Dear all,
I would appreciate any comments, references etc. about the following
estimation problem in observational longitudinal studies with recurrent
events:
I have the following study design:
- Longitudinal observational study investigating the occurrence of repeated
events of an infectious disease.
- All individuals enter and leave the study at a fixed date.
- To analyse risk factors we choose a dynamic time to event approach
(extended Cox model) using the gap time between repeated infections as
analysis time scale. Other time scales (age, study time, calendar month
etc.) were included as time-varying covariate in the model.
- Estimating time-varying rates (e.g. rate for dynamic age bands, etc). we
observed the following bias because of the observational design:
- Late entry of individuals: Rate is overestimated at the beginning: Since
individual entered the study at a specific data and not when exposure to
risk began (i.e. after the last event occurred), for most individuals the
time to first event is substantially underestimated. (in fact E(t1_obs) is
˝*t1, can I assume that?)
-Censoring : Rate is underestimated at the end: At the end of the study,
after the last event during the observational period has occurred, each
individual which in fact is at risk for the next event is withdrawn from the
study, i.e. an censored event time is added to the total person-time (in
fact E(tL_obs) is 3/2*tL, can I assume that?).
If the rate is constant during the follow up, the observed overall rate
should not be affected by this bias (The person time I “loose” at the
beginning I’ll “win” at the end!)
But what about the observed time-varying rates, aren’t they substantially
affected by this bias, because this bias is time-dependent, dependent on the
prop. of ind. whose first event has already occurred and those whose last
event has not occurred yet. In fact it is only possible to estimate unbiased
rates when the exact person time is know for all individuals at risk and
this is when the first event already has occurred and the last not yet!
Well, maybe a possibility how to avoid this bias is to exclude the time to
first event for each ind. and also the last censored event time.
Is there any statistical technique to adjust for this estimation bias
without excluding observations?
Thanks Bernd
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Dr Bernd Genser
MSc, PhD
BGStats Consulting
Statistical Consulting - Data Analysis - Medical Research Support
email: [log in to unmask]
HYPERLINK "http://www.bgstats.com"www.bgstats.com
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