[R-meta] Meta-Analysis: Proportion in overall survival rate

Wed May 27 20:01:32 CEST 2020

Dear Michael, Gerta and List,

I would like to cross-check with you what I have done.

I have restricted myself to Kaplan-Meier studies which gave the number at
risk at 2 years, and also n_0 at baseline.

I then estimated the absolute number of those surviving as *n_t *= n_0*S(t)
following Gerta's idea. I took the reported proportions at 2 years to
represent the S(t).

I calculated the standard error (SE) using the formula: *se *= square root (
*p*(1-*p*)/n). Where *p* = proportion at 2 years i.e. S(t)
, n = *n_t*, the estimated number of of those surviving.

I then used the random effects model in metafor as follows:
rma(yi = *p*, sei = *se*, data=mydata, method="REML")

The resulting estimate seems reasonable to me. But I want to confirm with
you if this is the way one would input SE and the proportion to the
function.

Welcome any comments.

Sincerely,
nelly

On Mon, May 25, 2020 at 9:34 AM ne gic <negic4 using gmail.com> wrote:

> Dear Gerta and Michael,
>
> I thank both of you very much for your insights.
>
> Sincerely,
> nelly
>
> On Sun, May 24, 2020 at 12:47 PM Dr. Gerta Rücker <
> ruecker using imbi.uni-freiburg.de> wrote:
>
>> Dear Nelly, dear Michael,
>>
>> Maybe I have misundersood something, but I do not understand why (as
>> Michael said) the number at risk at two years should be relevant if you
>> want to know the survival proportion at two years. The survival proportion,
>> as I understand it, is the proportion who survived two years, relative to
>> those who were there at baseline. By contrast, the number at risk at 2
>> years are those that are living just before the 2 years date.
>>
>> The problem is this:
>>
>>    1. For studies that provide proportions (absolute numbers, or
>>    two-by-two tables) for the 2 years time point you know the number (per
>>    group) at baseline (n_0) and the number living after two years. However,
>>    the proportion calculated therefrom ignores that some individuals may have
>>    been censored during the two years and are perhaps still alive, but not
>>    known, and thus the survival proportion is underestimated.
>>    2. For studies providing a Kaplan-Meier estimate at 2 years (and also
>>    n_0 at baseline), you have an unbiased estimate of the survival proportion
>>    (because censoring is accounted for, provided the censoring assumptions are
>>    valid), and you can simply estimate the absolute number of surviving as n_t
>>    = n_0*S(t).
>>
>> In other words, the problem is not calculation, but the difference in
>> interpretation of both kinds of numbers: The studies of type 1 do not
>> account for censoring, while those of type 2 do.
>>
>> Best,
>>
>> Gerta
>> Am 24.05.2020 um 12:25 schrieb Michael Dewey:
>>
>> Dear Nelly
>>
>> Comments in-line
>>
>> On 23/05/2020 16:27, ne gic wrote:
>>
>> Dear List and Gerta,
>>
>> Once more am interested in overall survival and my aim is to analyse the
>> proportion(s) of patients left in the study at the 2 years time point as
>> reported by Kaplan-Meir (KM) curves. Of course there are those that are
>> censored and those that experience the event as time goes by as expected
>> in
>> KM curves. I have now double checked all the studies to be included in my
>> meta-analysis dataset and I have selected all those that report the
>> proportion of patients left in the study at 2 years.
>> A number of those in the subset also included a risk table, thus I have
>> access to those at risk at this 2 year time point should I need them.
>>
>> However, as I cannot directly infer the number of events(event) and total
>> at risk(n) from the curves at 2 years time point which would have been
>> convenient to plug into metaprop,
>> I thought that I could instead try Gerta's advice and see if I can use
>> the
>> proportion (from each of the studies) and it's standard error (SE) -
>> manually calculated instead.
>>
>> Questions:
>>
>>     1. Is it correct to manually calculate the SE using the formula: SE =
>>     square root (p(1-p)/n). Where p = proportion, n = total at risk?
>>
>>
>> But you said you do not have the n necessary to do this so it is not
>> going to help I think.
>>
>>     2. Which R/Stata/SAS software function can then take in the
>> proportion
>>     and SE and give me a pooled proportion with CI and forest plot?
>>
>>
>> The two most used R packages are meta and metafor either of which will do
>> what you want.
>>
>> I welcome any comments and hints. If this is not reasonable, anything
>> else
>> I can do?
>>
>>
>> I think you are going to have to restrict yourself to those studies which
>> do give the number at risk at 2 years. I must say I would be rather nervous
>> about doing this if the degree of and reasons for censoring were likely to
>> be different between studies.
>>
>> Michael
>>
>> Sincerely,
>> nelly
>>
>> On Tue, May 19, 2020 at 2:32 PM Gerta Ruecker
>> <ruecker using imbi.uni-freiburg.de> <ruecker using imbi.uni-freiburg.de>
>> wrote:
>>
>> Dear Nelly,
>>
>> You could do this, at least in principle, if all proportions refer to
>> the same timepoint, for example 5 years. The problem is that the data
>> you obtain from studies with a time-to-event endpoint are different from
>> those that directly provide a five-year survival proportion: The
>> time-to-event analysis accounts for censoring, while the proportion of
>> living after five years relatively to all patients at baseline usually
>> does not account for censoring or missing data (and thus may
>> underestimate the true proportion).
>>
>> If I understand you correctly, you want to pool survival proportions
>> (single-arm), not hazard ratios (comparing two arms).
>>
>> The technical thing is that you have survival proportions with standard
>> error from the time-to-event studies and single proportions (survived/n)
>> from other studies. Survival proportions with standard errors can be
>> pooled usingthe  generic inverse variance method. Proportions are best
>> be pooled using generalized linear models. See, for example, the
>> examples for function metaprop() in R package meta.
>>
>> Best,
>>
>> Gerta
>>
>> Am 19.05.2020 um 14:15 schrieb ne gic:
>>
>> Dear List,
>>
>>   From time to event data, it's common to calculate a combined HR for
>> instance from included studies - this I understand.
>>
>> Does it make sense to perform a meta-analysis of the proportion (%) one
>> gets from overall time survival e.g. Overall 5y survival? imagine a
>> scenario where different studies are reporting different proportions of
>> patients surviving at this time point and I want to report a summary
>> proportion from all the studies at this time point.
>>
>> If this is possible, does just collecting the proportion at that time
>>
>> point
>>
>> e.g. 5 year suffice as the data to use for this calculation? Or what
>>
>> would
>>
>> you suggest? Haven't seen a package that just takes a proportion.
>>
>> Sincerely,
>> nelly
>>
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>>
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>>
>> --
>>
>> Dr. rer. nat. Gerta Rücker, Dipl.-Math.
>>
>> Institute of Medical Biometry and Statistics,
>> Faculty of Medicine and Medical Center - University of Freiburg
>>
>> Stefan-Meier-Str. 26, D-79104 Freiburg, Germany
>>
>> Phone:    +49/761/203-6673
>> Fax:      +49/761/203-6680
>> Mail:     ruecker using imbi.uni-freiburg.de
>> Homepage: https://www.uniklinik-freiburg.de/imbi.html
>>
>>
>>
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>>

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