Pattern mixture models for the analysis of repeated attempt designs

It is not uncommon in follow-up studies to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful or not provides useful information for the purposes of assessing the missing at random (MAR) assumption and facilitating missing not at random (MNAR) modeling. This is because measurements from subjects who provide this data after multiple failed attempts may differ from those who provide the measurement after fewer attempts. This type of "continuum of resistance" to providing a measurement has hitherto been modeled in a selection model framework, where the outcome data is modeled jointly with the success or failure of the attempts given these outcomes. Here, we present a pattern mixture approach to model this type of data. We re-analyze the repeated attempt data from a trial that was previously analyzed using a selection model approach. Our pattern mixture model is more flexible and is more transparent in terms of parameter identifiability than the models that have previously been used to model repeated attempt data and allows for sensitivity analysis. We conclude that our approach to modeling this type of data provides a fully viable alternative to the more established selection model.