How to estimate disease prevalence using logistic regression when some people are measured several times I have a binary variable indicating the presence or absence of a disease as well as variables for time and other covariates. SOME (not all) people are observed (tested) several times.
Suppose I want to estimate the prevalence of disease for a given year. I believe that if there was just one observation per person I could do that with an intercept only logistic regression where the estimated intercept is the prevalence. However, because there are several observations per subject Im unsure how to proceed. If I modelled all the data and accounted for subject id e.g. using a mixed model or clustered standard errors, I believe the standard errors will be valid but I cannot see how the point estimate is valid. Im imagining  an extreme example where one person accounts for the majority of the data who has the disease present in all of his/her observations; that will surely increase the point estimate of the prevalence which would not be realistic. I might be thinking about this all wrong...would really appreciate some help!
Update / clarification:
Suppose in a population of 10 people, each person is measured once. 5 people are positive for the disease whilst 5 are negative. The prevalence is 50% which can be estimated using the formula for prevalence, or using poisson (aggregated counts) or logistic (binary data) regression. Now, suppose one of the subjects is actually measured 20 times. How does one calculate the "correct" prevalence using 1. Formula method, 2 Poisson regression, 3. Logistic regression?

Why don't you bootstrap your data (replace with  sampling) B times and apply logistric regression and use majority voting.. your variance will be smaller.
Duplicate data means your data has already been  bootstrap little bit but not enough, I think...
