Significant attention has been given to developing data-driven methods for tailoring patient care based on individual patient characteristics. Dynamic treatment regimes formalize this approach through a sequence of decision rules that map patient information to a suggested treatment. The data for estimating and evaluating treatment regimes are ideally gathered through the use of Sequential Multiple Assignment Randomized Trials (SMARTs), though longitudinal observational studies are commonly used due to the potentially prohibitive costs of conducting a SMART. Observational studies are typically powered for simple comparisons of fixed treatment sequences; a priori power or sample size calculations for tailored strategies are rarely if ever undertaken. This has lead to many studies that fail to find a statistically significant benefit to tailoring treatment. We develop power analyses for the estimation of dynamic treatment regimes from observational studies. Our approach uses pilot data to estimate the power for comparing the value of the optimal regime, i.e., the expected outcome if all patients in the population were treated by following the optimal regime, with a known comparison mean. This allows for calculations that ensure a study has sufficient power to detect the need for tailoring, should it be present. Our approach also ensures the value of the estimated optimal treatment regime has a high probability of being within a range of the value of the true optimal regime, set a priori. We examine the performance of the proposed procedure with a simulation study and use it to size a study for reducing depressive symptoms using data from electronic health records.
In a randomized study, leveraging covariates related to the outcome (e.g. disease status) may produce less variable estimates of the effect of exposure. For contagion processes operating on a contact network, transmission can only occur through ties that connect affected and unaffected individuals; the outcome of such a process is known to depend intimately on the structure of the network. In this paper, we investigate the use of contact network features as efficiency covariates in exposure effect estimation. Using augmented generalized estimating equations (GEE), we estimate how gains in efficiency depend on the network structure and spread of the contagious agent or behavior. We apply this approach to simulated randomized trials using a stochastic compartmental contagion model on a collection of model-based contact networks and compare the bias, power, and variance of the estimated exposure effects using an assortment of network covariate adjustment strategies. We also demonstrate the use of network-augmented GEEs on a clustered randomized trial evaluating the effects of wastewater monitoring on COVID-19 cases in residential buildings at the the University of California San Diego.
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