Exact properties of Efron's biased coin randomization procedure

Efron [Biometrika 58 (1971) 403--417] developed a restricted randomization procedure to promote balance between two treatment groups in a sequential clinical trial. He called this the biased coin design. He also introduced the concept of accidental bias, and investigated properties of the procedure with respect to both accidental and selection bias, balance, and randomization-based inference using the steady-state properties of the induced Markov chain. In this paper we revisit this procedure, and derive closed-form expressions for the exact properties of the measures derived asymptotically in Efron's paper. In particular, we derive the exact distribution of the treatment imbalance and the variance-covariance matrix of the treatment assignments. These results have application in the design and analysis of clinical trials, by providing exact formulas to determine the role of the coin's bias probability in the context of selection and accidental bias, balancing properties and randomization-based inference.Comment: Published in at http://dx.doi.org/10.1214/09-AOS758 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Street Redesign for Safety in San Francisco and Santa Clara

Several existing streets and roads in the Bay Area have many vehicles causing traffic deaths and injuries. To address this issue, new design approaches and policies that claim traffic deaths are preventable and traffic design can account for human failure in its approach. This project is a street redesign of 19th Avenue in San Francisco and El Camino Real in Santa Clara. To address past crashes on each intersection and street corridor, several alternative designs were created. In these redesigns, past crash incidents, pedestrian needs, vehicular needs, and biking needs are addressed. Alternative analysis was conducted to recommend new, safer designs for these streets and intersections. For El Camino Real, added bike lanes and various safety features were recommended. For 19th and Winston Drive, added lanes and signal timing changes were recommended. Finally, for 19th and Sloat Boulevard, an added left turning lane was recommended