## Theoretical Examples of observations in a patient population that are non-uniformly distributed with response surface model predictions developed from a volunteer study population

Once the anesthetic is terminated, the model prediction of unresponsiveness drops from > 99% to 0% over a period of 20-30 minutes. We observe the model predicted probability for which the patient awoke and plot the cumulative distribution of the studied patient population.

### Example 1: All patients awoke at model predictions of unresponsiveness > 90%

In this case, the model predictions are not consistent with patient observations. For example, when the model predicts 50% of laboratory volunteers unresponsive, 0% of the patients were unresponsive (ignoring the linear interpolation of the line in the plot).

### Example 2: All patients awoke at model predictions of unresponsiveness = 50%

In this case, the observations are inconsistent with model predictions, except for near 50%. For example, when the model predicts 35% of laboratory volunteers unresponsive, 0% of the patients were unresponsive (ignoring the linear interpolation of the line in the plot). While this could still be a useful model (i.e., because the patients consistently wake up near 50%, we can predict when they wake up), it would be an unexpected result and need additional understand of why the patient population responses differ so much from the volunteer population from which the model was constructed.

### Example 3: Patients awoke at very high and very low model predictions of unresponsiveness

In this case, the observations are distributed around the 50% model prediction, but no patient actually awoke near the 50% mark. The observations are nearly always inconsistent with the model predicted probabilities. The ideal distribution would be the line of identity, where for example 30% of the patient population were unresponsive when the model predicted probability of unresponsiveness is 30% (same for 5%, 25%, 50%, 95%, etc.)