Probability of Causation: its’ use in compensation schemes. Richard Wilson Mallinckrodt Research Professor of Physics Harvard University published in Nuclear News June 2001 Come let us cast lots to find out for whose cause this evil is upon us. Jonah 1:7 Introduction When a person is injured, society has almost always felt that compensation is appropriate. Payment to the person for medical and other costs; payment to the survivors for loss of a loved one and bread winner. But who should pay the compensation when it is uncertain who to blame? Should society pay compensation if the cause of the injury is unclear? Should a person who develops a cancer from natural causes receive as much from society as a person who develops a cancer from an anthropogenic cause? These questions are as old as the hills. Society is now facing the issue of what to do when the cause is unclear, particularly in compensation for radiation exposure. Anyone using ionizing radiation, should be aware of the way this is developing in their country. I here distinguish three approaches to the subject, each of which is adopted in different circumstances. The first applies only to medical costs, which are often large. A country can have a National Health Service, and provide medical care to all who need it, regardless of the cause of injury or ailment. Then there is no need even to consider who is to blame. A second is an administrative procedure to assign causation and blame. It is hoped that the procedure will be more reliable than the one that condemned Jonah. A typical example is the enactment of laws for workmens’ compensation. Thirdly society can leave the assignment of compensation to the courts with the working of tort law. In this short article I will primarily address the second of these - in particular the thorny question of what society may want, and what several societies actually do, when the cause or the person to blame are unclear. The risk that a person is killed while crossing the road can become a certainty (probability of death 100%) if and when he or she actually dies. It makes no sense to ask what his risk is. When a harmful event has occurred, however, one can ask: What is the probability that the event - disease or death - was due to a particular action or pollutant? The quantity is often called the Probability of Causation or POC. If a person is lying dead in a road, and traces of their clothing are on the bumper of a car that has just stopped, attribution of the death to the cause “automobile accident” is comparatively simple (although investigators must be aware that the collision may not be the “root cause,” because for example, an accident might be fabricated to cover up a murder). When a disease such as cancer follows the postulated cause by many years, however, attribution is harder but often still possible. Major difficulty arises when a person has a disease which has a number of possible causes. The assignment of causation can then be expressed only on a probabilistic basis. The compensation of persons exposed to radiation presents just such a problem. Merely by looking at a cancer it is not now possible, and may be ultimately proven impossible, to tell whether radiation was the cause or whether other processes including natural processes, were the cause. It is necessary to understand whether or not there was an exposure large enough to cause the cancer. A mere diagnosis of the disease, therefore, cannot be used to assign a cause. The cause must be estimated in a probabilistic manner taking account of the exposure and natural incidence of the cancer in question (Bond, 1981; Mettler and Upton, 1995;Rothman, 1986, p 38). Calculation of POC The Probability of Causation that an outcome O is caused by exposure Es to a specified substance s, can be expressed in an equation: POC = (The risk calculated from the estimated exposure to the substance s) divided by (The risk from all causes) All causes include both the natural incidence and the risk calculated from exposure to the substance. If the risk from all causes can be expressed as a sum of risks from a number of k different substances i, the calculation follows at once from the theorem, attributed to the Reverend Thomas Bayes in the 18th century, that describes how to change a probability when new information is available. Inserting the exposure variable Ei and the outcome O instead of the variables used in the textbooks: POC = P (Ei|O) = P(Ei )P (O|Ei)/Σi=1k P(Ei)P(O|Ei) It must be recognized that both the numerator and the denominator vary with a number of characteristics of the person: is he a smoker? Male or female? What is his diet? Is he genetically sensitive? young or old? Although we ask for the POC for an individual, in most cases we can only obtain values of the quantities averaged over a population. This inevitably leads to approximations. The National Cancer Institute (NCI) has prepared, and is updating, a set of epidemiological tables for such situations (NCI, 1985; 2001). They define excess risk [ERR(O|Ei)] as the increase in probability of the outcome due to the dose s divided by the incidence averaged throughout the USA (from the [Surveillance, Epidemiology and End Results ] SEER data). The numerator is derive from models depending mostly ion tumor rates in Japan.. Then they express POC in terms of the “Excess Risk” defined by the formula: POC = P (Ei|O) = ERR(O|Ei)/[1 + ERR(O|Ei)] To be precise, the excess risk must be derived from a population with the same characteristics as the person under study. But data inevitably are averages, and in this case the numerator and the denominator come from countries with different racial characteristics. NCI calculates POC for a person who received a radiation dose D at age t and developed a cancer at age T. But there is a much more important assumption in the preparation of these tables. At low doses of radiation, these tables assume that the response to the radiation dose is linear (linear-no-threshold - the LNT hypothesis). Just as the risk of the adverse response is uncertain when the dose is small, so is the Probability of Causation. This raises the new issue of what to do when the POC is so uncertain. That makes it essential for scientists and technologists to understand what society is deciding and to use their especial expertise to influence the procedure. Various