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

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 at imbi.uni-freiburg.de> <ruecker at 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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