Meta-Meta-Analysis – Celebrex Litigation – The Claims – Part One

In the Celebrex/Bextra litigation, both sides acknowledged the general acceptance and validity of meta-analysis, for both observational studies and clinical trials, but attacked the other side’s witnesses’ meta-analyses on grounds specific to how they were conducted.  See, e.g., Pfizer Defendants’ Motion to Exclude Certain Plaintiffs’ Experts’ Causation Opinion Regarding Celebrex – Memorandum of Points and Authorities in Support Thereof at 14, 16 (describing meta-analysis as “appropriate” and a “useful way to evaluate the presence and consistency of an effect,” and “a valid technique for analyzing the results of both randomized clinical trials and observational studies”)(dated July 20, 2007), submitted in MDL 1699, In re Bextra and Celebrex Marketing Sales Practices & Prod. Liab. Litig., Case No. 05-CV-01699 CRB (N.D. Calif.) [hereafter MDL 1699]; Plaintiffs’ Memorandum of Law in Support of Their Motion to Exclude Expert Testimony by Defendants’ Expert Dr. Lee-Jen Wei at 2 (July 23, 2009) (“While use of a properly conducted meta-analysis is appropriate, there are underlying scientific principles and techniques to be used in meta-analysis that are widely accepted among biostatisticians and epidemiologists. Wei’s meta-analysis – which he acknowledges is based in part on an admittedly novel approach that is not generally recognized by the scientific community – fails to follow certain of these key principles.”), submitted in In re Pfizer, Inc. Securities Litig., Nos. 04 Civ. 9866(LTS)(JLC), 05 md 1688(LTS) (S.D.N.Y.)[hereafter Securities Litig.]

The plaintiffs and defendants expended a great deal of energy in attacking the other side’s meta-analyses as conducted.  With all the briefing in the federal MDL, the New York state cases, and the securities fraud class action, hundreds of pages were written on the suspected flaws in meta-analyses.  The courts, in both the products liability MDL cases and in the securities case, denied the challenges in a few sentences.  Indeed, it is difficult if not impossible to discern what the challenges were from reading the courts’ decisions. In re Pfizer Inc. Securities Litig., 2010 WL 1047618 (S.D.N.Y. 2010); In re Bextra and Celebrex, 2008 N.Y. Misc. LEXIS 720; 239 N.Y.L.J. 27(2008); In re Bextra and Celebrex Marketing Sales Practices and Product Liability Litig., MDL No. 1699, 524 F.Supp. 2d 1166 (N.D. Calif. 2007)

Although the issues shifted some over the course of these litigations, certain important themes recurred.  The plaintiffs focused their attack upon the meta-analyses conducted by defense expert witness, Lee-Jen Wei, a professor of biostatistics at the Harvard School of Public Health.

The plaintiffs maintained that Professor Wei’s meta-analyses should be excluded under Rule 702, or the New York case law, because of

  • inclusion of short-term clinical trials
  • failure to weight risk ratios by person years
  • inclusion of zero-event trials with use of imputation methods
  • use of risk difference instead of risk ratios
  • use of exact confidence intervals instead of estimated intervals

See generally Plaintiffs’ Memorandum of Law in Support of Their Motion to Exclude Expert Testimony by Defendants’ Expert Dr. Lee-Jen Wei (July 23, 2009), in Securities Litig.

The plaintiffs advanced meta-analyses conducted by Professor David Madigan, Professor and Chair in the Department of Statistics, Columbia University.  The essence of the defendants’ challenges revolved around claims of flawed outcome and endpoint ascertainment and definitions:

  • invalid clinical endpoints
  • flawed data collection procedures
  • ad hoc changes in procedure and methods
  • novel methodologies “never used in the history of clinical research”
  • lack of documentation for classifying events
  • absence of expert clinical judgment in classifying event for inclusion in meta-analysis
  • creation of composite endpoints that included events unrelated to plaintiffs’ theory of thrombotic mechanism
  • lack of blinding to medication use when categorizing events
  • failure to adjust for multiple comparisons in meta-analyses

See generally Pfizer Defendants’ Motion to Exclude Certain Plaintiffs’ Experts’ Causation Opinion Regarding Celebrex – Memorandum of Points and Authorities in Support Thereof (dated July 20, 2007), in MDL 1699; Pfizer defendants’ [Proposed] Findings of Fact and Conclusions of Law with Respect to Motion to Exclude Certain Plaintiffs’ Experts’ Opinions Regarding Celebrex and Bextra, and Plaintiffs’ Motion to Exclude Defendants’ Expert Dr. Lee-Jen Wei, Document 175, submitted in Securities Litig. (Dec. 4, 2009).

