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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.Michiels S., et al. Meta-analysis when only the median survival times are known: a comparison with individual patient d

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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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