Re: st: Combining catagories of risk

[David Hoaglin <dchoaglin@gmail.com>]

Claire,

It would probably be reasonable to take a weighted average of the
category-specific HRs, using weights proportional to the categories'
shares of the total population of patients in that study.  You could
also use weights based on another population of interest.

Estimating the variance of that weighted average could be a challenge.
 If the HRs for the categories came from separate (i.e.,
category-specific) models, you would not need to take into account
correlations among the estimates.  If, however, the HRs came from a
single model (with a reference category and indicators for the other
categories), then you would need to take into account correlations
among them (and that information is unlikely to be available).
Treating those correlations as zero would probably yield an
overestimate of the variance of the weighted average.

Even if the HRs came from separate models, however, combining them may
not be as simple as it seems.  If those models included covariates
(and hence produced adjusted HRs), but the models for the various
categories did not all use the same set of covariates, then the
adjusted HRs would differ in definition and would not be truly
comparable.  The single model (for all the categories) avoids this
complication by adjusting the HR in the same way for all categories
(assuming that the model does not also contain category-by-covariate
interactions), so it would be preferable, but it would have the
problem of unavailable correlations mentioned above.

I hope this discussion helps.

David Hoaglin

On Fri, Mar 28, 2014 at 6:58 AM, Claire Rushton <c.a.rushton@keele.ac.uk> wrote:
> Thank you for this. However the groups I am considering combining are
> mutually exclusive and for the same outcome. For example they are two
> groups of patients that were stratified by their different levels of
> renal dysfunction. I want to extract a single estimate for both groups
> of patients with 'any dysfunction'. I am looking for the most
> appropriate way of averaging the groups.
>
> Any advice - much appreciated.
>
> Claire
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