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- 1. Meta Analysis Statistical analysis for Systematic Reviews of Randomised Clinical Trials Contents
- 2. Contents - Example - History – Fisher/Cochran, Peto, Cochrane, EBM - Cochrane centre and Cochrane collaboration. - Systematic reviews - Statistical methodology - combining results - testing heterogeneity - comparability and quality of studies - publication bias - Examples and Stata analysis - Current issues – x-over trials, non RCTs, epidemiological studies - Conclusions blockers eg
- 3. Example: Reports of several clinical trials of the effect of blockers on survival after Myocardial Infarction are available (Yusuf et al looked at 65 trials of different types). The main outcome variable is live/dead status at 1 month after treatment started. The main test statistic is the Odds Ratio of surviving (treatment .v. placebo). The statistical problems are: - How to combine the ORs and obtain an overall OR with CLs - How to assess and allow for the ‘true’ ORs varying with study ( Heterogeneity ) - How to assess and allow for the quality and comparability of the studies - How to assess whether these studies can be assumed a random sample of all such studies i.e. are some studies with different (?non-significant) results not being published – Publication Bias History 1
- 4. History 2: Origins In the 1970s Richard Peto and others, because clinical trials of treatments for heart disease were often small and thus of low power, performed and published a number of systematic reviews of such trials. Peto identified or devised appropriate methods for combining test statistics such as odds ratios, relative risks and differences between proportions and means from different studies. In essence the problem is the same as that of multi-centre trials. But variation in patient types, treatment regimes, outcome measures, study design and general trial procedures is much greater between unrelated studies than between centres following the same trial protocol. This means that the aggregation of results has to be done very carefully and interpreted equally cautiously. History 3
- 5. History 6: The Cochrane Collaboration In 1992 Iain Chalmers at the Oxford Perinatal Research Unit and others set up the Cochrane Centre in Oxford to encourage and document systematic reviews of the effectiveness of Health interventions. It was named after a distinguished epidemiologist Archie Cochrane who in 1979 had written: "It is surely a great criticism of our profession (Medicine) that we have not organised a critical summary, by specialty or subspecialty, adapted periodically, of all relevant randomized controlled trials.” http://hiru.mcmaster.ca/cochrane/cochrane/archieco.htm In October 1993 - at what was to become the first in a series of annual Cochrane Colloquia - 77 people from eleven countries co-founded 'The Cochrane Collaboration’ to encourage and document systematic reviews world-wide. This happened in parallel with the ‘Evidence based medicine’ movement started by Sackett and others. Systematic reviews
- 6. Proposers need to specify: - the condition or disease - the treatment comparisons of interest - the types of study to be reviewed - the strategy for searching the literature and elsewhere - the outcome variables and planned analysis. The Cochrane Collaboration publish guidelines entitled “ How to conduct a Cochrane review” Systematic Reviews Stroke eg
- 7. Results from 9 studies comparing Length of Stay (LOS) in hospital of Stroke patients receiving Specialist and Routine care Specialist care Routine management Mean Mean N LOS SD N LOS SD 155 55 47 156 75 64 31 27 7 32 29 4 75 64 17 71 119 29 18 66 20 18 137 48 8 14 8 13 18 11 57 19 7 52 18 4 34 52 45 33 41 34 110 21 16 183 31 27 60 30 27 52 23 20 paired plot
- 8. Stroke studies paired mean LOS Mostly shorter LOS with specialist care, but some evidence of heterogeneity Formulae Paired t test structure
- 9. Combining Results The primary outcome in this study is the mean length of stay (LOS). So for study i we have: Study Treatment 1 Treatment 2 Difference i No. Mean s.d. No. Mean s.d. 1 N 11 y 11 s 11 N 12 y 12 s 12 . .. .. .. .. .. .. i N i1 y i1 s i1 N i2 y i2 s i2 y i = y i1 - y i2 . .. .. .. .. .. .. k N k1 y k1 s k1 N k2 y k2 s k2 pooled variance s pi 2 = (( N i1 -1) s i1 2 + ( N i2 -1) s i1 2 )/( N i1 + N i2 -2) var ( y i ) = s i 2 = s pi 2 (1/ N i1 + 1/ N i2 ) W i = 1/ s i 2 Combined estimate = W i y i / W i with variance = 1 / W i General Formulae
- 10. Formulae for combining test statistics Normand, S-L. T (1999) Statist. Med 18, 321-359 Fixed-effects model: ~ Stroke results
- 11. Results from 9 studies comparing Length of Stay (LOS) in hospital of Stroke patients receiving Specialist and Routine care Difference 95% CLs Weights W i . bet. Means Low High Fixed Random -20 -32.5 -7.5 0.0246 0.0036 -2 -4.8 0.8 0.4886 0.0042 -55 -62.7 -47.3 0.0654 0.0040 -71 -95.0 -47.0 0.0067 0.0026 -4 -12.8 4.8 0.0495 0.0039 1 -1.2 3.2 0.8173 0.0043 11 -8.1 30.1 0.0105 0.0030 -10 -15.6 -4.4 0.1245 0.0041 7 -1.9 15.9 0.0483 0.0039 Combined estimate MD w = W i y i / W i = -3.5 with variance = 1 / W i = 0.6115 ............. Q = W i ( y i - MD w ) 2 = 241.1 ~ 2 8 Forest plot
