Providing terminally ill patients with access to experimental treatments, as allowed by recent “right to try” laws and “expanded access” programs, poses a variety of ethical questions. While practitioners and investigators may assume it is impossible to learn the effects of these treatment without randomized trials, this paper describes a simple tool to estimate the effects of these experimental treatments on those who take them, despite the problem of selection into treatment, and without assumptions about the selection process. The key assumption is that the average outcome, such as survival, would remain stable over time in the absence of the new treatment. Such an assumption is unprovable, but can often be credibly judged by reference to historical data and by experts familiar with the disease and its treatment. Further, where this assumption may be violated, the result can be adjusted to account for a hypothesized change in the non-treatment outcome, or to conduct a sensitivity analysis. The method is simple to understand and implement, requiring just four numbers to form a point estimate. Such an approach can be used not only to learn which experimental treatments are promising, but also to warn us when treatments are actually harmful – especially when they might otherwise appear to be beneficial, as illustrated by example here. While this note focuses on experimental medical treatments as a motivating case, more generally this approach can be employed where a new treatment becomes available or has a large increase in uptake, where selection bias is a concern, and where an assumption on the change in average non-treatment outcome over time can credibly be imposed.