Current Issues with Meta-analysis in Medical Research

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1 Current Issues with Meta-analysis in Medical Research Demissie Alemayehu Pfizer & Columbia Semanade Bioinformatica, Bioestadistica Analists de Supervivencia Instituto Panamericano de Estudios Avanzados en Probabilidad y Estadistica May 2-8, 2, 2010

2 Abstract In the absence of definitive trials on the comparative safety and effectiveness of drugs, a systematic synthesis of available data may provide critical information to help decision making by medical professionals, patients and other stakeholders. However, uncritical and lopsided use of pooled data to inform decision about important health-care issues may have consequences that adversely impact public health, stifle innovation, and confound medical science. In this talk, current methodological issues in meta-analysis are highlighted, and advantages and disadvantages of alternative techniques are evaluated. The need for a more integrated strategy toward the synthesis, interpretation and dissemination of pooled data is suggested. The talk, intended for applied statisticians and others involved in medical research, will involve review of case studies to illustrate relevant issues. 2

3 Outline Part I: Standard Meta-analysis A Case Study: The Avandia Analysis Procedures for Meta-analysis Criteria for Causality The Avandia Analysis Revisited Part II: Non-standard Meta-analysis Cumulative Meta-analysis Indirect Comparison Observational Data Analysis Comparative Effectiveness Research Concluding Remarks 3

4 Avandia Meta-analysis analysis Nissen & Wolski, N Engl J Med 2007;356: Diabetes drug called heart death risk Steve Sternberg Source: USA Today: May 22,

5 Definition: Meta-analysis analysis Meta-Analysis is a statistical approach for combining information from independent studies to address a pre-specified hypothesis of interest. Based on systematic literature review Provides precise estimate of treatment effect, giving due weight to studies included 5

6 Benefits of Meta-analysis analysis Precision / Power Individual clinical trials may lack power to provide conclusive results Particularly useful for rare events To assess consistency (generalizability)) of results To settle controversies arising from conflicting studies Answer questions not posed by the individual studies generate new hypotheses 6

7 When to do a Meta-analysis analysis Data are available from more than one study There are no major differences in the study characteristics Outcome has been measured in similar ways 7

8 When not to do a Meta-analysis analysis Garbage in - garbage out A meta-analysis analysis is only as good as the studies in it Beware of mixing apples with oranges Compare like with like Beware of reporting biases 8

9 Steps in Meta-analysis analysis 1. Detailed written protocol development 2. Comprehensive / systematic search for eligible studies 3. Presentation of results 4. Sensitivity analysis / test for heterogeneity performed 5. Discussion of limitations of analysis 6. Reporting of results in light of available body of knowledge 9

10 Protocol Development Formulation of problem to be addressed Eligibility criteria for studies to be included defined a priori Statistical methods for combining the data 10

11 Selection of Studies Minimize Sources of Bias Publication Bias Positive studies more likely to be published than negative studies Reviewer Bias Tendency to include only studies that favor the hypothesis of interest Define universe of studies to be considered Define explicit & objective criteria for study inclusion/ rejection based on quality grounds Hierarchy of Evidence Harbour R, Miller J. A new system for grading recommendations in evidence based guidelines. BMJ 2001;323:

12 Selection of Studies, cont d Popular Databases PubMed / MedLine Cochrane Review Trial result registries Other Sources Hand Search: FDA, library Personal references, s Web: Google, etc. 12

13 Publication Bias Decision to publish is influenced by study result Small studies of no effect unlikely to be published Overestimation of treatment effect. Detection: No universally accepted methods Funnel plots treatment effect against its precision (sample size or variance) Egger s Weighted Regression Statistic Begg s Test Most methods heuristic. Operating characteristics not well-studied 13

14 Publication Bias Funnel Plot: Plots of Variability or Sample Size vs. Effect Size Precision: increasing function of study size In absence of bias, results from small studies scatter widely at bottom of graph Publication bias: asymmetrical funnel plots 14

15 Publication Bias (cont.) Egger s Weighted Regression Statistic Test for asymmetry of the funnel plot. Effect size regressed on precision (inverse of se) Begg and Mazumdar Test for interdependence of variance and effect size using Kendall s tau If publication bias, expect that high se s (i.e., small studies) would be associated with larger effect sizes. 15

16 Summary of Treatment Effects Mean Difference Odds Ratio Risk Difference Number Needed to Treat (NNT) Inference: Statistical Methods Different approaches exist, but there is no single "correct" method Two General Approaches Fixed Effect Models Random Effects Models Bayesian Meta-analysis analysis 16

