Please find the summary below.
Thanks.
> How can one interprete a case, when relative risk
> (hazard ratio) estimate of a continuous explanatory
> variable in a multivariate Cox PH model being
> approximately equal to 1 i.e 0.9999 or 1.0001 etc
> given that the p-value shows significance i.e <
0.05.
> Also, the relative risk estimate for this variable
is
> approximately equal to the lower limit for its 95%
CI
> for relative risk.
>
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I often see this in papers I referee. The solution is
to change the
units in which you report this variable. As a simple
example if age
was of prognostic importance and you reported age in
days, it
would give hazard ratios close to 1. If you reported
in years or even
decades, you would obtain the type of discrimination
you would
like to obtain, and confidence intervals would become
interpretable.
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I would say that the effect of that explanatory
variable, though
statistically significant, is negligible. With a
sample size large
enough any small effect would be statistically
significant but this
does not mean that the effect is important.
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That is a very interesting situation.
I think this is a clear situation in which the
interpretation can never
been done out of the contest. Hence I wouldn't focus
too much attention
on the statistical significance as I can guess that
the significance is
much due to the sample size than to the importance of
the difference in
log hazard between the two groups. Thus, if the event
of interest is
very rare, I would be tempted to conclude that the two
groups differ in
risk of event and that the hazard in one group is 1
per 10.000 higher/lower than in the other. But is the
event is relatively frequent, I would conclude that
the hazard are comparable between the two groups.
I would be happy to hear what expert have suggested.
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Without seeing your data or knowing what software you
use one cannot be
sure, but it is important to remember that the
coefficients in the case
of a continuous predictor are log ratios per unit
change in the
predictor. So if it has a range of 1000 a value of
0.9999 may be different
from 1. What is the standard error of the values?
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It may be a matter of scale and rounding. Try dividing
your continuous
variable by 1000 or more and redoing the analysis.
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