Hello,

As requested, I am forwarding to the list, the
responses to the question I had earlier posed.

The question:
> I have dichotomous exposure variable and the outcome
> being the first incidence of malaria (reference time
> being recruitment time i.e people involved were
> malaria negative at baseline).
>
> I computed the Incidence rate for the exposed and
> unexposed and also the rate ratio (ratio of
incidence
> rates of exposed to unexposed) and found the 95% CI
> for the rate ratio showing excess of malaria among
> the exposed as compared to unexposed, with
p->value<0.001.
>
> When the same exposure variable is modelled
> univariately in a Cox PH model, the outcome being
> the time to first malaria episode, it shows no
> significance at all in the prediction of time to 1st
> episode.
>
> Could someone, explain to me why is it differing in
> importance as far as incidence and ph modelling are
> concerned?
>

The following are the responses:
***********************
It sounds odd and I can't explain it. I would suggest
analysing a Simulation in which the data resembles the
data you have but is created by a known process. It
should be possible to check what kind of results are
reasonable.

***********************
There are two issues with that. First, p-values depend
heavily on the power of your test, and one would
expect the test derived from a coxph model to be less
powerful since the model is far more complex and
flexible, i.e. you are modelling more details which in
return makes your results less credible (that's my
guess - I have no proof of any kind for that).

Second, time to incidence and incidence rates depend
on different aspects of the disease and the study
design. E.g. if you are interested in a disease with
long times to incidence but your follow up time is
short, when analysing times to incidence you can't
distinguish well between people developing incidence
and those who don't. On the other hand, even with
"complete" follow up: when you've got long times to
incidence, and high risk of incidence anyway, it might
be difficult to distinguish between incidence by cause
of interest and incidence by other causes. In both
cases, a simple cross table might be more powerful.

The main problem with time to incidence is that you
discard the
information of non-developed disease by modelling it
as censored, i.e. - under certain circumstances (see
below) - almost as missing. That is because you try to
model times to incidence. So the better performing
group, you have much missing data, no wonder it is
difficult to compare with the other group.

*******************************
The two analyses are not answering the same question.
The risk ratio analysis ignores the time of occurrence
of the events and focuses only on the events
themselves.  What really matters is whether the event
has occured or not at the end of your study. It
answers the question whether the incidence rates is
the same for both groups regardless of the time they
occur. Here the censoring is not incorparated.

The Cox model tells you a slightly different story. It
will tell you whether the event occurs sooner in
either group. It basically combines all information
from all timepoints and also incorporates censoring in
defining the risk set at each time point.

Note that the exposed group may have a higher
incidence rate but its events may occur relatively
later than those in the non exposed group.
This is probably what is happening in your data.
***********************


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