17 Statistical Methods, cont d Fixed Effect Models If it is reasonable to assume underlying effect is the SAME for all studies Only one source of sampling error: - within study Problems with ignoring heterogeneity: confidence intervals too narrow Y~N, ( 2 θ σ ) i i i θ i = θ 17

18 Fixed Effect Models, cont d Inverse-variance variance r = number of studies in the meta-analysis, and 18

19 Mantel-Haenszel Confidence interval for the Mantel-Haenszel odds ratio calculated using the Robins, Breslow and Greenland variance formula (Robins et al., 1986) Peto-Method Fixed Effect Models, cont d Often used for rare events 19

20 Statistical Methods, cont d Random Effects Models True effect could vary from study to study E.g., effect size higher in older subjects Sources of sampling error: within study between studies Gives wider confidence interval Y~N, Random Effects θ i ~ ( 2 θ σ ) i i i 2 N( θ, τ ) Y N θ σ τ 2 2 i ~ ( i, i + ) 20

21 Statistical Methods, cont d Random Effects Models Common method: DerSimonian-Laird * 21

22 Bayesian Meta-analysis 22

23 Bayesian Hierarchical Model Priors on (θ, τ 2 ): Usually noninformative normal prior on θ For both fixed and random effects For random effects: Noninformative inverse gamma or uniform prior on τ 2 Inferences sensitive to prior on τ 2 23

24 Bayesian Meta-analysis Advantages Allows probability statements: E.g. Post probability median survival of drug A > that of drug B. Multiplicities not an issue: For decision making Can incorporate probabilistic loss function 24

25 Bayesian Meta-analysis Disadvantages Use of subjective prior beliefs Eliciting prior beliefs is a non-trivial exercise Few guidelines to help the Bayesian analyst. Different prior distributions can generate varying results Computational complexity 25

26 Meta-analysis of Rare Events Large-sample procedures may not be appropriate for pooling rare events Comparison of procedures: Bradburn et al, Stat Med 2007;26: Event rates < 1%: Peto one-step odds ratio Reasonable bias, power Bias substantial, unbalanced case Event rates 2%-5%: Logistic Regression, Exact Method, MH OR better performance (in terms of bias) than Peto Risk difference Conservative confidence intervals No need to exclude studies with 0 events in both groups 26

27 Meta-analysis: analysis: Heterogeneity If study results differ greatly, it may not be appropriate to combine Differences in patient groups studied Differences in interventions studied Differences in primary outcome studies Studies carried out in distinct settings e.g., different countries Cochran s s Q Test Low power, esp. when # of studies is small Liberal if number of studies is large Graphical Exploration 27

28 Heterogeneity Cochran s Q Statistic Weighted sum of squared differences between individual study effects and the pooled effect across studies Distributed as a chi-square statistic with k-1 df Low power, especially when the number of studies is small Too much power, if the number of studies is large 28

29 I 2 Statistic Heterogeneity Percentage of variation across studies due to heterogeneity rather than chance Higher percentage (greater than 50%) indicates heterogeneity Operating characteristics influenced by number of studies and study sizes. 29

30 Handling Heterogeneity If heterogeneity is suspected: Stratify the studies into homogeneous subgroups and then fit separate fixed effects Post-hoc nature Multiplicities Construct a random effects estimate across all studies. Concern: if heterogeneity exists among studies, a summary measure across those studies should not be provided? Fit a meta-regression model that explains the heterogeneity in terms of study-level covariates. 30

31 Meta-Regression with Summary Data Can fit with standard weighted linear regression model With individual patient data, can fit by two-step process 31

32 Meta-regression: Issues Ecological fallacy Group averages don't represent individuals well Averages have little between-study variation Post-hoc specification of prognostic factors may lead to bias/spurious results Number of studies usually small Data may be unavailable (not conceived or not reported) Cannot handle factors that vary by patient within study 32

33 Meta-analysis: analysis: Data Presentation Graphical display of results from individual studies on a common scale: Blobbograms Also referred to as forest plots 33

34 Meta-analysis: analysis: Sensitivity Analysis Examine Robustness of Findings Examine effects in certain studies, certain groups of patients, or certain interventions Robustness to departures from model assumptions Sensitivity to departure from study selection criteria 34

35 Discuss Limitations of Analysis Bias: Publication Use of aggregate data: Confounding factors Model assumptions Heterogeneity Meta-analysis: analysis: Study Limitations 35

36 Meta-analysis: analysis: Communication of Findings Results summarized in light of available body of knowledge? Association is not the same as causation 36

37 Assessment of Causality Strength of Association Validity of measure: OR, RR, etc. Clinical / statistical significance Assessment of Consistency Review similar reports for drug Review similar reports for class Biological Plausibility Known potential biologic basis to suggest a causal link Reference pharmacogenomic evidence 37

