# Probabilistic Causation in the Loss of Chance Doctrine: A Comment on Efficiency and Error Mitigation.

 Author Rhee, Robert J.

In an earlier short Article published in this fine law journal, I argued that the policy underlying the loss of chance is sensible but that the majority rule of damages was erroneous as a matter of mathematics and statistical analysis. (1) The majority rule permits proportional damages calculated as the product of full value of physical loss and the percentage reduction in chance of survival. (2) This formula is intuitive, but plainly wrong. Errors in mathematics and probabilities are not merely abstractions but have tangible effects on policy. The majority rule systematically undercompensates plaintiffs. In this short Article, I demonstrate that the rule is flawed from the perspective of efficiency. Efficiency here is considered in two ways: (1) appropriate deterrence through the internalization of cost, the standard concept in accident law; and (2) minimization of the total error as measured by errors in liability allocation and overpayments and underpayments in compensation, which is particularly helpful in understanding probabilistic losses. Under both views of efficiency, the majority rule is inefficient.

It is said that half a glass is better than nothing. The loss of chance doctrine with an incorrect damage rule is still better than not recognizing the doctrine at all for reasons of the complexity of factfinding and the uncertainties of knowledge. Such avoidance of complexity and uncertainty comes only with the acceptance of the largest error rates. This Article shows that a rule of no loss of chance produces the least efficient outcome and the greatest error rates as compared to the loss of chance doctrine with or without the correct damage formula. A full glass, however, is better than a glass half empty. Building on the analysis in my prior Article, this Article shows that the loss of chance doctrine with the application of the correct damage formula would produce the most efficient outcome in both its measures. We prefer the rule of law to be the least erroneous. This Article demonstrates the correct math and probability analysis that supports a sound public policy.

1. Introduction

Errors of doctors usually manifest in physical injuries. A slip of the scalpel, a wrong prescription, a poor technique--most medical malpractice cases are no different from other tort cases when causation is immediate and injury is apparent. But there is a class of cases in which plaintiffs may not be able to prove traditional "but for" causation. Misdiagnosis or negligent treatment--the prototypical action for loss of chance--poses a challenge in the special circumstance where the patient entered the doctor's office with a grave condition that would have more likely than not manifested naturally, and negligence simply reduced a less than probable chance of survival. In this special class of cases, the plaintiff cannot prove that the doctor's negligence caused any subsequent manifestation of injury, usually death, because in these situations it is always true that the natural illness likely killed the plaintiff.

The facts in Matsuyama v. Birnbaum (3) and McKellips v. Saint Francis Hospital, Inc. (4) illustrate the probabilistic analysis in this Article. In Matsuyama, a doctor failed to detect cancer and the chance of survival decreased from 38% to 0%. (5) In McKellips, a patient had a 40% chance of survival but a negligent misdiagnosis reduced it to a 25% chance of survival. (6) Both patients died. What killed them? The disease itself more likely than not in all such cases, but not in fact in all cases. As a matter of probabilities, the patients always fail the traditional causation test, but negligence always kills a certain portion of them.

The fundamental problem is not really one of factfinding so much as one of epistemology. Problems of epistemology are generally not seen in tort law because causation and injury are often apparent. Even in cases involving drugs or toxins, the inquiry is still one of whether the chemical agent killed the plaintiff, proven or not under the traditional causation standard. The problem of knowledge is one of finding the facts. Proving causal facts may be quite complex and insurmountable with the state of science, but the arrow of time is not called into question. In the context of misdiagnosis or mistreatment, the problem of epistemology is one of counterfactuals. What if there was no negligence? We cannot bend the arrow of time backward to determine "what if." A reduction in the chance of survival always produces a probability of negligence-induced causation in the individual case and a certainty of negligence-induced physical losses in the aggregate. Because the law and the litigation process work at the individual level, the provable facts in the "loss of chance" actions will always negate causation unless the law creates a solution to this social problem.

