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.

]]>In this article we construct a one-dimensional universal least favorable submodel for which the TMLE only takes one step, and thereby requires minimal extra fitting with data to achieve its goal of solving the efficient influence curve equation. We generalize these to universal least favorable submodels through the relevant part of the data distribution as required for targeted minimum loss-based estimation, and to universal score-specific submodels for solving any other desired equation beyond the efficient influence curve equation. We demonstrate the one-step targeted minimum loss-based estimators based on such universal least favorable submodels for a variety of examples showing that any of the goals for TMLE we previously achieved with local (typically multivariate) least favorable parametric submodels and an iterative TMLE can also be achieved with our new one-dimensional universal least favorable submodels, resulting in new one-step TMLEs for a large class of estimation problems previously addressed. Finally, remarkably, given a multidimensional target parameter, we develop a universal canonical one-dimensional submodel such that the one-step TMLE, only maximizing the log-likelihood over a univariate parameter, solves the multivariate efficient influence curve equation. This allows us to construct a one-step TMLE based on a one-dimensional parametric submodel through the initial estimator, that solves any multivariate desired set of estimating equations. ]]>

**Introduction**

** **Planning for the future would be easier if we knew how long we will live and, more importantly, how many years we will be healthy and able to enjoy it. There are few well-documented aids for predicting our future health. We attempted to meet this need for persons 65 years of age and older.

**Methods**

Data came from the Cardiovascular Health Study, a large longitudinal study of older adults that began in 1990. Years of life (YOL) were defined by measuring time to death. Years of healthy life (YHL) were defined by an annual question about self-rated health, and years of able life (YABL) by questions about activities of daily living. Years of healthy and able life (YHABL) were the number of years the person was both Healthy and Able. We created prediction equations for YOL, YHL, YABL, and YHABL based on the demographic and health characteristics that best predicted outcomes. Internal and external validity were assessed. The resulting CHS Healthy Life Calculator (CHSHLC) was created and underwent three waves of beta testing.

**Findings **

A regression equation based on 11 variables accounted for about 40% of the variability for each outcome. Internal validity was excellent, and external validity was satisfactory. As an example, a very healthy 70-year-old woman might expect an additional 20 YOL, 16.8 YHL, 16.5 YABL, and 14.2 YHABL. The CHSHLC also provides the percent in the sample who differed by more than 5 years from the estimate, to remind the user of variability.

**Discussion**

** **The CHSHLC is currently the only available calculator for YHL, YABL, and YHABL. It may have limitations if today’s users have better prospects for health than persons in 1990. But the external validity results were encouraging. The remaining variability is substantial, but this is one of the few calculators that describes the possible accuracy of the estimates.

**Conclusion**

** **The CHSHLC, currently at http://diehr.com/paula/healthspan, meets the need for a straightforward and well-documented estimate of future years of healthy and able life that older adults can use in planning for the future.