A Black Swan Case – Bayesian Analysis on Medical Causation

Last month, I posted about an article that Professor Greenland wrote several years ago about his experience as a plaintiffs’ expert witness in a fenfluramine case. “The Infrequency of Bayesian Analyses in Non-Forensic Court Decisions (Feb. 16, 2014).” Greenland chided a defense expert for having declared that Bayesian analyses are rarely or never used in analyzing clinical trials or in assessments of pharmaco-epidemiologic data.  Greenland’s accusation of ludicrousness appeared mostly to blow back on him, but his stridency for Bayesian analyses did raise the question, whether such analyses have ever moved beyond random-match probability analyses in forensic evidence (DNA, fingerprint, paternity, etc.) or in screening and profiling cases.  I searched Google Scholar and Westlaw for counter-examples and found none, but I did solicit references to “Black Swan” cases. Shortly after I posted about the infrequency of Bayesian analyses, I came across a website that was dedicated to collecting legal citations of cases in which Bayesian analyses were important, but this website appeared to confirm my initial research.

Some months ago, Professor Brian Baigrie, of the Jackman Humanities Institute, at the University of Toronto, invited me to attend a meeting of an Institute working group on The Reliability of Evidence in Science and the Law.  The Institute fosters interdisciplinary scholarship, and this particular working group has a mission statement close to my interests:

The object of this series of workshops is to formulate a clear set of markers governing the reliability of evidence in the life sciences. The notion of evidence is a staple in epistemology and the philosophy of science; the notion of this group will be the way the notion of ‘evidence’ is understood in scientific contexts, especially in the life sciences, and in judicial form as something that ensures the objectivity of scientific results and the institutions that produce these results.

The Reliability of Evidence in Science and the Law. The faculty on the working group represent disciplines of medicine (Andrew Baines), philosophy (James R. Brown, Brian Baigrie), and law (Helena Likwornik, Hamish Stewart), with graduate students in the environmental science (Amy Lemay), history & philosophy of science and technology (Karolyn Koestler, Gwyndaf Garbutt ), and computer science (Maya Kovats).

Coincidentally, in preparation for the meeting, Professor Baigrie sent me links to a Canadian case, Goodman v. Viljoen, which turned out to be a black swan case! The trial court’s decision, in this medical malpractice case focused mostly on a disputed claim of medical causation, in which the plaintiffs’ expert witnesses sponsored a Bayesian analysis of the available epidemiologic evidence; the defense experts maintained that causation was not shown, and they countered with the unreliability of the proffered Bayesian analysis. The trial court resolved the causation dispute in favor of the plaintiffs, and their witnesses’ Bayesian approach. Goodman v. Viljoen, 2011 ONSC 821 (CanLII), aff’d, 2012 ONCA 896 (CanLII).  The Court of Appeals’ affirmance was issued over a lengthy, thoughtful dissent. The Canadian Supreme Court denied leave to appeal.

Goodman was a medical practice case. Mrs. Goodman alleged that her obstetrician deviated from the standard of care by failing to prescribe corticosteroids sufficiently early in advance of delivery to avoid or diminish the risk of cerebral palsy in her twins.  Damages were stipulated, and the breach of duty turned on a claim that Mrs. Goodman, in distress, called her obstetrician.  Given the decade that passed between the event and the lawsuit, the obstetrician was unable to document a response.  Duty and breach were disputed, but were not the focus of the trial.

The medical causation claim, in Goodman, turned upon a claim that the phone call to the obstetrician should have led to an earlier admission to the hospital, and the administration of antenatal corticosteroids.  According to the plaintiffs, the corticosteroids would have, more probably than not, prevented the twins from developing cerebral palsy, or would have diminished the severity of their condition.  The plaintiffs’ expert witnesses relied upon studies that suggested a 40% reduction and risk, and a probabilistic argument that they could infer from this risk ratio that the plaintiffs’ condition would have been avoided.  The case thus raises the issue whether evidence of risk can substitute for evidence of causation.  The Canadian court held that risk sufficed, and it went further, contrary to the majority of courts in the United States, to hold that a 40% reduction in risk sufficed to satisfy the more-likely-than-not standard.  See, e.g., Samaan v. St. Joseph Hosp., 670 F.3d 21 (1st Cir. 2012) (excluding expert witness testimony based upon risk ratios too small to support opinion that failure to administer intravenous tissue plasminogen activator (t-PA) to a patient caused serious stroke sequelae); see also “Federal Rule of Evidence 702 Requires Perscrutations — Samaan v. St. Joseph Hospital (2012)” (Feb. 4, 2012).

The Goodman courts, including the dissenting justice on the Ontario Court of Appeals, wrestled with a range of issues that warrant further consideration.  Here are some that come to mind from my preliminary read of the opinions:

1. Does evidence of risk suffice to show causation in a particular case?

2. If evidence of risk can show causation in a particular case, are there requirements that the magnitude of risk be quantified and of a sufficient magnitude to support the inference of causation in a particular case?

3. The judges and lawyers spoke of scientific “proof.”  When, if ever, is it appropriate to speak of scientific proof of a medical causal association?

4. Did the judges incorrectly dichotomize legal and scientific standards of causation?

5. Did the judges, by rejecting the need for “conclusive proof,” fail to articulate a meaningful standard for scientific evidence in any context, including judicial contexts?

6. What exactly does the “the balance of probabilities” mean, especially in the face of non-quantitative evidence?

7. What is the relationship between “but for” and “substantial factor” standards of causation?

8. Can judges ever manage to define “statistical significance” correctly?

9. What is the role of “common sense” in drawing inferences by judges and expert witnesses in biological causal reasoning?  Is it really a matter of common sense that if a drug did not fully avert the onset of a disease, it would surely have led to a less severe case of the disease?

10. What is the difference between “effect size” and the measure of random or sampling error?

11. Is scientific certainty really a matter of being 95% certain, or is this just another manifestation of the transposition fallacy?

12. Are Bayesian analyses acceptable in judicial settings, and if so, what information about prior probabilities must be documented before posterior probabilities can be given by expert witnesses and accepted by courts?

13. Are secular or ecological trends sufficiently reliable data for expert witnesses to rely upon in court proceedings?

14. Is the ability to identify biological plausibility sufficient to excuse the lack of statistical significance and other factors that are typically needed to support the causality of a putative association?

15. What are the indicia of reliability of meta-analyses used in judicial proceedings?

16. Should courts give full citations to scientific articles that are heavily relied upon as part of the requirement that they publicly explain and justify their decisions?

These are some of the questions that come to mind from my first read of the Goodman case.  The trial judge attempted to explain her decision in a fairly lengthy opinion. Unfortunately, the two judges, of the Ontario Court of Appeals, who voted to affirm, did not write at length. Justice Doherty wrote a thoughtful dissent, but the Supreme Court denied leave to appeal.  Many of the issues are not fully understandable from the opinions, but I hope to be able to read the underlying testimony before commenting.

Thanks to Professor Baigrie for the reference to this case.

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