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Heterogeneity in meta-analysis

Systematic review and meta-analysis

Source & acknowledgement

https://www.terripigott.com/meta-analysis https://mason.gmu.edu/~dwilsonb/ma.html https://www.campbellcollaboration.org/research-resources/training-courses.html https://handbook-5-1.cochrane.org/ https://www.youtube.com/user/Biostat100 https://www.youtube.com/user/collaborationtube https://www.meta-analysis.com/pages/videotutorials.php?cart=BWJJ3522355

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Heterogeneity in meta-analysis

  1. 1. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Heterogeneity in meta-analysis Dr. S. A. Rizwan M.D., Public Health Specialist & Lecturer, Saudi Board of Preventive Medicine – Riyadh, Ministry of Health, KSA 25.11.2019 1 With thanks to Martin Bland
  2. 2. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Outline • What is heterogeneity? • Sources of heterogeneity • Impact of heterogeneity on different parameters • Quantification of heterogeneity • Dealing with heterogeneity 25.11.2019 2
  3. 3. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What do we mean by Heterogeneity? 25.11.2019 3 It’sthe variance in trueeffects(not observed effects) that we careabout
  4. 4. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Where does it arise from? • Studies differ in terms of • Patients • Interventions • Outcome definitions • Design • This is called Clinical heterogeneity • Variation in true treatment effects in magnitude or direction • This is called Statistical heterogeneity 25.11.2019 4
  5. 5. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Where does it arise from? • Statistical heterogeneity may be caused by • clinical differences between trials • methodological differences between trials • unknown trial characteristics • Even if studies are clinically homogeneous there may be statistical heterogeneity 25.11.2019 5
  6. 6. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Why estimate heterogeneity? It affects weight, mean, SE and utility of effects 25.11.2019 6
  7. 7. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on Weight 25.11.2019 7
  8. 8. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the weights 25.11.2019 8
  9. 9. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course W = 1/ (V1) Weights when T2 = 0 25.11.2019 9
  10. 10. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Weights when T2 > 0 25.11.2019 10 1W = 1/ (V +T 2 )
  11. 11. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on Standard Error 25.11.2019 11
  12. 12. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the standard error 25.11.2019 12 … the confidence interval, and thep-value
  13. 13. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 13
  14. 14. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 14
  15. 15. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 15
  16. 16. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 140 25.11.2019 16
  17. 17. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Precision ofthe mean effect 25.11.2019 17
  18. 18. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Precision ofthe mean effect 25.11.2019 18
  19. 19. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Precision ofthe mean effect 25.11.2019 19
  20. 20. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on Mean ES 25.11.2019 20
  21. 21. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the mean ES 25.11.2019 21
  22. 22. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the mean ES • As heterogeneity increases, mean effect shifts away from larger studies and towards smaller studies 25.11.2019 22
  23. 23. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 23
  24. 24. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 24
  25. 25. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Impact on substantive utility 25.11.2019 25
  26. 26. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It affects the substantive utility 25.11.2019 26 Is the treatment effectivefor everyone, or effectivefor some and harmful for others?
  27. 27. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 27
  28. 28. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 28
  29. 29. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 150 25.11.2019 29
  30. 30. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 30
  31. 31. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 31
  32. 32. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 32
  33. 33. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 33
  34. 34. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Dispersion ofthe individual effects 25.11.2019 34
  35. 35. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Dispersion ofthe individual effects 25.11.2019 35
  36. 36. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course How do we quantify heterogeneity? 25.11.2019 36
  37. 37. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Two-step process • Isolate the real dispersion • Translate this into useful indices 25.11.2019 37
  38. 38. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 1. Isolate the real dispersion 25.11.2019 38
  39. 39. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What we’d like to see if the true effect is the same in all studies 25.11.2019 39
  40. 40. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What we might see if the true effect is the same in all studies 25.11.2019 40
  41. 41. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Is there real dispersion? 25.11.2019 41
