This dissertation addresses positivity assumption violations in observational longitudinal studies with a large number of time-varying covariates by using the data adaptive parameter estimation techniques of Longitudinal Targeted Maximum Likelihood Estimation (LTMLE) and simulation-based analysis for causal inference in complex longitudinal data settings. The positivity assumption violation poses a problem of identifiability from observed data. It often goes undiagnosed and can threaten valid inference. We develop a new semiparametric bootstrap simulation tool, simreal, for longitudinal data structures designed to simulate data that ”matches” the original, real data in its characteristics. We introduce a variance estimator based approach for detecting positivity assumption violations in complex longitudinal data settings and a roadmap for implementing mitigation options using an extensive simreal simulation analysis. We also introduce a practical positivity violation detection test that can be readily conducted in the ltmle package and can be used to alert users to severe positivity violations causing unreliable statistical inference. Furthermore, in the case of severe positivity assumption violations, we introduce a set of longitudinal realistic rules defined so that if the estimated conditional probability of receiving a treatment, given past treatments and covariates, falls under some user-supplied probability threshold level α, the rule assigns an alternative, viable, and well supported choice. Causal effect models under realistic treatment rules are fully identifiable from the observed data. These results were applied to the longitudinal study of around 3000 hypotensive patients in intensive care units at the onset of septic shock. The goal was to improve the current protocol and determine the optimal time to start the vasopressor treatment. Our results show that introducing vasopressors in the third hour of the critical six hour time period reduces hospital mortality. This result is statistically significant.
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