treatment, assuring that all of the sickest patients will receive the experimental treatment. Consequently, the design is sometimes called an “assured allocation” design (Finkelstein et al., 1996a; 1996b). Because the design is non-randomized, it should only be considered in those situations where a randomized trial would not be possible.

The design first requires a quantitative measure of risk, disease severity, or prognosis, which is observed at or before enrollment into the study, together with a pre-specified threshold for receiving the experimental therapy. All participants above the threshold receive the experimental treatment, while all participants below the threshold receive the standard treatment. The risk-based design also requires a prediction of what the outcomes would have been in the sicker patients if they had received the standard treatment. One example of such a model might be an appropriate regression model of the relationship between pre-treatment suicidal ideation on post-treatment suicidal ideation in a group of depressed patients treated with the standard antidepressant therapy. The validity of this model can then be tested by comparing the observed and predicted levels of the of suicidal ideation in the low-risk control participants that were given the standard treatment. This is the basis of another novel feature of the risk-based design: to estimate the difference in average outcome between the high-risk participants who received the experimental treatment, compared with what the same participants would have experienced on the standard treatment.

The model for the standard treatment (but only the standard treatment) needs to relate the average or expected outcome to specific values of the baseline measure of risk used for the allocation. Because the parameters of the model will be estimated from the concurrent control data and extrapolated to the high-risk patients, only the functional form of the model is required, not specific values of the model parameters. This offers a real advantage over historical estimates. All one needs to assume for the risk-based design is that the mathematical form of the model relating outcome to risk is correctly specified throughout the entire range of the risk measure. This is a strong assumption, to be sure, but with sufficient experience and prior data on the standard treatment, the form of the model can be validated.

The risk-based allocation clearly creates a “biased” allocation and, obviously, the statistical analysis appropriate to estimate the treatment effect is not the simple comparison of mean outcomes in the two groups, as it would be in a randomized trial. Instead, the theory of general empirical Bayes estimation can be applied (Robbins, 1993; Robbins and Zhang, 1988; Robbins and Zhang, 1989; Robbins and Zhang, 1991). There are several cautions to observe. The population of participants entering a trial with risk-based allocation should be the same as that for which the model

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