- Letter
- Open Access

# Response to: Practical methods for incorporating summary time-to-event data into meta-analysis

- Yu Wang
^{1, 2}and - Tingting Zeng
^{3}Email author

**14**:391

https://doi.org/10.1186/1745-6215-14-391

© Wang and Zeng; licensee BioMed Central Ltd. 2013

**Received:**19 April 2013**Accepted:**1 November 2013**Published:**19 November 2013

## Abstract

A response to and comment on Practical methods for incorporating summary time-to-event data into meta-analysis, by Jayne F Tierney *et al*.

## Keywords

- Practical Method
- Individual Trial
- Excel Spreadsheet
- Trial Report
- Estimate Hazard Ratio

## Findings

*P*-value and events in each arm (and the randomization ratio was 1:1), these data can be used to estimate the O-E using Tierney’s equation 14:

In the example of the present article, the log-rank *P*-value of 0.075 gave a z-score of 1.78 according to the latter part of Tierney’s equation 14. Nevertheless, we found 2-sided *P*-value of 0.075 gave a z-score of 1.78 by using the net tools [2]. But the z-score for the 2-sided *P*-value should be divided by 2 as described by Tierney and colleagues. Thus we can speculate that the z-score for a *P*-value of 0.075 should be 0.89, which was produced from 1.78/2.

We also advertently found that a right-tailed *P*-value of 0.0375 gave a z-score of 1.78 by using the previous mentioned net tools [2], and 0.0375 by chance equals 0.075/2. So we speculated that the latter part of equation 14 required a more accurate representation of z-score and *P*-value as: z-score for (*P*-value/2).

Tierney and colleagues reported that if a 1-sided *P*-value was reported, it can be used directly to calculate the z-score without dividing by 2. According to Li [3], a 1-sided *P*-value was used in log-rank test or Cox regression, and the exact *P*-value was given in the table for Chi-square (right-tailed test). However, we verified that a right-tailed *P*-value 0.075 gave a z-score of 1.44 by using the previous mentioned net tools [2].

Therefore, we can conclude that a 2-sided *P*-value can be used to directly to obtain the z-score. The latter part of equation 14 need to be modified into: z-score for *P*-value. Otherwise, a 1-sided *P*-value divided by 2 is required to obtain the z-score and the latter part of equation 14 should be expressed more exactly as: z-score for (*P*-value/2).

## Authors’ reply

Jayne F Tierney, Lesley A Stewart, Davina Ghersi, Sarah Burdett and Matthew R Sydes.

*P*-value that should be divided by 2 in equation 14 and not the z-score. This was the intention, and is more explicit in the original equation [4], provided in the appendix of Tierney and colleagues [1]:

and the related explanatory text altered accordingly: “As well as the events on each arm and overall, the z-score for half the two-sided *P*-value is required”

However, we disagree with the other points raised. It is suggested that one-sided *P*-values are used in log-rank tests and Cox regression models [3], whereas we find that it is standard practice to present two-sided (or two-tailed) *P*-values. Also, to our knowledge, all major statistical packages output two-sided *P*-values by default. It is therefore reasonable to assume that a *P*-value quoted in a trial publication will be two-sided unless otherwise stated, and to use this in equation 14. However, as described in the text [1]: “If a one-sided *P*-value is reported it can be used directly to obtain the z-score.”

This is justified by equation 14 being derived algebraically from the definition of the log-rank statistic as a normally-distributed random variable, and by the fact that a one-sided *P*-value (assuming the most extreme direction of effect) is half the magnitude of the corresponding two-sided *P*-value.

The correspondents go on to suggest that either a two-sided *P*-value or a one-sided *P*-value divided by 2 can be used directly in equation 14. In fact, this would produce an incorrect z-score and hazard ratio. Using the example in Tierney and colleagues, the z-score for the reported *P*-value of 0.075/2 (= 0.0375) is 1.78, as the correspondents themselves found using internet tools. This produces an O-E of 19.57 and hazard ratio of 0.85; the latter being identical to that reported in the trial publication [5]. If, as the correspondents suggested, we had used the reported *P*-value directly in equation 14, we would have obtained a z-score of 1.44, O-E of 15.82 and an incorrect hazard ratio of 0.88.

Finally, researchers wishing to estimate hazard ratios from published time-to-event data need not rely on deriving them manually using the equations provided [1], but instead can use the Excel spreadsheet that accompanies the paper. Moreover, they can use this to cross-check hazard ratios derived from different methods of estimation.

## Declarations

### Acknowledgements

We thank all the people who have been involved in our study.

## Authors’ Affiliations

## References

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## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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