- 12. The overall weighted mean differences are : Mean 95% CLs Fixed effects: -3.5 -5.0 -2.0 Random effects: -14.2 -24.8 -3.5 Test of heterogeneity: Q = 241.1 Treated as 2 with 8 df p = 0.0000 Funnel plot Individual and combined results
- 13. Assessing publication bias Meta analysis in RevMan
- 14. Meta analysis in Stata can be performed with the Metan command written by: Michael J Bradburn , Jonathan J Deeks , Douglas G Altman Institute of Health Sciences, Oxford Metan help etc... Lidocaine eg
- 15. Results Lidocaine treatment for MI v Placebo S-L T Normand Statist. Med (1999) 18, 321-359 Meta Analysis in RevMan
- 16. RevMan analysis of GBS data
- 17. RevMan forest plot
- 18. Review Manager (RevMan) from the Cochrane Collaboration http://www.cochrane.org/software/revman.htm New facilities in RevMan
- 19. <ul><li>New developments in RevMan </li></ul><ul><li>The generic inverse variance method; </li></ul><ul><li>2. The I 2 measure of heterogeneity. </li></ul> GIV theory
- 20. <ul><li>The generic inverse variance method </li></ul><ul><li>Traditionally each study needs to supply </li></ul><ul><li>the mean, sd and n of the outcomes or the number with a particular outcome with the denominator n for each of the two treatment groups; </li></ul><ul><li>RevMan then calculates </li></ul><ul><li>the mean difference (MD), odds ratio(OR) or relative risk (RR) as a comparison of the benefits of the two treatments; </li></ul><ul><li>a variance for the MD, OR or RR from the sds or proportions from each treatment group; </li></ul><ul><li>the square root of this variance as the standard error of the MD, OR or RR to obtain the confidence limits on the ‘forest’ plot; </li></ul><ul><li>the inverse of this variance is then used to weight the MDs, ORs or RRs from the individual studies in the calculation of the combined estimate; </li></ul> data
- 21. Only need the first two columns… Difference 95% CLs Weights W i bet. Means Var(diff) Low High Fixed Random -20 40.6 -32.5 -7.5 0.0246 0.0036 -2 2.1 -4.8 0.8 0.4886 0.0042 -55 15.3 -62.7 -47.3 0.0654 0.0040 -71 150.2 -95.0 -47.0 0.0067 0.0026 -4 20.2 -12.8 4.8 0.0495 0.0039 1 1.2 -1.2 3.2 0.8173 0.0043 11 95.4 -8.1 30.1 0.0105 0.0030 -10 8.0 -15.6 -4.4 0.1245 0.0041 7 20.7 -1.9 15.9 0.0483 0.0039 C ombined estimate MD w = W i y i / W i = -3.5 -14.1 with variance = 1 / W i = 0.6115 (-5.0,-2.0) (-24.5,-3.8) Q = W i ( y i - MD w ) 2 = 241.1 ~ 2 8 I 2 = 100*(Q – df)/Q = 96.7% forest plot
- 22. Trials in same order as table – GIV needs just 2 values for each trial Compare with previous
- 23. The overall weighted mean differences are : Mean 95% CLs Fixed effects: -3.5 -5.0 -2.0 Random effects: -14.2 -24.8 -3.5 Test of heterogeneity: Q = 241.1 Treated as 2 with 8 df p = 0.0000 Heterogeneity I 2 Individual and combined results
- 24. 2. The I 2 measure of heterogeneity(1) Heterogeneity – Systematic or Random Systematic heterogeneity may arise because studies differ for a specific reason e.g. quality of study, biases or errors, type of patient, other non-random factors … usually implies that studies should be omitted or analysed separately; Random heterogeneity between studies in the measures of the relative merits of two treatments is generally taken to represent differences that would occur in routine use of the treatments in similar institutions in the future. It is usually assumed to indicate that the combined estimate should be obtained using a random effects approach to take between study variation into account in the calculation of the combined estimate. Stroke trials
- 25. Trials in same order as table – GIV needs just 2 values for each trial outliers moved
- 26. All mean differences about –15 … I 2 = 24.6%
- 27. Areas - Cross - over trials (treated as 2 parallel groups is safe) - non randomised trials; - observational clinical studies; - epidemiological studies. Methodology - combining medians - linear model and survival data analysis results (GIV) - linear modelling approaches to combining study results; (stratifying by study quality, patient and treatment variations etc) - Bayesian methods - Others.... Current Issues Conclusions
- 28. Conclusions - Meta analysis of epidemiological studies is know to be fraught with many more problems than arise in the process of combining randomised clinical trials -- extra care is needed; - must be aware that study results are data like any other and the problems are not different in principle to those faced in any statistical analysis; - raw data from the studies is always better than summarised results; - those doing a review should consult the Cochrane Guidelines.They need an exhaustive search strategy and careful classification of studies; - The analysis needs to be cautious, although the particular method may not be crucial, and the form and nature of any heterogeneity found needs to be considered carefully in context and taken into account in the analysis. References
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