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Meta-analysis of Hazard Ratios

Meta-analysis of Hazard Ratios. Key References. Parmar M.K.B., et al. Extracting summary statistics to perform meta-analysis of the published literature for survival endpoints. Statist Med. 1998. 7; 2815-34.

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Meta-analysis of Hazard Ratios

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  1. Meta-analysis of Hazard Ratios

  2. Key References • Parmar M.K.B., et al. Extracting summary statistics to perform meta-analysis of the published literature for survival endpoints. Statist Med. 1998. 7; 2815-34. • Michiels S., et al. Meta-analysis when only the median survival times are known: a comparison with individual patient data results.

  3. Three ways to compare time-to-event outcomes • Point in time – Odds Ratio • Median time – Ratio of medians • Hazard Ratio

  4. Point in time • Odds ratio or other measure at a single point in time • Does not take censoring into account • Discards data • Choice of time point can change results • May be misleading if survival curves cross or are erratic

  5. Median Time • Ratio of median times-to-event • No concern about time point selection, but still somewhat arbitrary • Ignores censoring • Discards data • May be misleading • Methods to calculate variance unclear

  6. Hazard Ratio • The ratio of the survival functions of both treatment arms • Accounts for censoring • Includes all data • More tolerant of strange curve behaviour • Describes all of patient experience

  7. Michiels et al study • Used individual patient data from 13 meta-analyses to directly compare the three methods • Found 4 of 13 results discordant using OR vs. HR • Found 5 of 13 results discordant using MR vs. HR • “…neither the median ratio nor the OR can be recommended as a surrogate method for analyzing time to event outcomes.”

  8. In other words… • Conducting a meta-analysis using point-in-time or median times may be worse than doing nothing at all • If in error, likely to result in finding no significant effect when one exists

  9. So why not HR’s? • Because the &*$^%*$& researchers don’t report it! • Give p-values but no HR’s • Give HR’s but no confidence intervals • Give none of the above, only survival curves • More of a problem the older the study • Point-in-time measures are accessible in almost every study, so this method has been commonly used due to convenience

  10. Parmar Toolbox • Parmar et al provides a tool box of methods to get the info you need for an HR meta-analysis • Several different sets of formulas, based on what data you have • A method to derive the info from the survival curves if all else fails

  11. Extracting HR from curves • Done by measuring probabilities off of the curves and then feeding the measurements into an algorithm • Measured at multiple time points, but the exact number of points is arbitrary (no more than 20% events in any time period) • Should have two people (you and a student?) do the measurements • Requires a lot of calculations best implemented in Excel • Makes some assumptions regarding censoring, but you can use the known censoring as well

  12. Extracting HR from curves • Imprecise (roughly 1 or 2 decimal places), but not biased • Tedious and annoying, but feasible

  13. Meta-analysis Method • In RevMan, use the generic inverse variance method • For each study, you need the ln(HR) and the SE(ln(HR)) • RevMan can translate the ln(HR)’s back into HR’s automatically in forest plot

  14. Things to remember • Make sure all HR’s are expressed in the same manner (trmt/control) – may require taking the inverse of reported values • Do a face validity check of all the calculations – do they seem to be the right direction? Do the values seem right? • Use all of the given data as a cross check in the worksheet, but use reported HR’s in actual analysis for preference

  15. What if you don’t have enough data for all of the studies? • Option 1 - Don’t do the analysis • Probably best if you have ln(HR) and SE(ln(HR)) for less than half of the studies • A point-in-time analysis may be a fall-back position, but needs appropriate discussion of its drawbacks • May be worth contacting authors, if little is needed (such as a p-value)

  16. What if you don’t have enough data for all of the studies? • Option 2 - Do the analysis, and also a sensitivity analysis • Probably best if you have ln(HR) and SE(ln(HR)) for more than half of the studies, but still much less than all of them • Trim and fill can give you an idea regarding missing studies • Add dummy studies in for included but unanalyzed studies

  17. What if you don’t have enough data for all of the studies? • Option 3 - Do the analysis, with discussion • Probably ok if you have ln(HR) and SE(ln(HR)) for most of the studies, and there aren’t that many • Add discussion about the possible bias introduced by not including all known studies

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