  42. 42. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It depends on the precision 25.11.2019 42
  43. 43. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course It depends on the precision 25.11.2019 43
  44. 44. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Key point • We can easily compute variance of observed effects • But this is due partly to real differences in effects and partly to sampling error within studies • We need to isolate the between-studies variance 25.11.2019 44
  45. 45. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 45
  46. 46. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 46
  47. 47. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 47
  48. 48. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 170 To assess heterogeneity • Compute observed variance • Estimate how much variance would be expected if true effect is identical in all studies • Observed minus expected is estimate of true variance 25.11.2019 48
  49. 49. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Q df Q-df Isolating the real dispersion 25.11.2019 49
  50. 50. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 2. Translate into useful indices 25.11.2019 50
  51. 51. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Indices related to heterogeneity 25.11.2019 51 Q−df Basis for all indices p Test of null T Standard deviation of true effects T2 Variance of true effects I2 Proportion of true/total variance
  52. 52. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course P-value • Can we conclude that there is some variance in true effects • Depends on amount of excess variance and the amount of evidence 25.11.2019 52
  53. 53. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 53
  54. 54. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 54
  55. 55. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course 25.11.2019 55
  56. 56. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Statistics apply to both models 25.11.2019 56
  57. 57. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course I square – an alternative of Q • Q is statistically under-powered when the number of studies is low and when the sample size within the studies is low • Larger values of I2, the more heterogeneity • 75%: large heterogeneity • 50%: moderate heterogeneity • 25%: low heterogeneity 25.11.2019 57
  58. 58. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Caution! • I2 is NOT a measure of absolute heterogeneity • I2 tells us what proportion of the observed dispersion reflects differences in true scores rather than random sampling error 25.11.2019 58
  59. 59. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What proportion of the observed variance is real? 25.11.2019 59 I2
  60. 60. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Test for heterogeneity: χ2 = 4.91, df = 2, P=0.086 Heterogeneity 25.11.2019 60
  61. 61. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What happens when heterogeneity is not significant • No statistical evidence for difference between trials • But, test for heterogeneity has low power – the number of studies is usually low - and may fail to detect heterogeneity as statistically significant when it exists. • This cannot be interpreted as evidence of homogeneity. • To compensate for the low power of the test a higher significance level is sometimes taken, P < 0.1 for statistical significance. 25.11.2019 61
  62. 62. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course What happens when heterogeneity is significant • Differences between trials exist • It may be invalid to pool the results and generate a single summary result • Describe variation • Investigate sources of heterogeneity • Account for heterogeneity 25.11.2019 62
  63. 63. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Dealing with heterogeneity • Do not pool — narrative review. • Ignore heterogeneity and use fixed effect model: • confidence interval too narrow, • difficult to interpret pooled estimate, • may be biased. • Explore heterogeneity, can we explain it and remove it? • Allow for heterogeneity and use random effects model • Change the ES measure • Exclude extreme outlier studies (caution!) 25.11.2019 63
  64. 64. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating sources of heterogeneity • Subgroup analysis: • subsets of trials, • subsets of patients, • subsets should be pre-specified to avoid bias. • Relate size of effect to characteristics of the trials, e.g.: • average age, • proportion of females, • intended dose of drug, • baseline risk. • ‘Meta-regression’ can be used. 25.11.2019 64
  65. 65. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity – Subgroups • Split into 26 sub-studies with more uniform age groups. • Before adjustment for age: X2 = 127, df=9, P<0.001. • After adjustment for age: X2 = 45, df=23, P=0.005. • A considerable improvement, but still some heterogeneity present. 25.11.2019 65
  66. 66. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity – Subgroups • We want to see if the mean effect sizes for studies grouped by age of student differ from each other • Question: What are our assumptions about τ2 ? • Option 1: We assume that each group has its own underlying distribution of effect sizes, so that we are really estimating μ and separate variance components for each category of the age. • Usually we don’t have a large number of studies within each group, and our estimates of the variance components will not be precise • Option 2: Assume that we have a common variance component τ2 25.11.2019 66
