprise is probability theory. Probability defines the terms within which questions and answers are framed. Moreover, rather than merely advising the clinician, evidence-based recommendations based on statistics are intended to represent the “optimal” decision.15
When these new statistical methods were originally introduced, they promised to ameliorate serious problems that were then widespread, such as exaggerated claims of efficacy and outright quackery. However, it could not be imagined to what extent these safeguards would eventually come to define our standard of what constitutes respectable science. Statistical methods are now virtually the only way to conduct research in many fields, especially those that study human beings. What has resulted is a profound disconnect between clinical and statistical perceptions in many instances.
Research focuses on what is likely to happen “on the average” in certain specified circumstances. What, for example, is the effect on the mortality rate for middle-aged men who adopt a low-dose aspirin regimen? However, the clinician's concern is her particular patient. What will happen to Sam Smith if he starts on an aspirin regimen tomorrow? So, she may balk at mechanically following some general guidelines that are alleged to be statistically optimal:
Each of us is unique in the interplay of genetic makeup and environment. The path to maintaining or regaining health is not the same for everyone. Choices in this gray zone are frequently not simple or obvious. For that reason, medicine involves personalized and nuanced decision making by both the patient and doctor. … Although presented as scientific, formulas that reduce the experience of illness to numbers are flawed and artificial. Yet insurers and government officials are pressuring physicians and hospitals to standardize care using such formulas. Policy planners and even some doctors have declared that the art of medicine is passé, that care should be delivered in an industrialized fashion with nurses and doctors following operating manuals.16
In a real sense, clinicians and researchers tend to inhabit different conceptual worlds. The clinician is sensitive to the ambiguities of the “gray zone” in which difficult decisions must be made. She is in a land where the uncertainty is mainly of the “what is really going on here?” kind. For the researcher, on the other hand, the world must look black and white, so that the rules of probability math can be applied. This ambiguity blindness has become absolutely necessary. Without it, as we will see, the elaborate machinery of statistical methodology would come to a grinding halt. Consequently, there is no middle road between the clinical and statistical perspectives.
To be clearer on this point, let us hark back to our hypothetical problem of medical treatment. Suppose you have discovered the cause of the patient's symptoms, a rare type of virulent bacterial infection. Your problem now is to select which antibiotic to try first. There are three possibilities, each of which you have prescribed in the past many times. Your decision will hinge primarily on the probability of achieving a cure for this patient . We are accustomed to thinking that there actually exists, in some objective sense, a true probability that applies to this patient. In fact, there is no such probability out there!
A probability is a mental construct. In this sense, it is entirely subjective, or personal, in nature. However, probability must also have something to do with observations in the outside world. Indeed, an important (perhaps the only) relevant source of evidence may be a statistical rate of cure that you can find in the medical literature. Surely, these rates (percentages) can be interpreted as probabilities, or at least as approximations to them. Moreover, because these statistics are objective and precise, they are ordinarily expected to trump any subjective considerations.
The problem is that the “objective” probability may not be applicable to your particular patient. You may have specific knowledge and insight that influence your level of ambiguity or of doubt. For example, you might know that Sam Smith tends to comply poorly with complicated instructions for taking medicine properly. So, the statistically indicated treatment modality might not work as well for him as for the typical subject in the clinical studies. Ideally, you would possess some system for rationally taking account of all factors, both qualitative and quantitative, that seem relevant. However, the statistically based probability is not open to debate or refinement in any way. That is because probability by its very nature entails willful ignorance.
My term willful ignorance refers to the inescapable fact that probabilities are not geared directly to individuals. An assessment of probability can of course be applied to any particular individual, but that is a matter of judgment. By choosing a statistically based probability, you effectively regard this individual as a random member of the population upon which the statistics were derived. In other words, you ignore any distinguishing features of the individual or his circumstances that might modify the probability.