The use of thresholds has been considered as a means of making medical decisions for over 3 decades [1–3]. To utilize this method, physicians must be able to estimate the baseline risk of each individual patient. Knowing the risk of the patient, the physician must also be able to determine thresholds for risk above which they will order additional testing or initiate treatment. Furthermore, the physician must be able to determine how a patient's risk will change based on the result of a particular test. If the test has no chance of moving the patient's risk above the treatment threshold, for example, then the test should probably not be ordered.

There is, however, a body of evidence that documents physicians' inaccuracy in predicting the risk of individual patients [4–8] and specifically in patients with ocular hypertension[9]. There is also evidence that clinicians do not use the threshold method when making decisions [10] and that intuitive threshold estimates do not match observed thresholds for treatment[11]. Given these problems with the estimation of *a priori* risk levels, the threshold method becomes suspect as a prescriptive means of rational decision making. On the other hand, the concept of risk thresholds is potentially very useful for comparing physicians to one another or for comparing physicians to proposed rational standards. It may therefore be useful to consider these descriptive uses of thresholds differently from the problematic prescriptive methods mentioned above.

One approach to determining physician treatment thresholds is to provide the clinicians with case scenarios and then ask them for an estimate of the probability of disease and for their recommendation to treat or treat. By varying the risk of disease represented by the case scenarios, it is possible to identify a clinician's risk thresholds for either ordering additional testing or initiating treatment[12]. This method still requires clinicians to estimate probabilities and because of this requirement, it becomes very difficult to compare the threshold derived from one physician to that of another. Furthermore, there is no guarantee that the risk estimates are based on any rational synthesis of evidence. Finally, throughout the history of eliciting risk estimates, physicians have both been uncomfortable in providing numerical values and have expressed the need to communicate the uncertainty in those estimates[13].

Another approach to threshold determination removes the need for clinicians to explicitly estimate any risk whatsoever. Plasencia *et al.* described a method in which they used binary logistic regression to estimate treatment thresholds[14]. Their method depends on another advance in risk estimation, the synthesis of large population based studies to produce risk calculators that can be used to estimate disease risk for a particular patient. The Framingham study provides a good example of how risk factors found in epidemiologic studies can be combined to summarize the risk of an individual [15–17]. Since the risk associated with each patient can now often be estimated based on published evidence, it is no longer necessary to ask the clinicians for their estimate of that risk. Instead, they can be asked for their treatment recommendation only. Building on the work of Hartz *et al.*, [18] Plasencia and others used binary logistic regression to estimate treatment thresholds[14]. This method has the advantage of using the same risk for each case scenario rather than using the many intuitive estimates provided by clinicians. In this way, it is possible to compare decision thresholds across physicians.

One disadvantage of the logistic regression method is that it requires concrete binary decisions be made. Because uncertainty is an important component of clinical decision making,[19] we developed a method for assessing treatment thresholds that allowed clinicians to make explicit use of their uncertainty. Given a situation in which we can estimate the risk of glaucoma for any patient with ocular hypertension, we set out to determine whether ordinal (as opposed to binary) logistic regression could be used to derive physician treatment thresholds from treatment recommendations made on a set of clinical scenarios. By allowing for more than two levels of recommendation (yes or no), we are also allowing for physicians to express uncertainty.

As opposed to providing quantitative estimates of patient risk, clinicians routinely make recommendations that are presumably driven by that same patient risk, but implicitly so. We developed the proposed method to take advantage of this fact and to derive some estimate of physician interpretation of risk, as reflected by their explicit treatment recommendations. There is clearly still variability in physician behavior but the approach allows us to analyze usual physician behavior (treatment recommendations) rather than unusual behavior (assigning quantitative risk).

While the literature is clear about clinicians' inability to quantify risk, the literature has little to say about the ability of clinicians to state accurately whether a given patient is above or below that risk. In fact, there is reason to believe, given their general successful functioning, that they are good at this task. It is this task that we have quantified. As a first attempt at assessing this skill, we have created a de facto random effects model, where each clinician has their own threshold (and ability to compare with respect to that threshold) sampled, in turn, from a population threshold; it is that latter threshold that we estimate with our regression model. Furthermore, because prior research is clear that physicians are unable to reliably assign a numeric value to a particular patient's risk of a particular disease or outcome, we employed a method to *discover* the implicit risk levels at which physicians change their behaviour. This method will then let us compare the impact of interventions like risk calculators, clinical decision support tools, and physician education.

To evaluate our method, we chose to use ocular hypertension (elevated eye pressure) as the condition under study. Ocular hypertension is a known risk factor for developing glaucoma, a significant cause of blindness worldwide[20]. Because of its association with glaucoma, ocular hypertension was the subject of a large clinical trial, the Ocular Hypertension Treatment Study (OHTS)[21]. The OHTS randomized over 1600 patients with elevated eye pressure to either pressure lowering treatment or observation and then monitored both groups for development of glaucoma. Prior to the OHTS, it was not clear which patients with ocular hypertension would benefit from treatment to prevent glaucoma. Analysis of the study has since clarified the risk factors associated with the conversion from ocular hypertension to glaucoma. Among the most important outcomes of the OHTS have been risk calculators that can be used to estimate the risk of developing glaucoma in individual patients [22–24]. Such calculators may be able to help physicians identify those patients most at risk of developing glaucoma and are important as an objective measure of risk in the method we describe. Although we chose to evaluate this method using ocular hypertension as the disease in question, this approach will be applicable to any disease process for which experimenters can calculate the risk of an outcome for each patient presented to the physicians under study. Examples include cardiovascular risk or cancer mortality.