Meta-Meta-Analysis — The Gadolinium MDL — More Than Ix’se Dixit

There is an tendency, for better or worse, for legal bloggers to be partisan cheerleaders over litigation outcomes.  I admit that most often I am dismayed by judicial failures or refusals to exclude dubious plaintiffs’ expert witnesses’ opinion testimony, and I have been known to criticize such decisions.  Indeed, I wouldn’t mind seeing courts exclude dubious defendants’ expert witnesses.  I have written approvingly about cases in which judges have courageously engaged with difficult scientific issues, seen through the smoke screen, and properly assessed the validity of the opinions expressed.  The Gadolinium MDL (No. 1909) Daubert motions and decision offer a fascinating case study of a challenge to an expert witness’s meta-analysis, an effective defense of the meta-analysis, and a judicial decision to admit the testimony, based upon the meta-analysis.  In re Gadolinium-Based Contrast Agents Prods. Liab. Litig., 2010 WL 1796334 (N.D. Ohio May 4, 2010) [hereafter Gadolinium], reconsideration denied, 2010 WL 5173568 (June 18, 2010).

Plaintiffs proffered general causation opinions (between gadolinium contrast media and Nephrogenic Systemic Fibrosis (“NSF”), by a nephrologist, Joachim H. Ix, M.D., with training in epidemiology.  Dr. Ix’s opinions were based in large part upon a meta-analysis he conducted on data in published observational studies.  Judge Dan Aaron Polster, the MDL judge, itemized the defendant’s challenges to Dr. Ix’s proposed testimony:

“The previously-used procedures GEHC takes issue with are:

(1) the failure to consult with experts about which studies to include;

(2) the failure to independently verify which studies to select for the meta-analysis;

(3) using retrospective and non-randomized studies;

(4) relying on studies with wide confidence intervals; and

(5) using a “more likely than not” standard for causation that would not pass scientific scrutiny.”

Gadolinium at *23.  Judge Polster confidently dispatched these challenges.  Dr. Ix, as a nephrologist, had subject-matter expertise with which to develop inclusionary and exclusionary criteria on his own.  The defendant never articulated what, if any, studies were inappropriately included or excluded.  The complaint that Dr. Ix had used retrospective and non-randomized studies also rang hollow in the absence of any showing that there were randomized clinical trials with pertinent data at hand.  Once a serious concern of nephrotoxicity arose, clinical trials were unethical, and the defendant never explained why observational studies were somehow inappropriate for inclusion in a meta-analysis.

Relying upon studies with wide confidence intervals can be problematic, but that is one of the reasons to conduct a meta-analysis, assuming the model assumptions for the meta-analysis can be verified.  The plaintiffs effectively relied upon a published meta-analysis, which pre-dated their expert witness’s litigation effort, in which the authors used less conservative inclusionary criteria, and reported a statistically significant summary estimate of risk, with an even wider confidence interval.  R. Agarwal, et al., ” Gadolinium-based contrast agents and nephrogenic systemic fibrosis: a systematic review and meta-analysis,” 24 Nephrol. Dialysis & Transplantation 856 (2009).  As the plaintiffs noted in their opposition to the challenge to Dr. Ix:

“Furthermore, while GEHC criticizes Dr. Ix’s CI from his meta-analysis as being “wide” at (5.18864 and 25.326) it fails to share with the court that the peer-reviewed Agarwal meta-analysis, reported a wider CI of (10.27–69.44)… .”

Plaintiff’s Opposition to GE Healthcare’s Motion to Exclude the Opinion Testimony of Joachim Ix at 28 (Mar. 12, 2010)[hereafter Opposition].

Wider confidence intervals certainly suggest greater levels of random error, but Dr. Ix’s intervals suggested statistical significance, and he had carefully considered statistical heterogeneity.  Opposition at 19. (Heterogeneity was never advanced by the defense as an attack on Dr. Ix’s meta-analysis).  Remarkably, the defendant never advanced a sensitivity analysis to suggest or to show that reasonable changes to the evidentiary dataset could result in loss of statistical significance, as might be expected from the large intervals.  Rather, the defendant relied upon the fact that Dr. Ix had published other meta-analyses in which the confidence interval was much narrower, and then claimed that he had “required” these narrower confidence intervals for his professional, published research.  Memorandum of Law of GE Healthcare’s Motion to Exclude Certain Testimony of Plaintiffs’ Generic Expert, Joachim H. Ix, MD, MAS, In re Gadolinium MDL No. 1909, Case: 1:08-gd-50000-DAP  Doc #: 668   (Filed Feb. 12, 2010)[hereafter Challenge].  There never was, however, a showing that narrower intervals were required for publication, and the existence of the published Agarwal meta-analysis contradicted the suggestion.

Interestingly, the defense did not call attention to Dr. Ix’s providing an incorrect definition of the confidence interval!  Here is how Dr. Ix described the confidence interval, in language quoted by plaintiffs in their Opposition:

“The horizontal lines display the “95% confidence interval” around this estimate. This 95% confidence interval reflects the range of odds ratios that would be observed 95 times if the study was repeated 100 times, thus the narrower these confidence intervals, the more precise the estimate.”

