## Box 119 Estimating HRs from summary statistics

To calculate a HR we require estimates of the observed minus expected (O-E) number of events and its variance (V).

If the variance is presented, then O-E maybe calculated by simple manipulation of the x2 or p-value.

(no. events/no. entered)
 Surgery + CT Surgery O-E Variance GOG 52/113 62/112 -6.75 28.42 MDAH 12/18 15/17 -4.65 5.88 Mayo 12/22 11/23 0.21 5.71 NCI4 9/17 5/8 -1.42 2.64 NCI5 22/38 24/41 -0.33 11.47 NCI6 9/21 11/20 -2.00 4.90 EORTC 92/193 105/188 -13.31 48.84 DFCI 7/21 8/25 -0.20 3.74 ECOG 9/24 11/23 -1.70 4.96 Bergonie 11/28 19/26 -7.60 6.96 SSG 65/121 69/119 -5.35 32.72 Rizzoli 7/16 13/22 -2.10 4.85 IGSC 14/40 25/46 -5.09 9.73 SAKK 4/12 4/12 0.08 2.00 Total 325/684 382/682 -50.21 Surgery Surgery better + CT better Fig. 11.10 Example HR plot from a meta-analysis of chemotherapy in soft tissue sarcoma. Reproduced with permission from [36]. indicating the 95 per cent and 99 per cent confidence intervals. The size of the box is proportional to the statistical variance in the trial such that, the bigger the box, the greater the number of events and, usually, the bigger the trial. A trial reaches conventional levels of significance if the 95 per cent confidence intervals do not cross the equivalence line. The diamond at the bottom of the plot illustrates the combined results for all trials, with the edges denoting the 95 per cent confidence interval. An overall result reaches significance at the 5 per cent level if the edge of the diamond does not cross the equivalence line. Trials are often ordered chronologically with the oldest trial at the top.
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