Advances in the Analysis of Irregular Longitudinal Data Using Inverse Intensity Weighting

Abstract

The analysis of irregular longitudinal data can be complicated by the fact that the timing at which individuals are observed in the data are related to the longitudinal outcome. For example, this can occur when patients are more likely to visit a clinician when their symptoms are worse. In such settings, the observation process is referred to as informative, and any analysis that ignores the observation process can be biased. Inverse intensity weighting (IIW) is a method that has been developed to handle specific cases of informative observation processes. IIW weights observations by the inverse probability of being observed at any given time, and creates a pseudopopulation where the observation process is subsequently ignorable. IIW can also be easily combined with inverse probability of treatment weighting (IPTW) to handle non-ignorable treatment assignment processes. While IIW is relatively intuitive and easy to implement compared to other existing methods, there are few peer-reviewed papers examining IIW and its underlying assumptions.

In this thesis, we begin by evaluating a flexible weighting method which combines IIW and IPTW through multiplication to handle informative observation processes and non-randomized treatment assignment processes. We show that the FIPTIW weighting method is sensitive to violations of the noninformative censoring assumption and show that a previously proposed extension fails under such violations. We also show that variables confounding the observation and outcome processes should always be included in the observation intensity model. Finally, we show scenarios where weight trimming should and should not be used, and highlight sensitivities of the FIPTIW method to extreme weights. We also include an application of the methodology to a real data set to examine the impacts of household water sources on malaria diagnoses of children in Uganda.

Next, we investigate the impact of missing data on the estimation of IIW weights, and evaluate the performance of existing missing data methods through empirical simulation. We show that there is no "one-size-fits-all" approach to handling missing data in the IIW model, and show that the results are highly dependent on the type of covariates that are missing in the observation times model. We then apply the missing data methods to a real data set to estimate the association between sex assigned at birth and malaria diagnoses in children living in Uganda.

Finally, we provide an in-depth evaluation on the assumptions made on IIW across various peer-reviewed papers published in the literature. For each set of assumptions, we construct directed acyclic graphs (DAGs) to visualize the assumptions made on the observation and censoring processes which we use to highlight inconsistencies and potential ambiguity among the assumptions presented in existing works involving IIW. We also discuss when causal estimates of the marginal outcome model can be obtained, and propose a general set of assumptions for IIW.