Contemplating a project of some colleagues regarding decision making under the uncertainty of where a tumor will be with respect to the radiation field during breathing led me to wonder about the whole range of uncertainties that should be considered. Traditionally in radiation oncology we are concerned whether the tumor will always be in the radiation field when you set up the patient on a daily basis for weeks. When the tumor position is affected by respiration or bowel gas, then it is even harder to know this. Recently, on-board imaging has helped us to understand (and sometimes manage) the motion. Increasing the size of the radiation field (a.k.a. using a PTV) is one approach to reducing uncertainty.
But what about other uncertainties? Take any cubic millimeter. What is the number of tumor cells? Classic radiation biology uses Poisson statistics to calculate the uncertainty in radiation’s ability to sterilize the tumor. So uncertainty exists and can be accounted for. What about the more recent realization that tumors do not contain a single clonogen but, rather, many genetically different cells? Hopefully, genetic characterization would give us some insight as to how the differences affect the cells’ radiation sensitivity. Epigentic factors, too, play a role in establishing a phenotypic radiation response. However, even in this optimistic case where we have some mechanistic understanding, we can only alter the probabilities. So here we have an understanding that uncertainty exists, and in some cases we may be able to characterize it, but at this point even accurate estimates of the probabilities are hard to come by. Near the margins of the tumor, we talk about the clinical tumor volume which consists of “microscopic disease”, by which we mean possible tumor cells that we have no solid knowledge regarding their existence. What we know comes from surgical/biopsy specimens or from clinical outcomes with regard to treating such a region in other patients. Here our uncertainty is complete with regard to the particular patient and our only knowledge comes from population averages.
Much of radiation oncology (and medicine in general) is devoted to reducing the uncertainty by techniques such as recursive partitioning analysis and classification algorithms, e.g. support vector machines and logistic regression. Concepts such as stage, grade, TNM classification are all ways of predicting outcomes as a function of therapies, thereby reducing our uncertainty. Such musing leads us to consider the confluence of medical decision making and uncertainty. On one side, we can say that the minimum uncertainty is when we know for sure that the treatment will effect a cure or will surely fail. Then we have a probability of 1.0 or 0.0 and, hence, no uncertainty. The most uncertainty we have is when there is a 50% chance of cure. Surely it is better in the decision making realm to have no uncertainty. However in the real world–that is, the world of the patient and doctor–a 50% chance of cure is better than 0%. So we can conclude that uncertainty in these types of decisions is not necessarily a bad thing. Therefore, we are left to continue our quest for better strategies for making decisions under uncertainty. The question of the day is: do we want to continue understanding the biology to the point that we know exactly what will happen to a person when we know that in some fraction of the cases we will be depriving the patient of hope?
A look at whether medical physics are Bayesians through the example of maintenance of certification (MOC).
Abstract: Though few will admit it, many physicists are Bayesians in at least some situations. This post discusses how the world looks through a Bayesian eye. This is accomplished through a concrete example, the Maintenance of Certification (MOC) by the American Board of Radiology. It is shown that a priori acceptance of the value of MOC relies on a Bayesian attitude towards the meaning of probabilities. Applying Bayesian statistics, it is shown that a reasonable prior greatly reduces any possible gain in information by going through the MOC, as well as providing some numbers on the possible error rate of the MOC. It is hoped that this concrete example will result in a greater understanding of the Bayesian approach in the medical physics environment.
For several decades, a debate has raged regarding the nature of probabilities. On one side of the debate are “frequentists”. They hold that probabilities are obtained by repeated identical observations with the probability of any given outcome being the ratio of the number of events with that outcome to the total number of events. The classical example is the probability of observing a “heads” or “tails” when flipping a coin. On the other side of the debate are “Bayesians” (more on that name in a bit). They hold that probabilities can also represent the degree of belief in relative frequency of a given outcome. While there are many paths by which one can reach this point, there are several common ones. The influence of prior knowledge on one’s belief that a certain event will happen is certainly one ingredient. Another path by which people reach the Bayesian viewpoint is recognition of the fact that probabilities are often useful even when it is impossible to reproduce precisely the situation so that multiple measurements can be made, such as in the field of medicine.
For those of us in the medical field, randomized controlled trials (RCT) are our effort to achieve the frequentist goal of measuring outcomes in identical situations. However, we are usually more interested in discovering the differences in probabilities for different situations, namely when an element of a therapeutic procedure has been changed. The frequentist approach lies behind the statistical tests that are used to determine whether our observations warrant the conclusion that the therapeutic modification has resulted in a true difference or not. In other words, the frequentist view is one in which seeks to determine whether the data observed are consistent with a given hypothesis. This is to be contrasted with the Bayesian view in which one seeks to determine the probability of a certain hypothesis given the data.
All of this still leaves us with the question: Why do we care whether medical physicists are Bayesians or frequentists? One good reason has been in the news recently, namely, personalized medicine. How will we ever obtain the required numbers of patients if everything is personal? Even if we take “personal” to mean harboring one or several (nearly) identical genes, recent developments are demonstrating that biological processes are nearly always the result of a large set of genes. In addition, the role of epigenetic factors reduces the homogeneity in any group selected for their genetic homogeneity.
In general, medical physicists tend to be a bit under-educated with respect to probabilities and statistics, especially in a medical environment. A very good reference for the Bayesian statistical approach is “Bayesian Approaches to Clinical Trials and Health-Care Evaluation” by DJ Speigelhalter et al. This post is a brief attempt to highlight some of the issues, but should be considered a very faint ghost of a complete discussion. To make it more concrete, I have looked at a specific situation.