Response to invited commentary. Rose et al. respond to "G-computation and standardization in epidemiology".

We thank Vansteelandt and Keiding (1) for their commentary on our article (2), in which we implemented G-computation, a maximum likelihood-based substitution estimator of the G-formula. The goals of that article included 1) translating G-computation into the applied epidemiology literature by using a point-treatment example and marginal parameter, 2) drawing connections between traditional regression and G-computation, 3) demonstrating G-computation in a simple simulated data set, and 4) briefly presenting related topics, such as super learning (3, 4). Their commentary provides valuable background on G-computation that was outside the scope of our article. Standardization was addressed, albeit briefly, in our article, and we disagree that our chosen presentation of G-computation was divorced from the literature. We respond to their remaining commentary via a road map for effect estimation (4), which can be a useful component of epidemiologic analysis and can guide investigators to address issues raised by Vansteelandt and Keiding (1). The road map for effect estimation we follow includes definition of the research question, the estimator, and inference (not discussed here) (4). Defining the research question involves describing the data, model, and target parameter. Suppose the data are n i.i.d. observations of the random variable O, where O has probability distribution P. A statistical model is the set of possible probability distributions, and the model is the statistical model augmented with possible additional causal assumptions. The target parameter is a specific feature of P. Vansteelandt and Keiding (1) discussed near violation of the positivity assumption and the problem of extrapolation when using G-computation. Near violations of the positivity assumption should be addressed for all estimators. Positivity is a testable statistical assumption, part of the statistical model in the road map, and we refer readers to the article by Petersen et al. (5) for information regarding diagnosis of and response to violations of this assumption. Vansteelandt and Keiding (1) also discussed marginal versus conditional parameters. If a conditional parameter is most appropriate for the research question, this fact will be translated into the statistical question when defining the target parameter in the road map. The second step in the road map is the choice and implementation of an estimator. Vansteelandt and Keiding (1) discuss inverse probability-of-treatment weighting estimators (6, 7) and ‘‘doubly robust standardization’’ (8, 9). Inverse probability-of-treatment weighting estimators are not asymptotically efficient and can lead to problems in finite samples (4, 10, 11). Doubly robust standardization is a substitution estimator that relies on weighting and a parametric regression statistical model. Robins et al. (9) describe situations in which this estimator may not perform well. The targeted maximum likelihood estimator (TMLE) (4, 12–14) is a doubly robust efficient loss-based substitution estimator with appealing asymptotic and finite sample properties. One first obtains an estimator of the data-generating distribution and then defines a parametric working submodel to fluctuate the initial estimator in a step targeted toward making the optimal bias-variance trade-off for the target parameter. Estimator comparisons involving TMLEs have been presented elsewhere (4, 15–19). The doubly robust estimator of Scharfstein et al. (20), which is a special case of a TMLE (21), and the TMLE with linear fluctuation function (12) were also examined in the article by Robins et al. (9) that was referenced by Vansteelandt and Keiding (1). For discussion of these estimators, we refer to previous publications (18, 21). A valid TMLE for continuous outcomes has been recently presented