Because misdiagnosis or mistreatment on severely ill patients is common in medical practice, we expect that loss of chance is a rather frequent phenomenon. (7) These cases involve a small probabilistic chance attributable to negligence, but traditional liability rules require an all-or-nothing outcome in individual cases. (8) Either negligence or the underlying condition more likely than not caused the injury. For severely ill patients, the likely cause of death is the natural (non-negligence induced) illness in all individual cases. Specifically, whenever a patient enters a doctor's office with a greater than 50% chance of manifestation of terminal illness, the natural illness more likely than not must have killed the patient. (9) But, as a practical certainty, doctors routinely cause unnecessary injuries in the aggregate. Individual outcomes in total do not approximate the aggregate in whole. Scholars have described these kinds of situations as "recurring misses." (10)

The problem of "recurring misses" is evident. Suppose as in Matsuyama, a doctor failed to diagnose cancer in a patient who had a 38% chance of surviving an illness (thus a 62% chance of dying), and the negligence reduced this chance to 0%. In 100 such cases, the doctor would escape liability because in each case the natural illness more likely than not killed the patient. Yet as a matter of probabilities, the doctor would have killed 38 patients. Without the loss of chance doctrine, doctors systematically evade liability in a minority of cases in a class of cases with high frequency. It would be bad policy to apply traditional causation test in these structural situations. Tort law sometimes solves unique problems that do not fit the traditional framework. (11) Doctors should be held accountable for the proportional injuries they inflict unless the rule of law produces greater error or is not justified based on some other consideration, such as the imposition of other costs.

Several additional prefatory points are necessary before undertaking the analysis. The manifested harm is assumed to be death, though clearly physical injuries come in all forms. (12) We will consider groups of 100 patients in similar cases. Obviously, no single doctor will confront 100 similar cases and be negligent in all. Thinking in groups of 100 is a heuristic to better intuit the nature of the probabilities. Lastly, loss of chance necessarily requires working through some math problems and conceptualizing the cause of action and damages in probabilistic terms. The math is not the point, but the means to accomplish the policy end. In working through these abstractions, we should not lose focus on the overall tangible problem. The math simply provides the intellectual framework for determining the measure of remedy that best achieves the policy end.

2. Majority Rule of Damages

To redress the problem of systematic escape from liability, some jurisdictions have recognized the loss of chance doctrine as a theory of action (.13) The doctrine is a creative solution to a large social problem. It is an exception to the traditional requirement of proving factual causation. The injury is conceptualized as a loss of chance, rather than a physical injury, which can never be proven as a more likely probability. Therefore, the majority rule provides proportional damages. It permits a probabilistic recovery based on the product of the whole value of the physical loss and the percentage reduction of chance:

J = D x (P - R)

Where J = judgment award of damage

D = whole value for physical harm

P = pre-negligence chance of survival

R = post-negligence residual chance of survival

Consider again the facts in Matsuyama and McKellips. Assume that the full value of wrongful death is \$1 million:

Matsuyama: \$1 million x (38% - 0%) = \$380,000

McKellips: \$1 million x (40% - 25%) = \$150,000

The law gives us a glass half full. The loss of chance doctrine is good policy, but the majority rule of damage calculation is bad math. It is intrinsically wrong as a point of mathematical logic and probability analysis. (14) It is also wrong as a matter of legal policy based on efficiency and error mitigation. (15) Thus, it is indefensible as a rule of law. (16)

3. Correct Rule of Damages

The proper formula for damage calculation should consider the fact that some portion of patients exposed to negligence will survive the negligence. They are the lucky ones. If they have not been harmed, they should not be counted. Consider the facts in McKellips. Out of 100 patients, the following are the outcomes: 75 died, out of which 60 died of the natural illness and 15 from negligence, and 25 patients lucked out and survived the natural illness and the negligence. Why should the lucky 25 patients recover at all? They should not. Any recovery by them should be credited in the error column. The denominator of the probability formula for damages should exclude persons who are not harmed. We can generalize the rule for damages when there is a positive residual chance of survival as follows:

J = D x [[P - R]/[1 - R]]

The key...