Our first set of observations suggests that the use of higher-order concepts and making explicit relations between concepts are associated with diagnostic accuracy. Bordage and Chang [10, 11] have demonstrated that diagnostic accuracy correlates with semantic level of the problem's description. The use of semantic qualifiers that describe the content at a more abstract level was associated with better diagnostic accuracy. Abstractions from observation concepts constitute interpretations. Those interpretations confer additional meaning . Qualifying pneumonia as recurrent or persistent is an interpretation of a series of events and adds to the meaning of the concept of pneumonia and may thus increase diagnostic accuracy.
In another experiment, Nendaz and Bordage  instructed students how to use more semantic qualifiers. They found that students could learn to introduce more semantic qualifiers but there was no difference in diagnostic accuracy suggesting that the use of semantic qualifiers correlates with diagnosis but may not be causal.
Our observations may provide a possible explanation to this apparent lack of causation between use of semantic qualifiers and diagnostic accuracy. We found that relations between concepts need to be established. Absence of explicit relations between concepts in problem formulation was associated with incorrect diagnosis. The use of conceptual abstraction may be necessary but not sufficient for problem formulation; a critical element is the structure resulting from relations established between concepts. Establishing meaningful relations has also been shown by Norman  to be important in problem solving. Physicians with different levels of experience were presented with complex nephrology problems and asked to solve them while thinking aloud. Experienced physicians solved the problems by clustering data into more meaningful relations than less experienced ones. We have observed that conceptual relations need to be established early in the problem formulation.
Why would establishing relations between concepts be associated with better diagnostic accuracy? Our observations suggest that the structure of problem formulation is analogous to that of a model of a theory . In the semantic view of theory, a model can be a linguistic entity on which observation concepts are abstracted into theoretical terms. Those are organized in a structure which contains as minimal requirements: concepts and a set of relations or operations on those concepts. The relations are made explicit. With such a structure the model may represent the world and have an explanatory function . Like a model, a problem formulation can make explicit functional and causal relations between concepts. A model of a case of endocarditis will link bacteremia, valvular disease and embolic phenomena in causal relationships and these have explanatory utility. The formulated problem will allow the physician to see the case as belonging to a 'theory' of endocarditis. What is shared between the model and the theory is not only a set of features of individual concepts but the same pattern of abstract relationships. Choosing the pertinent concepts and establishing relations most likely involve analytic and non-analytic processes . Non-analytical recognition of similar cases from past experience has been associated with expertise  and likely involves seeing relations between concepts. On the other hand, analysis of specific features, weighting prior probability, and consideration for simplicity must also play a role in formulating the problem.
In the second set of observations, we found that a majority of students could readily recognize the disease when presented with an already formulated problem. This was in contrast to the groups of students presented with the original case. A possible explanation would be that students who made the diagnosis had already structured knowledge of endocarditis. Why those groups would have such a structured knowledge is unexpected since there was no new course or teaching on the subject in those groups. Moreover, several preceding groups had significant difficulty in making the diagnosis.
More likely, the explanation would be that when presented with the original complex case, the difficulty was in structuring the elements of the problem into a recognizable form. Very few students identified the regurgitant murmur as an essential feature. Possibly, when presented with the formulated case in which the murmur is mentioned, students recognized the disease as endocarditis. Faced with the large amount of clinical data of the original case, students may have had problem seeing relations between pertinent clinical features. Medin  has shown that when relationships between properties were exhibited, particularly causal relationships, subject were better able to assign objects to a similar category.
There are several limitations to our study. These were observations made during teaching sessions. The groups of students were not randomized and were seen in sequence with the last five groups presented with the formulated case. It is possible that students who made the diagnosis had different prior experiences with similar cases or different knowledge structures. This should not invalidate the observations on the structure of problem formulation but would cast doubt on our hypothesis that problem formulation is a creative ability. The formulated problem and the criteria for higher-order concepts and what constitutes relations between concepts were not validated by other physicians. The formulated problem was based on accepted clinical criteria of endocarditis and unlikely would cause significant dissension among experts. The choice of higher-order concepts and relations would be subject to interpretation. However, the interpretation would concern more the type of relations or concepts than whether a relation is made explicit or not or whether a new conceptual category is introduced or not. No observational term was accepted as new concept. This study was also limited to the use of one complex case. Conceptual analysis with abstractions and relations may not be so important in other cases. In many instances, the single ability to detect critical features may be more important. These observations may not apply to less complex case. No doubt, there are many ways to adequately formulate a problem.