Opposition at 20.  The confidence interval does not provide a probability distribution of the parameter of interest; rather the distribution of confidence intervals has a probability of covering the hypothesized “true value” of the parameter.

Finally, the defendant never showed any basis for suggesting that a scientific opinion on causation requires something more than a “more likely than not” basis.

Judge Polster also addressed some more serious challenges:

“Defendants contend that Dr. Ix’s testimony should also be excluded because the methodology he utilized for his generic expert report, along with varying from his normal practice, was unreliable. Specifically, Defendants assert that:

(1) Dr. Ix could not identify a source he relied upon to conduct his meta-analysis;

(2) Dr. Ix imputed data into the study;

(3) Dr. Ix failed to consider studies not reporting an association between GBCAs and NSF; and

(4) Dr. Ix ignored confounding factors.”

Gadolinium at *24


The first point, above – the alleged failure to identify a source for conducting the meta-analysis – rings fairly hollow, and Judge Polster easily deflected it.  The second point raised a more interesting challenge.  In the words of defense counsel:

“However, in arriving at this estimate, Dr. Ix imputed, i.e., added, data into four of the five studies.  (See Sept. 22 Ix Dep. Tr. (Ex. 20), at 149:10-151:4.)  Specifically, Dr. Ix added a single case of NSF without antecedent GBCA exposure to the patient data in the underlying studies.

* * *

During his deposition, Dr. Ix could not provide any authority for his decision to impute the additional data into his litigation meta-analysis.  (See Sept. 22 Ix Dep. Tr. (Ex. 20), at 149:10-151:4.)  When pressed for any authority supporting his decision, Dr. Ix quipped that ‘this may be a good question to ask a Ph.D level biostatistician about whether there are methods to [calculate an odds ratio] without imputing a case [of NSF without antecedent GBCA exposure]’.”

Challenge at 12-13.

The deposition reference suggests that the examiner had scored a debating point by catching Dr. Ix unprepared, but by the time the parties briefed the challenge, the plaintiffs had the issue well in hand, citing A. W. F. Edwards, “The Measure of Association in a 2 × 2 Table,” 126 J. Royal Stat. Soc. Series A 109 (1963); R.L. Plackett, “The Continuity Correction in 2 x 2 Tables,” 51 Biometrika 327 (1964).  Opposition at 36 (describing the process of imputation in the event of zero counts in the cells of a 2 x 2 table for odds ratios).  There are qualms to be stated about imputation, but the defense failed to make them.  As a result, the challenge overall lost momentum and credibility.  As the trial court stated the matter:

“Next, there is no dispute that Dr. Ix imputed data into his meta-analysis. However, as Defendants acknowledge, there are valid scientific reasons to impute data into a study. Here, Dr. Ix had a valid basis for imputing data. As explained by Plaintiffs, Dr. Ix’s imputed data is an acceptable technique for avoiding the calculation of an infinite odds ratio that does not accurately measure association.7 Moreover, Dr. Ix chose the most conservative of the widely accepted approaches for imputing data.8 Therefore, Dr. Ix’s decision to impute data does not call into question the reliability of his meta-analysis.”

Gadolinium at *24.


The defense’s challenged including a claim that Dr. Ix had arbitrarily excluded studies in which there was no reported incidence of NSF. The defense brief unfortunately does not describe the studies excluded, and what, if any, effect their inclusion in the meta-analysis would have had.  This was, after all, the crucial issue. The abstract nature of the defense claim left the matter ripe for misrepresentation by the plaintiffs:

“GEHC continues to misunderstand the role of a meta-analysis and the need for studies that included patients both that did or did not receive GBCAs and reported on the incidence of NSF, despite Dr. Ix’s clear elucidation during his deposition. (Ix Depo. TR [Exh.1] at 97-98).  Meta-analyses such as performed by Dr. Ix and Dr. Agarwal search for whether or not there is a statistically valid association between exposure and disease event. In order to ascertain the relationship between the exposure and event one must have an event to evaluate. In other words, if you have a study in which the exposed group consists of 10,000 people that are exposed to GBCAs and none develop NSF, compared to a non-exposed group of 10,000 who were not exposed to GBCAs and did not develop NSF, the study provides no information about the association between GBCAs and NSF or the relative risk of developing NSF.”

Challenge at 37 – 38 (emphasis in original).  What is fascinating about this particular challenge, and the plaintiffs’ response, is the methodological hypocrisy exhibited.  In essence, the plaintiffs argued that imputation was appropriate in a case-control study, in which one cell contained a zero, but they would ignore a great deal of data in a cohort study with data.  To be sure, case-control studies are more efficient than cohort studies for identifying and assessing risk ratios for rare outcomes.  Nevertheless, the plaintiffs could easily have been hoisted with their own hypothetical petard.  No one in 10,000 gadolinium-exposed patients developed NSF; and no one in a control group did either.  The hypothetical study suggests that the rate of NSF is low and not different in the exposed and in the unexposed patients.  The risk ratio could be obtained by imputing an integer for the cells containing zero, and a confidence interval calculated.  The risk ratio, of course, would be 1.0.