38 Epidemiology Consider the expected rate in the general population for comparable demographic groups False Positive Findings Address issue of multiplicity FDR Assessment of Causality, cont d Imbalance Imbalance (wrt Relevant Confounding Factors) Identify relevant risk factors Pharmacovigilance Databases Recent advances in analysis of such data Measures of disproportionality 38

39 QUOROM Statement Moher D, Cook DJ, Eastwood S, Olkin I, Rennie D, Stroup DF. Improving the Quality of Reports of Meta-Analyses of Randomised Controlled Trials: The QUOROM Statement. Quality of Reporting of Meta-Analyses, Lancet 1999;354:

40 Major Limitations of Study by: Nissen & Wolski, N Engl J Med 2007;356: ? 40

41 Part II 41

42 Outline Cumulative Meta-analysis Study Ordering Limitations Indirect Comparison Adjusted Indirect Comparison Mixed Treatment Comparison Network Meta-analysis Issues with Indirect and MT Comparisons Observational Data Analysis Sources of Bias Methodological Issues Comparative Effectiveness Research Background Relation to Traditional Meta-analysis Current Status Summary and Conclusion 42

43 Cumulative Meta-Analysis Commonly executed with chronologically ordered RCTs Perform a new statistical pooling every time a new RCT becomes available Impact of each study on the pooled estimate may be assessed Reveals (temporal) trend towards superiority of the treatment or the control, or towards indifference Performed retrospectively, the year when a treatment could have been found to be effective could be identified Performed prospectively, an effective treatment may be identified at the earliest possible moment 43

44 Cumulative Meta-analysis: Study Ordering By control group event rate Low control event rates require large n to establish efficacy Arrangement by descending or ascending order helps assess study heterogeneity Study size Small studies imply high variability, and publication bias Pooling only small studies lead to overestimation of treat effect Study quality Need a scoring algorithm for RCTs To evaluate impact of poorly designed/conducted trials Effect size Impacts of inconclusive trials on results of analysis 44

45 Cumulative Meta-Analysis: Issues Statistical: Typically, frequentist approaches employed Inflation of Type I error with repeated analyses. Evolution of treatment effect over time Changes in patient demographics Changes in healthcare delivery Evolving medical practices 45

46 Indirect Comparison Well-conducted randomized controlled trials (RCTs) provide the most valid estimates of the relative efficacy of competing healthcare interventions However, many interventions have not been directly compared in RCTs Comparison of different healthcare interventions using data from disparate studies Often used because of a lack of, or sufficient, evidence from head-to-head comparative trials. 46

47 Indirect Comparison 47

48 Indirect Comparisons: Basic Assumptions Exchangeability/Similarity All trials comparing pairs of tx arms estimate same effect Different sets of trials being used are similar Independence between pairwise comparisons: Not true for more than 2 arm trials in Bucher s method. 48

49 Statistical Issues in Indirect Comparisons Reliable statistical procedures unavailable to validate assumptions of exchangeability/consistency Available procedures do not readily adjust for study heterogeneity Adjusted indirect comparison, misleading term Rigorous study of the operating characteristics of commonly used techniques not available Low power, as a result of use of two separate variances, Impacts reliability of non-inferiority conclusions Often leads to indeterminate results, due to inflated Type II error 49

50 Challenges with Observational Data Sources of Bias with Observational Data Overt and hidden biases Data quality Controlling for overt biases Regression approaches Propensity score analysis Post-hoc nature of analysis Controlling for hidden biases Prior Events Rate Ratio (PERR) adjustment Stringent assumptions Tannen et al. BMJ 2009;338:b81 doi: /bmj.b81 50

51 Challenges with Observational Data (cont.) Basic notion of PERR Hazard ratio of the exposed to unexposed for a specific outcome before the start of the study reflects the combined effect of all confounders Corollary: Division of the Incident Rate Ratio (IRR) during a study, by the IRR preceding the start of the study should correct for all confounders (both measured and unmeasured). PERRadj IRR = (REs/RUs) / (REp/RUp) Where R =rate, E = exposed group, U = Unexposed group, p = prior events, and s = study events (Cf. Tannen et al. BMJ 2009;338:b81 doi: /bmj.b81) Assumptions Constant covariate effect over time No treatment by-confounder interaction Independence of pre- and post-treatment event rates Events likely to occur both pre- and post therapy periods 51

52 Challenges with Observational Data (cont.) Research needed for Controlling for hidden bias Assessment of consistency between RCTs and Observational studies Methods for combining RCTs and non-rcts Conditions for and appropriateness of combining RCTs and non-rcts 52

