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

ne gic neg|c4 @end|ng |rom gm@||@com
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.

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
>>
>>
>> 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) -
>>
>> 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
>>
>>        [[alternative HTML version deleted]]
>>
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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
>>
>>
>>
>>     [[alternative HTML version deleted]]
>>
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>>
>>
>>

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