[R-meta] Power analysis of meta-analysis

Paul Chang p@u|ch@ng1231 @end|ng |rom gm@||@com
Thu Jun 18 03:48:44 CEST 2020

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

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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