Longitudinal data analysis in the presence of informative sampling: weighted distribution or joint modelling

Weighted distributions, as an example of informative sampling, work appropriately under the missing at random mechanism since they neglect missing values and only completely observed subjects are used in the study plan. However, length-biased distributions, as a special case of weighted distributions, remove the subjects with short length deliberately, which surely meet the missing not at random mechanism. Accordingly, applying length-biased distributions jeopardizes the results by producing biased estimates. Hence, an alternate method has to be used such that the results are improved by means of valid inferences. We propose methods that are based on weighted distributions and joint modelling procedure and compare them in analysing longitudinal data. After introducing three methods in use, a set of simulation studies and analysis of two real longitudinal datasets affirm our claim.