Interestingly, most of the poor performance in the CIs for CTMLE0 is from the over-estimated point estimate, while for CTMLE0* is mainly from under-estimation of the point estimate. Open in a separate window Figure 3. Comparison of CTMLE0 and CTMLE0*. interval coverage. In addition, the propensity score model selected by collaborative minimum loss-based estimation could be applied to other propensity score-based Rabbit Polyclonal to Chk2 (phospho-Thr387) estimators, which also resulted in substantive improvement for both point estimation and confidence interval coverage. We illustrate the discussed concepts through an empirical example comparing the effects of nonselective nonsteroidal anti-inflammatory drugs with selective COX-2 inhibitors on gastrointestinal complications in a population of Medicare beneficiaries. independent and identically distributed (i.i.d.) observations, O( 1,, is a vector of some pre-treatment baseline covariates of VD3-D6 the is a binary indicator taking on a value of 1 1 if observation is in the treatment group and is 0 otherwise. Further, suppose that each observation has a counterfactual outcome pair, is in the control group (0) or the treatment group (1). Thus, for each observation, we only observe one of the potential outcomes, or as the conditional expectation of represent the expectation under the unknown true data generating distribution given = can be written as given = can be written as with for is consistent, the resulting estimator is also consistent. Another widely used estimator is the Inverse Probability of Treatment Weighting (IPW) estimator. It only relies on the estimator of is usually fitted by a supervised model (e.g. logistic regression), which regresses on the pre-treatment confounders is replaced by the weight normalization term is a consistent estimator. All of the estimators mentioned above are not robust in the sense that misspecification of the first stage modeling (of conditional outcome, or the PS) could lead to biased estimation for the causal parameter of interest. This is the reason why double robust (DR) estimators are preferable. DR estimators usually rely on the estimation of both and by minimizing the weighted empirical loss is the loss function. The estimator VD3-D6 for the causal parameter is defined as ? also relies on both and represent a binary variable, or a continuous variable within the range (0, 1).a The TMLE estimator for the ATE can be written as (which is within the range (0, 1)) is updated from an initial estimate, and is binary. The ATE, therefore, should be between [?1, 1]. However, some competing estimators may produce estimates out of such bounds. Since TMLE maps the targeted estimate of and is too close to 0 or 1. 4.?Brief review of collaborative TMLE 4.1. C-TMLE for variable selection In the TMLE algorithm, the estimate of is updated by the fluctuation step, while the estimate of gis estimated externally and then held fixed. One extension of TMLE is to find a way to estimate in a manner. Motivated by the second advantage of TMLE, collaborative TMLE was proposed to make this extension feasible.24 Here we first briefly review the general template for C-TMLE: Compute the initial estimate of and for gand respectively, with = 1,…, increasing, the empirical loss for both and would decrease. In addition, we require to be asymptotically consistent for that minimizes the cross-validated risk, and denote this TMLE estimator as the C-TMLE estimator. This is a high-level template for the general C-TMLE algorithm. There are many VD3-D6 variations of instantiations of this template. For example, the greedy C-TMLE was proposed by the authors in literature24,25 for variable selection in a discrete setting. The following are some details of greedy C-TMLE: In step 2 2, the greedy C-TMLE algorithm starts from an intercept VD3-D6 model (which fits the PS with its mean), and then builds the sequence of by using a forward selection algorithm: during each iteration and by equation (4). For all with the smallest empirical loss. For simplicity we call this the forward selection step at the mentioned above do not improve the empirical fit compared to and rerun the forward selection step at the are guaranteed to have a better empirical fit compared to their initial estimate is monotonically decreasing. Ju et al.26 also proposed scalable versions of the discrete C-TMLE algorithm as new instantiations of the C-TMLE template. These scalable C-TMLE algorithms avoid the forward selection step by enforcing a user-specified ordering of the covariates. Ju et al.26 showed that these scalable C-TMLE.

Interestingly, most of the poor performance in the CIs for CTMLE0 is from the over-estimated point estimate, while for CTMLE0* is mainly from under-estimation of the point estimate