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

[ne gic]

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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>
> --
>
> 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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