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

Dr. Gerta Rücker ruecker @end|ng |rom |mb|@un|-|re|burg@de
Sun May 24 12:47:22 CEST 2020

```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>
>> 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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