Meta-Analysis : Simultaneous Statistical  Analysis
of Multiple Datasets using Random-Effects Models

Thur 1-2,  Rm  Mth 2400                                                                 S '04

Eric Slud       Statistics Program, Math Department, Rm 2314

Interested participants should get in touch with me at

Research Focus:   This activity is a RIT `research interaction' seminar on Meta-Analysis.
Briefly, meta-analysis concerns the simultaneous statistical analysis of a number of related
studies or datasets within a single statistical model. The fact that parameters are shared
across datasets (e.g. a treatment-effectiveness parameter assumed constant across a number
of separately conducted  clinical studies of  the effectiveness of the same treatment regimen for
the same disease) allows the possiblity of increasing sensitivity or power of statistical tests.
However, such an increase in precision comes at the price of model simultaneous assumptions
whose compatibility with the data must be validated. This RIT is an outgrowth of the Fall '03 RIT
on Large Cross-Classified Datasets.

The statistical ideas involved in this RIT are similar to but not identical to those addressed in
Large Cross-Classified Datasets. The methods here are very much associated with Bayesian
or empirical-Bayesian approaches to hierarchical models. The point is that similar models, with
at least some shared parameters, are to be fitted on disparate datasets and analyzed within a
single (parametric) framework. The appeal of this kind of analysis in applications is that numerous
studies which may not be large individually can hope to yield definitive conclusions when analyzed
together, at least if model assumptions can be introduced which realistically account for the
differences in the separate experimental settings, study populations, etc.  We will address issues
of the goodness of fit of models used in meta-analyses wherever possible.

There is a large literature on meta-analyses in social science research (combining little studies on
the same topic) and another literature on meta-analyses in biomedical (eg clinical) research. Our
attention will largely focus on the latter. Initially, only biomedical-related papers are listed below.

Graduate Prerequisites: To benefit from this research activity, a graduate student
should have completed Stat 700 and at least one of Stat 740, 741, 750, or 770, and
preferably should have some familiarity with Statistical Computing at the level of
Stat 430 (SAS programming) or Stat 798C (Splus and SAS).

Undergraduate Prerequisites: An interested undergraduate should have had at
least one course in Mathematical Statistics (e.g. Stat 401 or 420) and considerable
experience -- either in courses or projects --- with numerical computing or
data analysis.

Graduate Program: Graduate students will be involved in reading and presenting
papers from the statistical literature.

Undergraduate Program: Undergraduate students, if any, will be urged toward computational
projects involving (re-)analysis of real and simulated datasets by meta-analysis methods.

Work Schedule:  We will meet weekly in the spring of 2004. Students will choose
papers or book-chapters on Meta-analysis from the following list of Topics and Papers
(which will regularly be augmented on this web-page) and present the material in
subsequent weeks. Presentations can be informal, but should be detailed enough and
present enough background that we can understand the issues and ideas clearly. It is
expected that many presentations will extend to a second week.

        Topics & Papers

Topics:  empirical Bayes methodology,
                random-effect GLM's,
                hierarchical models,
                meta-analysis in linear and categorical data settings,
                goodness of fit testing (model assessment),
                Survival Analysis or biomedical meta-analyses.

Text references:

These entries must still be filled in. There are many suitable, and highly relevant texts
on Bayes and empirical-Bayes methods, eg:

Bayes and Empirical Bayes methods for data analysis,
by Bradley P. Carlin and Thomas A. Louis (2000)

and also a number of texts in the Library involving Meta-analysis in the title, e.g.:

 Meta-analysis of controlled clinical trials, by  Anne Whitehead (2002).

Papers on biomedical meta-analyses:

The Carlin and Louis text suggests the following (review-) papers related to
Empirical Bayes  and Meta-Analysis:

N. Breslow (1990), "Biostatistics and Bayes (with discussion)". Statistical Science
    5, 269-298.

W. DuMouchel & J. Harris (1983), "Bayes methods for combining the results of
     cancer studies in humans and other species (with discussion)". Jour. Amer. Statist.
    Assoc. 78, 293-315.

