Abstract:
A number of sophisticated estimators of longitudinal effects have been proposed for estimating the
intervention-specific mean outcome. However, there is a relative paucity of research comparing these methods directly to one another. In this study, we compare various approaches to estimating a causal effect in a
longitudinal treatment setting using both simulated data and data measured from a human immunodeficiency
virus cohort. Six distinct estimators are considered: (i) an iterated conditional expectation representation, (ii) an
inverse propensity weighted method, (iii) an augmented inverse propensity weighted method, (iv) a double ro-
bust iterated conditional expectation estimator, (v) a modified version of the double robust iterated conditional
expectation estimator, and (vi) a targeted minimum loss-based estimator. The details of each estimator and
its implementation are presented along with nuisance parameter estimation details, which include potentially
pooling the observed data across all subjects regardless of treatment history and using data adaptive machine
learning algorithms. Simulations are constructed over six time points, with each time point steadily increasing
in positivity violations. Estimation is carried out for both the simulations and applied example using each of
the six estimators under both stratified and pooled approaches of nuisance parameter estimation. Simulation
results show that double robust estimators remained without meaningful bias as long as at least one of the two
nuisance parameters were estimated with a correctly specified model. Under full misspecification, the bias of
the double robust estimators remained better than that of the inverse propensity estimator under misspecifica-
tion, but worse than the iterated conditional expectation estimator. Weighted estimators tended to show better
performance than the covariate estimators. As positivity violations increased, the mean squared error and bias
of all estimators considered became worse, with covariate-based double robust estimators especially suscepti-
ble. Applied analyses showed similar estimates at most time points, with the important exception of the inverse
propensity estimator which deviated markedly as positivity violations increased. Given its efficiency, ability
to respect the parameter space, and observed performance, we recommend the pooled and weighted targeted
minimum loss-based estimator.