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Re: st: RE: Why don't my IRs and Cox HRs echo each other?


From   sjsamuels@gmail.com
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Why don't my IRs and Cox HRs echo each other?
Date   Thu, 7 May 2009 12:14:06 -0400

--


Chelsea-

I would not expect the two kinds of estimates to align.

The ratio of Deaths1/PY1  to Deaths2/PY2  is guaranteed to estimate
the hazard ratio only in special circumstances. One is that the data
are generated bya two-group exponential model with no time-dependent
covariates and constant hazards.

There could be many reasons for the dissimilar estimates. Kieran has
described an important one.  A related issue with time dependent
covariates is that  the risk sets and exposure for different levels of
time-dependent covariates may not cover the same time-periods, whereas
the Cox model automatically compares people at risk at the same
follow-up times.  Confounding could also contribute to the
discrepancy, even in the ideal exponential case, because you are
computing  the PY-based hazard ratios one factor at a time.

You can explore distributional shapes for time-dependent groups if you
designate the groups as strata.  There are also some good ideas for
plotting in Applied Longitudinal Data Analysis: Modeling Change and
Event Occurrence by Judith D. Singer and John B. Willett

-Steve

On Wed, May 6, 2009 at 7:35 PM, Polis, Chelsea B. <cpolis@jhsph.edu> wrote:
> I apologize for the formatting of my table, it looked ok when I sent it.  Please let me try again.
>
>
> Variable  Deaths  PY at risk    IR      HR      95% CI  p-value
>
> HC use                                                          0.07
>  No         91  1262.7  7.21    1.00
>  Yes        13  293.0           4.44    0.58    0.32-1.04
> Current age                                                             0.38
>  15-24    20    394.0           5.08    1.00
>  25-34    49    711.8           6.88    0.73    0.43-1.24
>  35+        35  449.9           7.78    0.68    0.38-1.20
> Sex partners in past year                                       0.01
>  None       18  241.2           7.46    1.00
>  One        76  1204.6  6.31    1.31    0.78-2.21
>  Two+       10  109.9           9.10    3.40    1.54-7.54
>
>
> Dear statalisters,
>
> I am doing survival analysis on time to death with time-varying covariates on an open, population
> -based cohort study.  The base sample is essentially a census of individuals in 56 villages, and
> I am utilizing information from all female incident HIV seroconverters.
>
> I computed incidence rates based on the raw data ((number of deaths/person-time at risk)*100 - I obtained
> time at risk using the stdes command), but the IRs don't seem to echo trends in the univariate Cox HRs.
>
> In the sample data below, things appear reasonable for HC use (deaths per 100 person years is lower
> if HC=yes, and the HR reflects this).  But for current age, deaths are higher in the 25-34 category
> than in the 15-24 category, but the HR trends suggests that being 25-34 is protective (though not
> significantly).  Also, the magnitude seems off, for example, in the variable "Sex partners in past
> year" - having two or more seems to more than triple the hazard in the Cox regression, but merely
> increases from 7.46 to 9.10 in the deaths per 100 p-y.
>
> Am I missing something in expecting these numbers to echo trends in each other?  Is this just a
> matter of non-significance within individual categories?  Or a difference in time-to-event versus
> person-time analysis?  Or because I am doing an analysis with time-varying covariates?  Should I not
> expect these to align? Any help is appreciated!
>

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