53 Comparative Effectiveness Research (CER) 53

54 Background The American Recovery and Reinvestment Act (ARRA) appropriated $1.1B for comparative effectiveness research (CER): $400M allocated to the NIH $300M to the Agency for Healthcare Research and Quality (AHRQ), and $400M to Office of the Secretary of HHS Objective: To conduct research comparing "clinical outcomes, effectiveness, and appropriateness of items, services, and procedures that are used to prevent, diagnose, or treat diseases, disorders, and other health conditions." 54

55 Comparative Effectiveness Research (cont.) Congressional Budget Office: A rigorous evaluation of the impact of different options that are available for treating a given medical condition for a particular set of patients. Institute of Medicine (IOM): Generation and synthesis that compares the benefits and harms of alternative methods to prevent, diagnose, treat, and monitor a clinical condition or to improve the delivery of care The purpose is to assist consumers, clinicians, purchasers, and policy makers to make the informed decisions that will improve health care at both the individual and population levels. 55

56 Comparative Effectiveness Research A type of systematic review Synthesizes available scientific evidence on a special topic Expands the scope of a typical systematic review Goes beyond the effectiveness of a single intervention Compares the relative benefits and harms among a range of available treatments or interventions for a given condition Parallels decisions facing clinicians, patients, and policy makers who must choose among a variety of alternatives in making diagnostic, treatment, and health-care delivery decisions 56

57 Limitations of Traditional Meta-Analysis also Apply to CER Quality Publication bias Garbage in garbage out phenomenon Heterogeneity Apples and oranges phenomenon Methodological issues Lack of uniform approaches Handling heterogeneity Assessing bias Covariate issues 57

58 Current Status of CER NIH and AHRQ funding grants with ARRA CER funds Initial focus on development of methods AHRQ/NIH sponsored panels/workshops Academic institutions 2010 University of Pennsylvania Annual Conference on Statistical Issues in Clinical Trials: 58

59 A New Frontier for Statistical Research Opportunity to take another look at old problems Issues with traditional meta-analysis Opportunity to apply existing results to new area Role for decision theory and Bayesian approaches New problems that require fresh approaches. Defining therapeutic indices for CER 59

60 Concluding Remarks Meta-analysis and CER pose considerable practical and methodological challenges Critical role for statisticians to engage in methodological work Without sound methodological foundation, potential for adverse impacts on public health 60

61 Selected References on Indirect Comparisons Bucher HC, Guyatt GH, Griffith LE, Walter SD. The results of direct and indirect treatment comparisons in meta-analysis of randomized controlled trials. J Clin Epidemiol 1997;50(6): Eddy DM, Hasselblad V, Shachter R. An introduction to a Bayesian method for meta-analysis: The confidence profile method. Med Decis Making Jan-Mar;10(1): Song F, Altman DG, Glenny AM, Deeks JJ. Validity of indirect comparison for estimating efficacy of competing interventions: empirical evidence from published meta-analyses. BMJ. 2003;326:472. Lu G, Ades AE. Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med 2004;23: Caldwell DM, Ades AE, Higgins JP. Simultaneous comparison of multiple treatments: combining direct and indirect evidence. BMJ 2005;331: Jansen JP, Crawford B, Bergman G, Stam W. Bayesian meta-analysis of multiple treatment comparisons: an introduction to mixed treatment comparisons. Value Health. 2008; 11: Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med. 2009;28: Song F, Loke YK, Walsh T, Glenny AM, Eastwood AJ, Altman DG. Methodological problems in the use of indirect comparisons for evaluating healthcare interventions: survey of published systematic reviews. BMJ Apr 3;338 Lumley T. Network meta-analysis for indirect treatment comparisons. Stat Med 2002;21(16): Ades AE. A chain of evidence with mixed comparisons: models for multi-parameter synthesis and consistency of evidence. Stat Med 2003;22(19): Caldwell DM, Ades AE, Higgins JP. Simultaneous comparison and indirect evidence. BMJ 2005;331(7521): Vandermeer BW, Buscemi N, Liang Y, Witmans M. Comparison of meta-analytic results of indirect, direct, and combined comparisons of drugs for chronic insomnia in adults: a case study. Med Care 2007;45(10 Supl 2):S166-S172. Song F, Harvey I, Lilford R. Adjusted indirect comparison may be less biased than direct comparison for evaluating new pharmaceutical interventions. J Clin Epidemiol 2008;61(5): Glenny AM, Altman DG, Song F, Sakarovitch C, Deeks JJ, D'Amico R, et al. Indirect comparisons of competing interventions. Health Technol Assess 2005;9(26): Nissen SE, Wolski K. Effect of Rosiglitazone on the risk of myocardial infarction and death from cardiovascular causes. The New England Journal of Medicine 2007; 356(24):

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