[R-meta] Power analysis of meta-analysis

CHAPPELL Francesca F@Ch@ppe|| @end|ng |rom ed@@c@uk
Thu Jun 18 12:05:47 CEST 2020

There is a statistical literature against performing power calculations for existing datasets. Please see

https://www.tandfonline.com/doi/pdf/10.1198/000313001300339897?needAccess=true  or https://journals.lww.com/annalsofsurgery/Fulltext/2019/01000/Don_t_Calculate_Post_hoc_Power_Using_Observed.46.aspx#O2-46-4 or

This last one has a subsection on post hoc power calculations in the Section “Common Pitfalls”. I would gently point this out to the editors.


-----Original Message-----
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf Of Paul Chang
Sent: 18 June 2020 02:49
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Power analysis of meta-analysis

Dear list,

I recently got the opportunity to revise my manuscript, which is a systematic review and prognostic meta-analysis. The effect estimates of the included studies are time-to-event data, i.e. ln(HR) and standard error of ln(HR). All the included studies are retrospective cohort studies, and the adjusted hazard ratios from multivariate cox regression model or from the propensity score matching cohort in the included studies were extracted for meta-analysis.

The editors and reviewers commented that I cannot assume that either because all available data was included or because the total sample size is large that power was sufficient. They suggested that I should incorporate one of the following approach to justify the sample size.
1. Perform power analysis: use a traditional sample size calculation to report the power with the given sample size to detect the difference considered to be clinically important (can assume independence of the observations across studies for the calculation) 2. Perform Trial sequential analysis (TSA)

Due to the fact that the currently available TSA software developed by Copenhagen Trial Unit can only take care of continuous and binary data in the raw form, but not time-to-event data or any pre-calculated effect estimates, the first option seems to be the only solution. However, I'm not sure how to perform power analysis in meta-analysis. I've found a few websites to calculate power for meta-analysis, but they required the "effect size", which I assume is the Cohens' d from continuous data, and I have no idea how to convert the pooled hazard ratios to Cohens' d. Also, I'm aware that the powerEpi.default() function in "powerSurvEpi" package in R may be the solution. Yet, this function accounts for only two covariates but most of the hazard ratios I extracted were adjusted for more than two covariates in the multivariate Cox regression model. Moreover, some of the studies report only hazard ratios without reporting the event number, which is a required argument in the function. Finally, the function also requires to input the square of the correlation between the covariate of interest and the other covariate, which I certainly don't have.

Can someone please give me some hints on how to solve this problem?
Thank you in advance and take care !

Chang, Chun-Yu (Paul)
Class 2018, School of Medicine, Tzu Chi University
Post-graduate-year doctor, Taipei Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, New Taipei, Taiwan
E-mail: paulchang1231 using gmail.com <paulchan1231 using gmail.com>
Cell: 0978000933

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