longitudinal models for prevalence I am trying to analyze some prevalence data and estimate the effect on prevalence of some health condition of an intervention that was introduced at some time point. The data concern a number of clusters and I have summary data (number of diseased and cluster sizes) for each cluster, at each discrete time point. The intervention was not introduced at the same time point for each cluster. So the data I have are of the form $x_{ij}, N_i, I_{ij}$, denoting for cluster $i$ and time point $j$ the number of diseased people, total size of cluster (i.e. diseased plus non diseased) and indicator variable for the presence/absence of intervention.
What is needed is estimation of the effect of the intervention on the prevalence of disease.
Any suggestions on models relevant for this problem would be very much appreciated.
Thanks.
 A: As I understand it, you have a set of clusters and are assigning each cluster to receive the intervention at a random time point, and assessing whether receipt of the intervention changes the disease prevalence in the cluster. 
So, you want to know either the prevalence difference E[Y|intervention=1] - E[Y|intervention=0] or the prevalence ratio E[Y|intervention=1]/E[Y|intervention=0]. Where Y = prevalence = $x_{ij}/N_{i}$. 
If you think the intervention has a single unique effect in each cluster (time-invariant effect), then you should probably just be calculating those from your data. You may get bias if you have within-cluster time-varying confounding, in any given cluster - ex. other reasons the prevalence of disease naturally changes over time. So you may want to consider measuring any important confounders of that type.
If you believe instead that there is a single time-invariant effect of the intervention on average over all the clusters, and wanted to adjust for the fact that clusters are matched to themselves, you could analyze this like a crossover study and run a conditional logistic regression $clogit(Y) = \beta_{0,i} +\beta_1I_{i,j}$. However, you will once again have to worry about bias if there are time-varying confounders within the clusters. You can adjust for this by including these variables in the regression model. This gives you the prevalence odds, but since you have a longitudinal study, you should be able to validly convert that back to the prevalence by taking the expit.
If you think the effect varies over time, then I'm not sure what the best approach is.
