  In observational surveys, post-stratification is used to reduce bias
resulting from differences between the survey population and the population
under investigation. However, this can lead to inflated post-stratification
weights and, therefore, appropriate methods are required to obtain less
variable estimates. Proposed methods include collapsing post-strata, trimming
post-stratification weights, generalized regression estimators (GREG) and
weight smoothing models, the latter defined by random-effects models that
induce shrinkage across post-stratum means. Here, we first describe the
weight-smoothing model for prevalence estimation from binary survey outcomes in
observational surveys. Second, we propose an extension of this method for trend
estimation. And, third, a method is provided such that the GREG can be used for
prevalence and trend estimation for observational surveys. Variance estimates
of all methods are described. A simulation study is performed to compare the
proposed methods with other established methods. The performance of the
nonparametric GREG is consistent over all simulation conditions and therefore
serves as a valuable solution for prevalence and trend estimation from
observational surveys. The method is applied to the estimation of the
prevalence and incidence trend of influenza-like illness using the 2010/2011
Great Influenza Survey in Flanders, Belgium.
