We present a new covariate-adjusted response-adaptive randomized controlled trial design and inferential procedure built on top of it. The procedure is targeted in the sense that (i) the sequence of randomization schemes is group-sequentially determined by targeting a user-specified optimal randomization design based on accruing data and, (ii) our estimator of the user-specified parameter of interest, seen as the value of a functional evaluated at the true, unknown distribution of the data, is targeted toward it by following the paradigm of targeted minimum loss estimation. We focus for clarity on the case that the parameter of interest is the marginal effect of a binary treatment and that the targeted optimal design is the Neyman allocation, in an effort to produce an estimator with smaller asymptotic variance. For clarity too, we consider the case that the estimator of the conditional outcome given treatment and baseline covariates, a key element of the procedure, is obtained by LASSO regression. Under mild assumptions, the resulting sequence of randomization schemes converges to a limiting design, and the TMLE estimator is consistent and asymptotically Gaussian. Its asymptotic variance can be estimated too. Thus we can build valid confidence intervals of given asymptotic levels. A simulation study confirms our theoretical results.



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