Current Index to Statistics Hits for "Meta-Analysis, Biostatistics "

      1. Hartung, Joachim , and Knapp, Guido (2001), ``A refined method for the
meta-analysis of controlled clinical trials with binary outcome'',
Statistics in Medicine, 20 (24) , 3875-3889

      2. Stijnen, Theo (2000), ``Comment on ``Tutorial in biostatistics. Meta-
analysis: Formulating, evaluating, combining, and reporting'' (1999 V18
p321-359), Statistics in Medicine, 19 (5) , 759-761.

Hit(s) for "Meta-Analysis, Royal Statistical Society"

      1. Shi, Jian Qing , and Copas, John (2002), ``Publication bias and meta-
analysis for 2 × 2 tables: An average Markov chain Monte Carlo EM algorithm'',
Journal of the Royal Statistical Society, Series B, Methodological, 64, 221-236.

      2. Tudur, Catrin , Williamson, Paula R. , Khan, Saboor , and Best, Lesley Y.
(2001), ``The value of the aggregate data approach in meta-analysis with time-to-
event outcomes'', Journal of the Royal Statistical Society, Series A, General,
164 (2) ,  357-370.

      3. Copas, John (1999), ``What works?: Selectivity models and meta-analysis'',
Journal of the Royal Statistical Society, Series A, General, 162 , 95-109.

      4. Begg, Colin B. , and Berlin, Jesse A.  (1988), ``Publication bias: A problem in
interpreting medical data (C/R: p445-463)'', Journal of the Royal Statistical
Society, Series A, General, 151, 419-445.

Hit(s) for "Meta-Analysis, Biometrics"

      1. Cook, Richard J. , Brumback, Babette B. , Wigg, Melanie B. , and Ryan,
Louise M.  (2001), ``Synthesis of evidence from epidemiological studies with interval-
censored exposure due to grouping'', Biometrics, 57 (3) , 671-680.

      2. Li, Zhengqing , and Li, Yan (2000), ``A homogeneity test in overviews with group
sequentially monitored clinical trials'', Biometrics, 56 (1) , 134-138.

      3. Wakefield, Jonathan , and Rahman, Nargis (2000), ``The combination of
population pharmacokinetic studies'', Biometrics, 56 (1) , 263-270.

      4. Böhning, Dankmar , and Sarol, Jesus, Jr.  (2000), ``Estimating risk difference in
multicenter studies under baseline-risk heterogeneity'', Biometrics, 56 (1) , 304-308.

      5. Lui, Kung-Jong , and Kelly, Colleen (2000), ``A revisit on tests for homogeneity
of the risk difference'', Biometrics, 56 (1) , 309-315.

      6. Duval, Sue , and Tweedie, Richard (2000), ``Trim and fill: A simple funnel-plot-
based method of testing and adjusting for publication bias in meta-analysis'',
Biometrics, 56 (2) , 455-463.

      7. Lloyd, Chris J.  (2000), ``Regression models for convex ROC  curves'',
Biometrics, 56 (3) , 862-867.

      8. Duchateau, Luc , Collette, Laurence , Sylvester, Richard, and Pignon, Jean-Pierre
(2000), ``Estimating number of events from the Kaplan-Meier curve for incorporation
in a  literature-based meta-analysis: What you don't see you can't get!'', Biometrics,
56 (3) , 886-892.

      9. Liao, J. G.  (1999), ``A hierarchical Bayesian model for combining multiple 2 × 2
tables using conditional likelihoods'', Biometrics, 55 , 268-272.

      10. Greenwood, Celia M. T. , Midgley, Julian P. , Matthew, Andrew G. , and Logan,
Alexander G.  (1999), ``Statistical issues in a metaregression analysis of randomized
trials: Impact on the dietary sodium intake and blood pressure relationship'',
Biometrics, 55 , 630-636.

      11. Follmann, Dean A. , and Proschan, Michael A.  (1999), ``Valid inference in
random effects meta-analysis'', Biometrics, 55 , 732-737.

      12. Mathew, Thomas , and Nordström, Kenneth (1999), ``On the equivalence of
meta-analysis using literature and using individual patient data'', Biometrics 55 , 1221-3.

      13. Fay, Michael P. , Graubard, Barry I. , Freedman, Laurence S. , and Midthune,
Douglas N.  (1998), ``Conditional logistic regression with sandwich estimators: Application
to a  meta-analysis'', Biometrics, 54 , 195-208.

      14. Olkin, Ingram , and Sampson, Allan (1998), ``Comparison of meta-analysis versus
analysis of variance of individual patient data'', Biometrics, 54 , 317-322.