Why did the three judges involved (Judge Breyer in the federal MDL; Justice Kornreich in the New York state cases; and Judge Swain in the federal securities putative class action) give such cursory attention to these Rule 702/Frye challenges?  The complexity of the issues, the lack of clarity in the lawyers’ briefings, and the stridency of both sides perhaps contributed to shorten judicial attention span.  Some of the claims were simply untenable, and may have obliterated more telling critiques.


Many of the Celebrex parties’ claims can be traced to a broader issue of what to include or exclude in a meta-analysis.  Consider for instance the plaintiffs’ challenge to Wei’s meta-analysis.  The plaintiffs faulted Wei for including short-term clinical trials in his meta-analysis, while sponsoring their own expert witness testimony that Celebrex could induce heart attack or stroke after first ingestion of the medication.  Having made the claim, the plaintiffs were hard pressed to exclude short-term trials, other than to argue that such trials frequently had zero adverse events in either the medication or placebo arms.  Many meta-analytic methods, which treat each included study as a 2 x 2 contingency table, and calculate an odds ratio for each table, cannot accommodate zero event data.

Whether or not hard pressed, the plaintiffs made the claim. The plaintiffs’ analogized to the lack of reliability of underpowered clinical trials to provide evidence of safety.  See Plaintiffs’ Reply Memorandum of Law in Further Support of Their Motion to Exclude Expert Testimony by Defendants’ Expert Dr. Lee-Jen Wei at 6 (May 5, 2010), in Securities Litig. (citing In re Neurontin Mktg., Sales Practices, and Prod. Liab. Litig., 612 F. Supp. 2d 116, 141 (D. Mass. 2009) (noting that many of Pfizer’s studies were “underpowered” to detect the alleged connection between Neurontin and suicide).  The power argument, however, does not make sense in the context of a meta-analysis, which is aggregating data across studies to overcome the alleged lack of power in a single study.

Not surprisingly, clinical trials of a non-cardiac medication will often report no event of the outcome of interest, such as heart attack.  These trials are referred to as a “zero event”, which can happen in one or both arms of a given trial.  Some searchers exclude these studies from a meta-analysis because of the impossibility of calculating an odds ratio without using imputation in the zero cells of the 2 x 2 tables. Although there are methods to address zero-event trials, some researchers believe that the existence of several zero-event trials essentially means that the sparse data from rare outcomes deprives statistical tests of their usual meaning.  Traditional statistical standards of significance (p < 0.05) are described as “tenuous,” and too high, in this situation. A.V. Hernandez, E. Walker, J. P. Ioannidis, M.W. Kattan, “Challenges in meta-analysis of randomized clinical trials for rare harmful cardiovascular events: the case of rosiglitazone,” 156 Am. Heart J. 23, 28 (2008).

The exclusion of zero-event trials from meta-analyses of rare outcomes can yield biased results. See generally M.J. Bradburn, J.J Deeks, J.A. Berlin, and A. Russell Localio,” Much ado about nothing: a comparison of the performance of meta-analytical methods with rare events,” 26 Statistics in Med. 53 (2007); M.J. Sweeting, A.J. Sutton, and P.C. Lambert, “What to add to nothing? Use and avoidance of continuity corrections in meta-analysis of sparse data,” 23 Statistics in Med. 1351 (2004)(erratum at 25 Statistics in Med. 2700 (2006) (“Many routinely used summary methods provide widely ranging estimates when applied to sparse data with high imbalance between the size of the studies’ arms. A sensitivity analysis using several methods and continuity correction factors is advocated for routine practice.”).

Others researchers include zero-event trials as providing helpful information about the absence of risk. Zero-event trials:

“provide relevant data by showing that event rates for both the intervention and control groups are low and relatively equal. Excluding such trial data potentially increases the risk of inflating the magnitude of the pooled treatment effect.”

