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BackgroundPopulation-level estimates of disease prevalence and control are needed to assess the effectiveness of prevention and treatment strategies. However, available data are often subject to differential missingness. Consider population-level HIV viral suppression: proportion of all HIV-positive persons who are suppressing viral replication. Individuals with measured HIV status, and, among HIV-positive individuals, those with measured viral suppression are likely to differ from those without such measurements.MethodsWe discuss three sets of assumptions sufficient to identify population-level suppression over time in the intervention arm of the SEARCH Study (NCT01864603), a community randomized trial in rural Kenya and Uganda (2013-2017). Using data on nearly 100,000 participants, we compare estimates from an unadjusted approach assuming data are missing-completely-at-random (MCAR); stratification on age group, sex, and community; and, targeted maximum likelihood estimation (TMLE) with Super Learner to adjust for baseline and time-updated predictors of measurement.ResultsDespite high annual coverage of testing, estimates of population-level viral suppression varied by identification assumption. Unadjusted estimates were most optimistic: 50% of HIV-positive persons suppressed at baseline, 80% at Year 1, 85% at Year 2, and 85% at Year 3. Stratification on baseline predictors yielded slightly lower estimates, and full adjustment reduced estimates further: 42% of HIV-positive persons suppressed at baseline, 71% at Year 1, 76% at Year 2, and 79% at Year 3.ConclusionsEstimation of population-level disease burden and treatment coverage require appropriate adjustment for missingness. Even in “Big Data” settings, estimates relying on the MCAR assumption or baseline stratification should be interpreted with caution.

This thesis discusses the Super Learner and Targeted Maximum Likelihood Estimation (TMLE) for longitudinal data structures in nonparametric statistical models. It focuses specifically on time-dependent data structures where the outcome of interest may be described as a counting process. A Super Learner for the conditional intensity of the counting process is proposed based on the minimization of squared error and negative Bernoulli loglikelihood risks. An analytic comparison of the oracle inequality for the cross validation selector of the squared error and negative Bernoulli loglikelihood risks is provided. TMLE is extended to enforce a calibration property, defined as an implicit constraint, on the Super Learner. Tradeoffs between calibration and risk minimization are explored through simulation. The final chapter discusses and implements a recently developed TMLE for the intervention-specific marginal mean in general longitudinal data structures. A modification of this general TMLE algorithm template is implemented to respect model constraints for the estimation of the cumulative event probability in survival data with time-dependent covariates and informative right-censoring. Each chapter is supplemented with practical examples of these estimators using data from the the Kaiser Permanente ATRIA-1 cohort study of adults with atrial fibrillation. The primary appendix presents a new Super Learner software implementation as a SAS (Statistical Analysis System) macro for data-adaptive machine learning. SAS macro code for the TMLEs are provided in secondary appendices.

Collaborative targeted maximum likelihood estimation is an extension to targeted maximum likelihood estimation (TMLE), first introduced by van der Laan and Rubin in 2006. TMLE is an efficient, double robust, semi-parametric methodology for estimating a pathwise differential parameter of a statistical distribution given censored data. The TMLE procedure involves a parametric fluctuation of an initial estimate of the relevant factor of the density of the observed data, Q, that involves estimating the nuisance portion of the likelihood---censoring mechanism, g. DR estimators are consistent when at least one of these is estimated consistently. Though the best approach to nuisance parameter estimation is a current topic of debate in the literature, methods typically rely on maximizing a likelihood for g, however, by establishing the collaborative double robustness of the efficient influence curve, van der Laan and Gruber (2010) provides a theoretical justification for moving away from the practice of external nuisance parameter estimation. That paper also presents the collaborative TMLE (C-TMLE), and provides an algorithm for constructing the estimator. This dissertation explores collaborative double robustness to provide an understanding of the requirements for effective nuisance parameter estimation that are the foundation of C-TMLE, and presents the forward-selection C-TMLE algorithm. This approach to targeted maximum likelihood estimation is especially useful when the true censoring mechanism is unknown, and adjusting for a large number of correlated confounders leads to highly variable estimates. It is also particularly effective when there is sparsity in the data that renders a statistical parameter borderline identifiable. Variations on the C-TMLE estimator are presented, and their behavior is compared and contrasted with several TMLEs and other estimators in the literature using simulated and real data. There is an emphasis on finite sample performance under sparsity and model misspecification, and the incorporation of data-adaptive techniques while still preserving influence-curve based inference. A method for ensuring that TMLEs respect known global constraints on the model is presented, and a guide to the R package tmle, for TMLE estimation of binary point treatment effects is provided in the Appendix.

Data-adaptive methods have been proposed to estimate nuisance parameters when using doubly robust semiparametric methods for estimating marginal causal effects. However, in the presence of near practical positivity violations, these methods can produce a separation of the two exposure groups in terms of propensity score densities which can lead to biased estimates of the treatment effect. To motivate the problem, we evaluated the Targeted Minimum Loss-based Estimation procedure using a simulation scenario to estimate the average treatment effect. We highlight the divergence in estimates obtained when using parametric and data-adaptive methods to estimate the propensity score. We then adapted an existing diagnostic tool based on a bootstrap resampling of the subjects and simulation of the outcome data in order to show that the estimation using data-adaptive methods for the propensity score in this study may lead to large bias and poor coverage. The adapted bootstrap procedure is able to identify this instability and can be used as a diagnostic tool.

The consistency of propensity score (PS) estimators relies on correct specification of the PS model. The PS is frequently estimated using main-effects logistic regression. However, the underlying model assumptions may not hold. Machine learning methods provide an alternative nonparametric approach to PS estimation. In this simulation study, we evaluated the benefit of using Super Learner (SL) for PS estimation. We created 1,000 simulated data sets (n = 500) under 4 different scenarios characterized by various degrees of deviance from the usual main-term logistic regression model for the true PS. We estimated the average treatment effect using PS matching and inverse probability of treatment weighting. The estimators' performance was evaluated in terms of PS prediction accuracy, covariate balance achieved, bias, standard error, coverage, and mean squared error. All methods exhibited adequate overall balancing properties, but in the case of model misspecification, SL performed better for highly unbalanced variables. The SL-based estimators were associated with the smallest bias in cases of severe model misspecification. Our results suggest that use of SL to estimate the PS can improve covariate balance and reduce bias in a meaningful manner in cases of serious model misspecification for treatment assignment.

We often seek to estimate the impact of an exposure naturally occurring or randomly assigned at the cluster-level. For example, the literature on neighborhood determinants of health continues to grow. Likewise, community randomized trials are applied to learn about real-world implementation, sustainability, and population effects of interventions with proven individual-level efficacy. In these settings, individual-level outcomes are correlated due to shared cluster-level factors, including the exposure, as well as social or biological interactions between individuals. To flexibly and efficiently estimate the effect of a cluster-level exposure, we present two targeted maximum likelihood estimators (TMLEs). The first TMLE is developed under a non-parametric causal model, which allows for arbitrary interactions between individuals within a cluster. These interactions include direct transmission of the outcome (i.e. contagion) and influence of one individual’s covariates on another’s outcome (i.e. covariate interference). The second TMLE is developed under a causal sub-model assuming the cluster-level and individual-specific covariates are sufficient to control for confounding. Simulations compare the alternative estimators and illustrate the potential gains from pairing individual-level risk factors and outcomes during estimation, while avoiding unwarranted assumptions. Our results suggest that estimation under the sub-model can result in bias and misleading inference in an observational setting. Incorporating working assumptions during estimation is more robust than assuming they hold in the underlying causal model. We illustrate our approach with an application to HIV prevention and treatment.