      15. Böhning, Dankmar , Dietz, Ekkehart , and Schlattmann, Peter (1998), ``Recent
developments in computer-assisted analysis of mixtures'', Biometrics, 54 , 525-536.

      16. Hung, H. M. James , O'Neill, Robert T. , Bauer, Peter , andKöhne, Karl (1997),
``The behavior of the P-value when the alternative hypothesis is true'',
Biometrics 53 , 11-22.

      17. Stram, Daniel O.  (1996), ``Meta-analysis of published data using a linear mixed-
effects model'', Biometrics, 52 , 536-544.

      18. Li, Zhaohai (1995), ``A multiplicative random effects model for meta-analysis
with application to estimation of a mixture component'', Biometrics, 51 , 864-873.

      19. Dear, Keith B. G.  (1994), ``Iterative generalized least squares for meta-analysis
of  survival data at multiple times'', Biometrics, 50 , 989-1002.

      20. Begg, Colin B. , and Mazumdar, Madhuchhanda (1994), ``Operating charac-
teristics of a rank correlation test for publication bias'', Biometrics, 50 , 1088-1101.

      21. Hughes, Michael D. , Freedman, Laurence S. , and Pocock, Stuart J.  (1992),
``The impact of stopping rules on heterogeneity of results in overviews of clinical trials'',
Biometrics, 48 , 41-53

      22. Begg, Colin B. , and Pilote, Louise (1991), ``A model for incorporating historical
controls into a meta-analysis'', Biometrics, 47 , 899-906

      23. Brown, Morton B.  (1975), ``A method for combining non-independent, one-
sided tests of significance (Corr: V32 p955)'', Biometrics, 31 , 987-992

      24. Radhakrishna, S.  (1965), ``Combination of results from several 2 × 2
contingency tables'', Biometrics, 21 , 86-98.

Other papers :

From one point of view, the problem in some large-data multiple-source experiments
like Microrarrays can be viewed as a problem in meta-analysis. (This is certainly not
how microrarrays are generally treated in the literature. But students might like to
consider microarray papers from this point of view in the RIT.

Many additional references on large datasets with particular reference to DNA
Microarrays (used in AMSC seminars and RITs in past terms) can be found here .
A web-site of microarray references, created by a statistician at LSU named
Barry Moser, may also be helpful.

There is also a Special Issue of Statistical Science (Feb. 2003) on Statistical
Challenges and Methods for Microarray Analysis which contains survey articles
and bibliographies with many items of interest for our RIT. Special Issues of
other journals (including Statistica Sinica) also were devoted to the topic.

Other related papers ...

Liu,  M.,Taylor,  J. and Belin, T. (2000)  Multiple imputation and posterior simulation for
  multivariate missing data in longitudinal studies. Biometrics 56, 1157-63.

Burzykowski, Tomasz , Molenberghs, Geert , Buyse, Marc ,  Geys, Helena , and Renard,
  Didier  (2001), Validation of surrogate end points in multiple randomized clinical trials
  with failure time end points, Applied Statistics, 50 (4) , 405-422.

Cleary, Richard J. , and Casella, George  (1997), An application of Gibbs sampling to
  estimation in meta-analysis: Accounting for publication bias, Journal of Educational and
    Behavioral Statistics [Formerly: @J(JEdStat)] 22 , 141-154.

Cappelleri, Joseph C. , Ioannidis, John P. A. , Schmid,  Christopher H. , de Ferranti,
  Sarah D. , Aubert, Michael , Chalmers,  Thomas C. , and Lau, Joseph  (1996), Large trials
  vs. meta-analysis of smaller trials -- How do their results compare ?,
  Jour. of Amer. Medical Assoc., 276 , 1332-1338.

Mengersen, K. L. , Tweedie, R. L. , and Biggerstaff, B.  (1995), The impact of method choice
   on meta-analysis, The Australian Journal of Statistics [now:J(AusNZJSt)], 37 , 19-44 .

Hughes, Michael D. , Freedman, Laurence S. , and Pocock, Stuart J. (1992), The impact of
   stopping rules on heterogeneity of results in overviews of clinical trials, Biometrics, 48 , 41-53.

Schedule of Talks --

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© Eric V Slud, May 20, 2004.