Applying targeted maximum likelihood estimation to longitudinal data can be computationally intensive. As the number of time points and/or number of intermediate factors grows, the computation resources consumed by these algorithms likewise increases. Different TMLE algorithms have different computational speeds and implementation challenges; there may also be efficiency differences of the corresponding estimators. The algorithm we describe here proceeds by solving the empirical efficient influence curve equation directly using numerical computation methods, rather than indirectly (by solving a score equation), which is the usual route. We believe that this estimator is the simplest of the TMLE procedures to implement in the longitudinal data structure simulated here, which mimics a sequential randomized controlled trial with dynamic treatment rules. Our choice of numerical methods is the well-known secant method for finding the root of a function. The resulting estimation algorithm has computational speed approximately equal to one of the two existing TMLE algorithms for the data generating distributions considered here.
Chaffee, Paul and van der Laan, Mark J., "Targeted Minimum Loss Based Estimation Based on Directly Solving the Efficient Influence Curve Equation" (July 2011). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 287.