J.O. Friedrich, N.K. Adhikari, J. Beyene, “Inclusion of zero total event trials in meta-analyses maintains analytic consistency and incorporates all available data,” 5 BMC Med. Res. Methodol. 2 (2007)[cited as Friedrich].  Zero event trials can be included in meta-analyses by using something called a standard “continuity correction,” which involves imputing events, or fractional events, in all cells of the 2 x 2 table. One approach, the zero is replaced with 0.5 and all other numbers are increased by 0.5. Friedrich at 7.

After examining the bias in several meta-analyses from excluding zero-event trials, Friedrich and colleagues recommended:

“We believe these trials [with zero events] should also be included if RR [relative risks] or OR [odds ratios] are the effect measures to provide a more conservative estimate of effect size(even if this change in effect size is very small for RR and OR), and to provide analytic consistency and include the same number of trials in the meta-analysis, regardless of the summary effect measure used. Inclusion of zero total event trials would enable the inclusion of all available randomized controlled data in a meta-analysis, thereby providing the most generalizable estimate of treatment effect.”

Friedrich at 5-6.

Wei addressed the problem of zero-event trials by using common imputation methods, not so different from what plaintiffs’ expert witness Dr. Ix used in the gadolinium litigation. See Meta-Meta-Analysis — The Gadolinium MDL — More Than Ix’se Dixit.  Given that plaintiffs advanced a mechanistic theory, which would explain cardiovascular thrombotic events almost immediately upon first ingestion of Celebrex, Professor Wei’s attempt to save the data inherent in zero-event trials by “continuity correction” or imputation methods seems reasonable and well within meta-analytic procedures.



Professor Wei did not limit himself to a single method or approach.  In addition to using imputation methods, Wei used risk difference, rather than risk ratios, as the parameter of interest.  The risk difference is simply the difference between two risks: the risk or probability of an event in one group less the risk or probability of that event in another group.  Contrary to the plaintiffs’ claims, there is nothing novel or subversive about conducting a meta-analysis with the risk difference as the parameter of interest, rather than a risk ratio.  In the context of randomized clinical trials, the risk difference is expected as a measure of absolute effect.  See generally, Michael Borenstein, L. V. Hedges, J. P. T. Higgins, and H. R. Rothstein, Introduction to Meta-Analysis (2009); Julian PT Higgins and Sally Green, eds., Cochrane Handbook for Systematic Reviews of Interventions (2008)

Like risk ratios, the risk difference yield a calculated confidence interval at any desired coefficient of confidence.  Confidence intervals for dichotomous events are often based upon approximate methods that build upon the normal approximation to the binomial distribution.  These approximate methods require assumptions of sample size that may not be met in cases involving sparse data.  With modern computers, calculating exact confidence intervals is not particularly difficult, and Professor Wei has published a methods paper in which he explains the desirability of using the risk difference with exact intervals in addressing meta-analyses of sparse data, such as was involved in the Celebrex litigation.  See L. Tian, T. Cai, M.A. Pfeffer, N. Piankov, P.Y. Cremieux, and L.J. Wei, “Exact and efficient inference procedure for meta-analysis and its application to the analysis of independent 2 x 2 tables with all available data but without artificial continuity correction,” 10 Biostatistics 275 (2009).

Plaintiffs attacked Wei’s approach as “novel” and not generally accepted.  Judge Swain appropriately dismissed this attack:

“Dr. Wei’s methodology, the validity of which Plaintiffs contest and the novelty of which Plaintiffs seek to highlight, appears to have survived the rigors of peer review at least once, and is subject to critique by virtue of its transparency. Dr. Wei’s report, supplemented by his declaration, is sufficient to meet Defendants’ burden of demonstrating that his testimony is the product of reliable principles and methods. He has explained his methods, which can be tested. Plaintiffs’ critiques of Dr. Wei’s choices regarding which trials to include in his own meta-analysis, the origins of the data he used, the date at which he undertook his meta-analysis, and at whose behest he performed his analysis all go to the weight of Dr. Wei’s testimony.”

In re Pfizer Inc. Securities Litig., 2010 WL 1047618, *7 (S.D.N.Y. 2010).  The approach taken by Wei is novel only in the sense that researchers have not previously tried to push the methodological envelope of meta-analysis to deploy the technique for rare outcomes and sparse data, with many zero-event trials.  The risk difference approach is well suited to the situation, and the use of exact confidence intervals is hardly novel or dubious.

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