  67. 67. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity – meta-regression • Line fitted by meta-regression. • Odds ratios of ischemic heart disease (and 95% CI) according to the average extent of serum cholesterol reduction achieved in each of 28 trials. • Overall summary of results is indicated by sloping line. • Results of the nine smallest trials have been combined. 25.11.2019 67
  68. 68. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • Alternative graphical representation to forest plot. • Horizontal axis: 1/standard error. • Horizontal axis will be zero if standard error is infinite, a study of zero size. • Vertical axis: effect/standard error. • This is the test statistic for the individual study. • For 95% of studies, we expect this to be within 2 units of the true effect. 25.11.2019 68
  69. 69. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • Corticosteroids for severe sepsis and septic shock (Annane et al., 2004) -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Long, low dose trials 25.11.2019 69 Galbraith plot for log OR Low doses & long duration trials
  70. 70. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We can add a line representing the pooled effect. • Plot (pooled effect)/se against 1/se. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 25.11.2019 70 Galbraith plot for log OR Low doses & long duration trials
  71. 71. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We can add a line representing the pooled effect. • Plot (pooled effect)/se against 1/se. • 95% limits will be 2 units above and below this line. • We expect 95% of points to be between these limits if there is no heterogeneity. • This is true for low dose, long duration trials. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits 25.11.2019 71 Galbraith plot for log OR Low doses & long duration trials
  72. 72. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We have two points outside the 95% limits and one on the line. • We can investigate them to see how these trials differ from the others. • The pooled effect is smaller so the line is less steep. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits 25.11.2019 72 Galbraith plot for log OR All trials
  73. 73. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating heterogeneity - Galbraith plot • We could reanalyse taking dosage and duration separately. • These trials are all of high dose or short duration treatments. -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Long, low dose Short, high dose Other 25.11.2019 73 Galbraith plot for log OR All trials
  74. 74. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Galbraith plot or Forest plot? Wagner CSG Klatersky Schumer Lucas Sprung Bone VASSCSG Luce Slusher Bollaert Briegel Chawla AnnaneYildiz -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits Pooled Yildiz Annane Chawla Briegel Bollaert Slusher Luce VASSCSG Bone Sprung Lucas Schumer Klatersky CSG Wagner .01 .1 1 10 100 Odds ratio of death 25.11.2019 74 “Conventional meta-analysis diagrams . . . are not very useful for investigating heterogeneity. A better diagramfor this purpose was proposed by Galbraith . . .” (Thompson, 1994). Is this really true?
  75. 75. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Galbraith plot or Forest plot? Wagner CSG Klatersky Schumer Lucas Sprung Bone VASSCSG Luce Slusher Bollaert Briegel Chawla AnnaneYildiz -4 -2 0 2 Difference/standarderror 0 2 4 6 1/standard error Pooled effect 95% limits Pooled Yildiz Annane Chawla Briegel Bollaert Slusher Luce VASSCSG Bone Sprung Lucas Schumer Klatersky CSG Wagner .01 .1 1 10 100 Odds ratio of death 25.11.2019 75 Trials outside the Galbraith limits will be trials where the 95% confidence interval does not contain the pooled estimate. We can spot them from the forest plot.
  76. 76. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course L’ abbe plot 25.11.2019 76 • Ideally a L'Abbé plot should have the symbols appropriate to the size of the trials. • There is an inset for the symbol size, and the two colours show trazodone used for erectile dysfunction in two different conditions (and with clear clinical heterogeneity). Trazodone for erectile dysfunction in psychogenic erectile dysfunction (dark symbols) and with physiological or mixed aetiology (light symbols)
  77. 77. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating sources of heterogeneity • Cannot always explain heterogeneity • Example: Effect of breast feeding in infancy on blood pressure in later life (Owen et al., 2003) • *In parenthesis: age at which blood pressure measured 25.11.2019 77
  78. 78. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Investigating sources of heterogeneity • Cannot always explain heterogeneity • X2=59.4, 25df, P<0.001 • Three age groups: P=0.6. • Born before or after 1980: P=0.8. • Have to accept it and take it into account by using a random effects model. 25.11.2019 78
  79. 79. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Take home messages • Heterogeneity is not a bad thing • It should not be ignored • It should be understood, explored and quantified • And it should be properly handled in analysis • Discussion of meta-analysis findings should include a major note on heterogeneity of effects 25.11.2019 79
  80. 80. Saudi Board of Preventive Medicine, Riyadh Ministry of Health, KSA Lecture 07/10 Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course Thank you Kindly email your queries to sarizwan1986@outlook.com 25.11.2019 80

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