Estimation and Testing in Targeted Group Sequential Covariate-adjusted Randomized Clinical Trials

This article is devoted to the construction and asymptotic study of adaptive group sequential covariate-adjusted randomized clinical trials analyzed through the prism of the semiparametric methodology of targeted maximum likelihood estimation (TMLE). We show how to build, as the data accrue group-sequentially, a sampling design which targets a user-supplied optimal design. We also show how to carry out a sound TMLE statistical inference based on such an adaptive sampling scheme (therefore extending some results known in the i.i.d setting only so far), and how group-sequential testing applies on top of it. The procedure is robust (i.e., consistent even if the working model is misspecified). A simulation study confirms the theoretical results, and validates the conjecture that the procedure may also be efficient

Targeting The Optimal Design In Randomized Clinical Trials With Binary Outcomes And No Covariate

This article is devoted to the asymptotic study of adaptive group sequential designs in the case of randomized clinical trials with binary treatment, binary outcome and no covariate. By adaptive design, we mean in this setting a clinical trial design that allows the investigator to dynamically modify its course through data-driven adjustment of the randomization probability based on data accrued so far, without negatively impacting on the statistical integrity of the trial. By adaptive group sequential design, we refer to the fact that group sequential testing methods can be equally well applied on top of adaptive designs. Prior to collection of the data, the trial protocol specifies the parameter of scientific interest. In the estimation framework, the trial protocol also a priori specifies the confidence level to be used in constructing frequentist confidence intervals for the latter parameter and the related inferential method, which will be based on the maximum likelihood principle. In the testing framework, the trial protocol also a priori specifies the null and alternative hypotheses regarding the latter parameter, the wished type I and type II errors, the rule for determining the maximal statistical information to be accrued, and the frequentist testing procedure, including conditions for early stopping. Furthermore, we assume that the protocol specifies a user-supplied optimal unknown choice of randomization scheme, and we will focus on that randomization scheme which minimizes the asymptotic variance of the maximum likelihood estimator of the parameter of interest. We obtain that, theoretically, the adaptive design converges almost surely to the targeted unknown randomization scheme. In the estimation framework, we obtain that our maximum likelihood estimator of the parameter of interest is a strongly consistent estimator, and it satisfies a central limit theorem. We can estimate its asymptotic variance, which is the same as that it would feature had we known in advance the targeted randomization scheme and independently sampled from it. Consequently, inference can be carried out as if we had resorted to independent and identically distributed (iid) sampling. In the testing framework, we obtain that the multidimensional t-statistics that we would use under iid sampling still converges to the same canonical distribution under adaptive sampling. Consequently, the same group sequential testing can be carried out as if we had resorted to iid sampling. Furthermore, a comprehensive simulation study that we undertake validates the theory. It notably shows in the estimation framework that the confidence intervals we obtain achieve the desired coverage even for moderate sample sizes. In addition, it shows in the testing framework that type I error control at the prescribed level is guaranteed, and that all sampling procedures only suffer from a very slight increase of the type II error. A three-sentence take-home message is: Adaptive designs do learn the targeted optimal design and inference and testing can be carried out under adaptive sampling as they would under the targeted optimal randomization probability iid sampling. In particular, adaptive designs achieve the same efficiency as the fixed oracle design. This is confirmed by a simulation study, at least for moderate or large sample sizes, across a large collection of targeted randomization probabilities

Targeted Covariate-Adjusted Response-Adaptive LASSO-Based Randomized Controlled Trials

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

Drawing Valid Targeted Inference When Covariate-adjusted Response-adaptive RCT Meets Data-adaptive Loss-based Estimation, With An Application To The LASSO

Adaptive clinical trial design methods have garnered growing attention in the recent years, in large part due to their greater flexibility over their traditional counterparts. One such design is the so-called covariate-adjusted, response-adaptive (CARA) randomized controlled trial (RCT). In a CARA RCT, the treatment randomization schemes are allowed to depend on the patient’s pre-treatment covariates, and the investigators have the opportunity to adjust these schemes during the course of the trial based on accruing information (including previous responses), in order to meet a pre-specified optimality criterion, while preserving the validity of the trial in learning its primary study parameter. In this article, we propose a new group-sequential CARA RCT design and corresponding analytical procedure that admits the use of flexible data-adaptive techniques. The proposed design framework can target general adaption optimality criteria that may not have a closed-form solution, thanks to a loss- based approach in defining and estimating the unknown optimal randomization scheme. Both in predicting the conditional response and in constructing the treatment randomization schemes, this framework uses loss-based data-adaptive estimation over general classes of functions (which may change with sample size). Since the randomization adaptation is response-adaptive, this innovative flexibility potentially translates into more effective adaptation towards the optimality criterion. To target the primary study parameter, the proposed analytical method provides robust inference of the parameter, despite arbitrarily mis-specified response models, under the most general settings. Specifically, we establish that, under appropriate entropy conditions on the classes of functions, the resulting sequence of randomization schemes converges to a fixed scheme, and the proposed treatment effect estimator is consistent (even under a mis-specified response model), asymptotically Gaussian, and gives rise to valid confidence intervals of given asymptotic levels. Moreover, the limiting randomization scheme coincides with the unknown optimal randomization scheme when, simultaneously, the response model is correctly specified and the optimal scheme belongs to the limit of the user-supplied classes of randomization schemes. We illustrate the applicability of these general theoretical results with a LASSO- based CARA RCT. In this example, both the response model and the optimal treatment randomization are estimated using a sequence of LASSO logistic models that may increase with sample size. It follows immediately from our general theorems that this LASSO-based CARA RCT converges to a fixed design and yields consistent and asymptotically Gaussian effect estimates, under minimal conditions on the smoothness of the basis functions in the LASSO logistic models. We exemplify the proposed methods with a simulation study

Targeted Learning of The Probability of Success of An In Vitro Fertilization Program Controlling for Time-dependent Confounders

Infertility is a global public health issue and various treatments are available. In vitro fertilization (IVF) is an increasingly common treatment method, but accurately assessing the success of IVF programs has proven challenging since they consist of multiple cycles. We present a double robust semiparametric method that incorporates machine learning to estimate the probability of success (i.e., delivery resulting from embryo transfer) of a program of at most four IVF cycles in the French Devenir Apr`es Interruption de la FIV (DAIFI) study and several simulation studies, controlling for time-dependent confounders. We find that the probability of success in the DAIFI study is 50% (95% confidence interval [0.48, 0.53]), therefore approximately half of future participants in a program of at most four IVF cycles can expect a delivery resulting from embryo transfer

Threshold Regression Models Adapted to Case-Control Studies, and the Risk of Lung Cancer Due to Occupational Exposure to Asbestos in France

Asbestos has been known for many years as a powerful carcinogen. Our purpose is quantify the relationship between an occupational exposure to asbestos and an increase of the risk of lung cancer. Furthermore, we wish to tackle the very delicate question of the evaluation, in subjects suffering from a lung cancer, of how much the amount of exposure to asbestos explains the occurrence of the cancer. For this purpose, we rely on a recent French case-control study. We build a large collection of threshold regression models, data-adaptively select a better model in it by multi-fold likelihood-based cross-validation, then fit the resulting better model by maximum likelihood. A necessary preliminary step to eliminate the bias due to the case-control sampling design is made possible because the probability distribution of being a case can be computed beforehand based on an independent study. The implications of the fitted model in terms of a notion of maximum number of years of life guaranteed free of lung cancer are discussed