This paper analyzes statistical decisions during the interim analyses of clinical trials. After some general remarks about the ethical and scientific demands of clinical trials, I introduce the notion of a hard-case clinical trial, explain the basic idea behind it, and provide a real example involving the interim analyses of zidovudine in asymptomatic HIV-infected patients. The example leads me to propose a decision analytic framework for handling ethical conflicts that might arise during the monitoring of hard-case clinical trials. I use computer simulations to show how the framework can assist in reconciling certain ethical conflicts. The framework is partial, lacking the precision of a complete systematization of statistical monitoring procedures in practice.