Unfortunately, the defense did not make this argument; nor did it explore where the meta-analysis might have come out had a more even-handed methodology been taken by Dr. Ix.  The gap allowed the trial court to brush the challenge aside:

“The failure to consider studies not reporting an association between GBCAs and NSF also does not render Dr. Ix’s meta-analysis unreliable. The purpose of Dr. Ix’s meta-analysis was to study the strength of the association between an exposure (receiving GBCA) and an outcome (development of NSF). In order to properly do this, Dr. Ix necessarily needed to examine studies where the exposed group developed NSF.”

Gadolinium at *24.  Judge Polster, with no help from the defense brief, missed the irony of Dr. Ix’s willingness to impute data in the case-control 2 x 2 contingency tables, but not in the relative risk tables.


Defendants complained that Dr. Ix had ignored the possibility that confounding factors had contributed to the development of NSF.  Challenge at 13.  Defendants went so far as to charge Dr. Ix with misleading the court by failing to consider other possible causative exposures or conditions.  Id.

Defendants never identified the existence, source, and likely magnitude of confounding factors.  As a result, the plaintiffs’ argument, based in the Reference Manual, that confounding was an unlikely explanation for a very large risk ratio was enthusiastically embraced by the trial court, virtually verbatim from the plaintiffs’ Opposition (at 14):

“Finally, the Court rejects Defendants’ argument that Dr. Ix failed to consider confounding factors. Plaintiffs argued and Defendants did not dispute that, applying the Bradford Hill criteria, Dr. Ix calculated a pooled odds ratio of 11.46 for the five studies examined, which is higher than the 10 to 1 odds ratio of smoking and lung cancer that the Reference Manual on Scientific Evidence deemed to be “so high that it is extremely difficult to imagine any bias or confounding factor that may account for it.” Id. at 376.  Thus, from Dr. Ix’s perspective, the odds ratio was so high that a confounding factor was improbable. Additionally, in his deposition, Dr. Ix acknowledged that the cofactors that have been suggested are difficult to confirm and therefore he did not try to specifically quantify them. (Doc # : 772-20, at 27.) This acknowledgement of cofactors is essentially equivalent to the Agarwal article’s representation that “[t]here may have been unmeasured variables in the studies confounding the relationship between GBCAs and NSF,” cited by Defendants as a representative model for properly considering confounding factors. (See Doc # : 772, at 4-5.)”

Gadolinium at *24.

The real problem is that the defendant’s challenge pointed only to possible, unidentified causal agents.  The smoking/lung cancer analogy, provided by the Reference Manual, was inapposite.  Smoking is indeed a large risk factor for lung cancer, with relative risks over 20.  Although there are other human lung carcinogens, none is consistently in the same order of magnitude (not even asbestos), and as a result, confounding can generally be excluded as an explanation for the large risk ratios seen in smoking studies.  It would be easy to imagine that there are confounders for NSF, especially given that it is relatively recently been identified, and that they might be of the same or greater magnitude as that suggested for the gadolinium contrast media.  The defense, however, failed to identify confounders that actually threatened the validity of any of the individual studies, or of the meta-analysis.


The defense hinted at the general unreliability of meta-analysis, with references to References Manual on Scientific Evidence at 381 (2d ed. 2000)(noting problems with meta-analysis), and other, relatively dated papers.  See, e.g., John Bailar, “Assessing Assessments,” 277 Science 529 (1997)(arguing that “problems have been so frequent and so deep, and overstatements of the strength of conclusions so extreme, that one might well conclude there is something seriously and fundamentally wrong with [meta-analysis].”).  The Reference Manual language carried over into the third edition, is out of date, and represents a failing of the new edition.  See The Treatment of Meta-Analysis in the Third Edition of the Reference Manual on Scientific Evidence” (Nov. 14, 2011).

The plaintiffs came forward with some descriptive statistics of the prevalence of meta-analysis in contemporary biomedical literature.  The defendants gave mostly argument; there is a dearth of citation to defense expert witnesses, affidavits, consensus papers on meta-analysis, textbooks, papers by leading authors, and the like.  The defense challenge suffered from being diffuse and unfocused; it lost persuasiveness by including weak, collateral issues such as claiming that Dr. Ix was opining “only” on a “more likely than not” basis, and that he had not consulted with other experts, and that he had failed to use randomized trial data.  The defense was quick to attack perceived deficiencies, but it did not illustrate how or why the alleged deficiencies threatened the validity of Dr. Ix’s meta-analysis.  Indeed, even when the defense made strong points, such as the exclusion of zero-event cohort studies, it failed to document that such studies existed, and that their inclusion might have made a difference.


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